Testing and isolation to prevent overloaded health care facilities and to reduce death rates in the SARS-CoV-2 pandemic in Italy

Background During the first wave of COVID-19, hospital and intensive care unit beds got overwhelmed in Italy leading to an increased death burden. Based on data from Italian regions, we disentangled the impact of various factors contributing to the bottleneck situation of health care facilities, not well addressed in classical SEIR-like models. A particular emphasis was set on the dark figure, on the dynamically changing hospital capacity, and on different testing, contact tracing, quarantine strategies.

We first estimated the dark figure for different Italian regions. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread, the model was optimized to fit data (infected, hospitalized, ICU, dead) published by the Italian Civil Protection.

We showed that testing influenced the infection dynamics by isolation of newly detected cases and subsequent interruption of infection chains. The time-varying reproduction number ( Rt) in high testing regions decreased to < 1 earlier compared to the low testing regions. While an early test and isolate (TI) scenario resulted in up to ∼ 32% peak reduction of hospital occupancy, the late TI scenario resulted in an overwhelmed health care system.

An early TI strategy would have decreased the overall hospital accessibility drastically and, hence, death toll (∼ 45% reduction in Lombardia) and could have mitigated the lack of health care facilities in the course of the pandemic, but it would not have kept the hospitalization amount within the pre-pandemic hospital limit. We showed that contact tracing and quarantine without testing would have a similar effect and might be an efficient strategy when sufficient test capacities are not available. April 21, 2022 1/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.

1 The COVID-19 outbreak created a worldwide pandemic causing more than 4,000,000 deaths 2 and over 190 million total cases worldwide as of July 2021 [1]. Many countries implemented 3 non-pharmaceutical interventions (NPIs), which were effective in reducing virus spreading. 4 This was further supported by social distancing, mask duty, and hygiene measures. Though 5 different models of NPIs and their implementation methods have been proposed, their impact and 6 effectiveness on disease dynamics are under scrutiny and remain a matter of global discussion [2–6]. 7 Singapore and Hong Kong were able to contain the virus by aggressive testing [7], while South 8 Korea adopted a trace, test, treatment strategy [8]. In a different but similarly effective approach, 9 Japan averted the risk of contagion by isolating the whole contact clusters and by heavily relying 10 on the self-awareness and discipline of the population [9]. 11 The COVID-19 outbreak originated in Wuhan, People’s Republic of China, in early December 12 2019. Within two months, it had erupted and unfolded with tremendous speed in Italy, which 13 became the European epicenter of disease spreading, forcing the government to impose a 14 lockdown on March 9 th, 2020. On March 19 th, 3405 people had already died in Italy, thereby 15 surpassing China, while 41035 people were diagnosed as COVID-19 positive. This induced Italy 16 to shut down all non-essential businesses on March 21 st. Despite the strict measures applied, in 17 Lombardia alone a total of 28545 symptomatic people were infected by April 8 th, accounting for 18 12976 hospital admissions, followed by Emilia Romagna (4130), Piemonte (3196), and Veneto 19 (1839) [10]. These large numbers led to the complete collapse of the health care system within 20 a few weeks of the first detection of COVID-19 cases, most notably in Lombardia where even 21 funeral homes had been overwhelmed and were incapable of responding in a reasonable time [11]. 22 Even though the state expanded the hospital and intensive care unit (ICU) capacities, it could 23 not prevent the bottleneck situation of the health care system and presumably caused a large 24 number of deaths for a prolonged period. 25 Many factors aggravated the COVID-19 situation in Italy, among which the distinct demo- 26 graphic structure of Italy with nearly 23% of the population of age 65 years or older [12], larger 27 household size, and the prevalence of three-generation households compared to Germany [13] as 28 well as limited hospital and ICU capacities. At the beginning of the pandemic, Italy focused on 29 testing symptomatic patients only, which resulted in a large proportion of positive tests and high 30 case fatality rates (CFR) compared to other countries [14]. A large proportion of cases remained 31 undetected, which became a major driver of new infections. A different study estimates that in 32 Italy the actual number of total infections was around 30 fold higher than reported, while for 33 Germany it was less than ten-fold [15] (data up to March 17 th 2020). 34 Compartmental models have been widely used to describe the dynamics of epidemics, for 35 example, SIR model [16] that consider three compartments, namely susceptible, infected and 36 recovered, or more complex SEIR models [17, 18] that take susceptible, exposed, infectious, and 37 recovered compartments into account. Typically, these models either exclude the undetected 38 index cases [4, 17, 18] or ignore their dynamic nature [19], and structurally these models are 39 not developed to address the load on the health care system. Besides these epidemic models, 40 simple algorithms exist in the literature for estimating the time-varying reproduction number 41 and have been widely used in the context of many infectious diseases (e.g., measles, H1N1 42 swine flu, polio, etc.) [20]. Several studies [21, 22] estimated the undetected case number in 43 Italy, but its dynamics in the context of different testing strategies and implications upon the 44 health care system was not considered. Even though the general compartmental SIR and SEIR 45 type models are useful in inferring epidemic spread and public health interventions, we needed 46 to introduce additional compartments to investigate how the pandemic is shaped by several 47 influential factors (e.g. dark numbers, regional testing strategies, hospital beds); for instance, we 48 included a specific compartment for infected undetected cases ( IX) to analyse the impact of the 49 region-wise undetected cases upon the evolution of the Rt. Similarly, hospital (HU andHR) and 50 ICU (UD and UR) compartments were introduced to monitor the load on the health care system. 51 April 21, 2022 2/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint Moreover, the absence of reliable symptom onset data and heterogeneity in the actual 52 infectious period among the asymptomatic, pre-symptomatic, and symptomatic individuals 53 require a more complex model that not only can accurately portray the dynamics of COVID-19 54 spread but also can disentangle the impact of intertwined factors like the variation of undetected 55 components, limited and changing hospital and ICU availability. 56 Existing modeling studies that analyze the COVID-19 situation in Italy [19, 23] or other 57 regions [4, 24–26] in general did not address some fundamental aspects of the ongoing pandemic 58 like temporal dynamics of undetected infections, the benefits of a high testing and isolation 59 strategy or the impact of a limited and dynamically changing health care capacity on the lives 60 lost. In this study, we address the bottleneck situation of the health care facility, benefits 61 of extending hospital infrastructure and the impact of an early testing and isolation strategy 62 onto the health care system with a COVID-19 specific mathematical model. To evaluate the 63 COVID-19 situation in Italy in a realistic framework, we first estimated the undetected fraction 64 (dark figure) of infections across different regions of Italy. We used this information to determine 65 the parameters of the model and showed that our model is structurally identifiable. We studied 66 the influence of the dark figure and implemented NPIs on the time-dependent reproduction 67 number,Rt. With data about regional hospital and ICU bed capacities, we estimated that 68 an extra 25% of people died in Lombardia due to the overwhelmed health care system. We 69 investigated the impact of early testing strategy and, alternatively, of contact tracing combined 70 with quarantine (∼ 10 fold more isolation of infected) policy in the setting of elevated hospital 71 capacity as it currently stands. This strategy would have significantly reduced the death toll by 72 20% to 50%. 73

74 SECIRD-model 75 To understand the impact of potential aggravating factors, namely infections from undetected 76 index cases, early vs late testing strategy, and limited heath care facilities on disease progression, 77 we developed a COVID-19-specific SECIRD-model parametrized for Italy. The SECIRD-model 78 distinguishes healthy individuals without immune memory of COVID-19 (susceptible,S), infected 79 individuals without symptoms but not yet infectious (exposed, E) and infected individuals 80 without symptoms who are infectious (carrier, CI, CR). The carriers are distinguished into a 81 fraction α of asymptomatic (CR) and (1−α) of pre-symptomatic infected (CI). The latter are 82 categorized into a fraction µ of detected symptomatic (IH and IR) and (1−µ) of undetected 83 mild-symptomatic (IX). Out of the CI, a fraction ρ gets hospitalized (IH) and (1−ρ) become 84 symptomatic but recover without hospitalization (IR). Further, compartments for hospitalization 85 (H) and intensive care units (U) were introduced to monitor the load on the health care system. 86 A fraction ϑ ofH requires treatment in ICU (HU) while a fraction (1−ϑ) recovers from hospital 87 without ICU treatment ( HR). δ and (1−δ) represent the fraction of patients in ICU who 88 subsequently die (UD) or recover (UR). The compartment ( R) consists of patients recovered 89 from different infection states. The Reference Model (Fig. 1; equations are in the Supplementary 90 Material) was solved with parameters in Table 1. 91 Initial condition 92 Italian regions started documenting epidemiological data at different dates, at the earliest 93 February 24th, 2020. As we considered a fixed incubation period of 5.2 days in our model, we 94 assumed that at minimum, the first entry in the dataset (number of total cases) was the exposed 95 number 5.2 days earlier. In addition to the documented infection, we calculated undocumented 96 cases based on the estimated region-wise dark number by a Bayesian MCMC framework (see 97 Supplementary Material). The sum of documented and undocumented cases was the initial 98 April 21, 2022 3/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint exposed population. We used regional population as the initial susceptible population. For all 99 other compartments, we started the simulation with zero. The simulation began from -5.2 days 100 with the aforementioned initial conditions, and undetected cases were split between asymptomatic 101 and symptomatic undetected cases according to the parameters used for those compartments. 102 Parameterization 103 We distinguished physiological and behavioral model parameters. Physiological parameters 104 depend on the nature of the virus (Rx,x = 2,..., 9) and remain unchanged throughout the analysis 105 of the pandemic. We first determined the range of physiological values for each parameter 106 from the literature [27, 28] (Table 1) and then estimated parameters’ values from a fit to the 107 exponential growth of case numbers (infection, hospitalized, ICUs and death cases) during the 108 first two weeks of the pandemic. In total, 56 data points (14 daily data for those four observables) 109 were used to estimate the physiological parameters. This initial phase was not yet affected by 110 NPIs, public awareness, or an overwhelmed health care system and, thus, reflects viral properties. 111 Some of the physiological parameters may be internally linked. For instance, hospitalization 112 and ICU cases increase with infection cases and disentangling those internal relations is difficult 113 with limited data availability. It is likely that the best combination of parameters contains those 114 internal relations. We assumed that the virus variant remained the same during the investigation 115 period, therefore we kept physiological parameters constant throughout. However, environmental 116 factors, testing policy, interventions, public behavior, self isolation, hospital accessibility, etc. 117 might have distorted such relations (e.g., the rate of increase in hospital and ICU cases as 118 infection increases differ in different phases of the pandemic) and substantially altered the disease 119 dynamics by impacting the transmission probability, dark number, hospitalizations and death 120 rate. These contingent factors affect the behavioral parameters ( ρ,ϑ,δ , R1, R10). We estimated 121 the behavioral model parameters by minimizing the sum of squared differences between the 122 observed data (active infections, hospitalized, ICU patients and death numbers (Italy Data on 123 Coronavirus 2020 [29])) and model simulations using Matlab’s nonlinear least-squares optimizer. 124 This procedure was repeated separately for each region in Italy in moving time windows of 7 days 125 to account for local specifics and temporal changes in disease transmission. This moving-window 126 technique with the size of a calendar week reduces periodic fluctuations that are an artifact of 127 the unequal distribution of tests among the weekdays. 128 Perturbation and parameter identifiability 129 To generate the standard deviation for Rt, we perturbed the behavioral parameters ( ρ,ϑ,δ,R 1, 130 R10) 10% of their optimized value and sampled uniformly within this range such that the total 131 parameter variation,κ, defined as log(κ) =∑L n=1|log kn k0 n | [48], remains within 10% of its reference 132 value. kn,k0 n andL represent the parameters of the altered system, the reference system and the 133 total number of parameters, respectively. We generated dynamics for 100 perturbed parameter 134 sets for the statistical analysis. 135 We addressed parameter identifiability in two ways: Structural identifiability based on 136 synthetic outbreak data and practical identifiability based on real data. In the first method, 137 we randomly sampled parameters within a range specified in Table 1 and by using random 138 initial conditions of model state variables. Then we used the resulting dynamics of the state 139 variables as model observables and checked for a unique solution in the parameter space. We 140 repeated this procedure 100 times (see Fig S5 for a typical result). In the second method, we 141 considered nationwide Italy data for the period February 24 th to May 22 nd, 2020 and fixed the 142 physiological parameters as described in the Parameterization section. As we are estimating 143 behavioral parameters (ρ,ϑ,δ,R 1, R10) by considering a moving time windows of 7 days, we 144 checked practical identifiability of these parameters in each time window. We found that the 145 April 21, 2022 4/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint Table 1: Parameter ranges used in the Reference Model : determination of the boundaries for literature-based parameter set was based on the interpretation of the values given in the

[27,28,30]. Parameter Comments/

Description Parameter ranges from literature Min Max R1 Time- dependent transmission probability of COVID-19 per each contact made with an infec- tious person (C I,C R,I X,I R and IH in the model) R2 [31–34] the inverse of R2 represents latent, non-infectious period following the trans- mission of COVID-19. 1 /R2 = 5.2 − 1/R3 ; median incubation period is 5.2 days R3 [31–34] the inverse of R3 represents the pre-symptomatic infec- tious period 1 4.2 2 5.2 R4 [35–37] the inverse of R4 represents the infectious period for the mild symptomatic cases without requiring hospital- ization (including the undetected symptomatic people (IX )) 1 14 1 7 R5 [27, 28, 38] the inverse of R5 represents the duration for which the hospitalized cases stay in general hospital care before discharge without requiring further intensive care 1 16 1 5 R6 [28, 39] the inverse of R6 represents the duration a patient stays at home before hospitalization 1 7 0.9 R7 [28, 38, 39] the inverse of R7 represents the time spent in general hospital care before admission to ICU 1 3.5 1 R8 [27, 40] the inverse of R8 represents the time spent in ICU before recovery 1 16 1 3 R9 the inverse of R9 represents the duration for which the asymptomatic cases remained infectious following their latent non-infectious period 1 R9 = 1 R3 + ( 0.5 × 1 R4 ) R10 Time- dependent [28, 39, 41] the inverse of R10 represents the time spent in ICU before dying 1 10 0.9 α fixed, [42 – 44] undocumented asymptomatic fraction 0.4 0.4 β Assumed the risk of infection from the registered and quarantined (IH +IR) patients 0.05 0.25 ρ Time- dependent the fraction of documented infections that require hos- pitalization 0.01 0.9 ϑ Time- dependent [45–47] the fraction of hospitalized patients that require further intensive treatment 0.01 0.7 δ Time- dependent [45–47] the fraction of ICU patients that have fatal outcome 0.3 0.9 ¯µ this fraction represent the total undocumented infection including the asymptomatic cases, estimated through MLE method of the Bayesian framework µ documented symptomatic fraction µ = 1−¯µ 1−α April 21, 2022 5/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint Recovered detected (1−α)R2 αR2 R1 N0 [CI+CR+IX+β(IH+IR)] μρR3 (1−μ)R3 μ(1−ρ)R3 R9R4 R4R5 R8 δR7 (1−δ)R7 R10 SECIRD Model (Reference) ϑR6 (1−ϑ)R6 Testing Model (1−α)R2 αR2 μρR3 μ(1−ρ)R3 R9 R4 μ2R3 μ1R3 Susceptible S Exposed E Carr. Recovering CR Carrier CI Infected undetected IX Recovered undetected RX Inf. Recovering IR Infected IH Hos. Recovering HR RZ Hospitalized HU ICU Recovering UR ICU UD Dead D IH IR Inf. newly Detected IXD Inf. Undetected IX CI CR RX S E fHlim= (exp(HR+HU−Hlim))10 (1+(exp(HR+HU−Hlim))10)10;fUlim= (exp(UR+UD−Ulim))10 (1+(exp(UR+UD−Ulim))10)10 R1 N0 [CI+CR+IX+β(IXD+IH+IR)] (1−μ)R3 Capacity Model R10 R7 (1−ϑ)R6(1−fHlim) ϑR6(1−fHlim) δR7(1−fUlim) (1−δ)R7(1−fUlim) R6fHlim R7fUlim HR HU UD UR D ID IH Fig 1: Model schemes. The Reference Model distinguishes healthy individuals with no immune memory of COVID-19 (susceptible, S), infected individuals without symptoms but not yet infectious (exposed, E), infected individuals without symptoms who are infectious (carrier, CR,I, asymptomatic and pre-symptomatic respectively), infected ( IX,H,R), hospitalized (HU,R) and ICU (UD,R) patients, dead (D) and recovered (RX,Z), who are assumed immune against reinfection. This scheme also applies to the Asymptomatic Model . The Testing Model is a modified branch of the Reference Model used to evaluate the impact of increasing case detection and isolation onto infection dynamics; IXD andIX describe newly detected and undetected cases, respectively. The Capacity Model is a modified branch of the Reference Model to investigate the impact of limited hospital and ICU access onto the death toll. fHlim and fUlim are steep exponential functions diverting the flux from IH and HU to D, respectively, when hospital and ICU occupancy reached their respective current capacities Hlim(t) and Ulim(t). Rx with x∈ [2,..., 9] are per day transition rates between different states. behavioral parameters ( ρ, ϑ, δ, R1 and R10) are subject to contingent factors, like NPIs, self-awareness, availability of hospital beds, etc., and, hence, are functions of time. parameters are identifiable in more than 75% of the cases (see Fig. S6 for a typical results when 146 all parameters are identifiable; and the Supplementary Material for more details). 147 Basic reproduction number 148 The basic reproduction numberR0 is defined as the expected number of secondary infections 149 produced by a single infection in a population where everyone (assuming no immune memory) is 150 susceptible [49] and reflects the transmission potential of a disease. For COVID-19, the dynamics 151 of the pandemic was influenced by several factors, like, the self-awareness in the community, 152 April 21, 2022 6/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint interventions and policies implemented by the authorities and immunisation of the population. 153 Therefore, the time-dependent reproduction number R(t) that describes the expected number of 154 secondary cases per infected person at a given time of the epidemic, is a more practically useful 155 quantity to understand the impact of interventions, behavioral changes, seasonal effects, etc. on 156 the disease dynamics [20,30]. 157 In multi-compartmental epidemic models,R0 can be derived with the next generation matrix 158

[50–52], where the Jacobian matrix consists of two factors, rate of appearance of new 159 infections into the infection compartment (F) and transfer of infected into other compartments 160 (V). The elements Gij of G =FV−1 represent the expected number of secondary infections 161 in compartment i caused by a single infected individual of compartment j. The reproduction 162 numberR0 is given by the dominant eigenvalue of G (the derivation ofR0 is provided in the 163 Supplementary Material): 164 R0 =R1 S0 N0 [1−α R3 +βµρ 1−α R6 + α R9 +βµ(1−ρ)1−α R4 + (1−µ)1−α R4 ] , (1) where N0 is the total population and S0 is the susceptible population, both at the start of 165 the pandemic (parameters are listed in Table 1). R0 was calculated using the parameter set 166 estimated by the initial fit that considers only the first two weeks of data points as described in 167 the Parameterization section. An ensemble of parameter sets (as described in the Perturbation 168 and parameter identifiability section) was used to calculate the standard deviation in the R0. 169 In order to understand the impact of awareness in the population, NPIs and policies im- 170 plemented by the authority upon the development of the time-varying reproduction number 171 (R(t)) [20], we fitted the model parameters to data in shifting time windows of one week. 172 This approach has two advantages: first, the reproduction number R(t) is determined as a 173 time-dependent variable and thus reflects the impact of NPIs on the infection dynamics; second, 174 the moving-window dampens sudden jumps in the data because of reporting delays. In each 175 time window, a best fit of the model parameters was found based on the cost function value 176 (squared difference between data and simulation). In the next window, the fitting was repeated 177 with initial conditions given by the model state in the previous time window. As described in 178 the Perturbation and parameter identifiability section, an ensemble of perturbed parameter sets 179 was used to calculate the standard deviation in the Rt. 180 R(t) in time window k reads [30]: 181 R(tk) =R1(tk)S(tk) N(tk) [1−α R3 +βµρ(tk)1−α R6 + α R9 +βµ(1−ρ(tk))1−α R4 + (1−µ)1−α R4 ] , (2) whereρ(tk) denotes the hospitalized fraction of identified symptomatic cases in the k-th time 182 window. Data analysis of the clinical state of all infected cases (up to June 22 nd) by the Istituto 183 Superiore di Sanit` a (ISS) showed∼ 30% asymptomatic cases, with increasing tendency [42 –44]. 184 In a study performed in Vo’ Euganeo, Veneto, the percentage of asymptomatic cases was found 185 to be in the range of 40% [53]. We set the asymptomatic fraction to α = 0.4. The fraction of 186 undetected cases ¯µ (see Supplementary text and Table 2) is by definition: 187 ¯µ :=α + (1−µ)(1−α) =⇒ µ = 1− ¯µ 1−α Asymptomatic Model 188 In the Asymptomatic Model, all symptomatic cases are detected, i.e. µ = 1. We compared the 189

from this model with those from the Reference Model to understand, in an ideal situation, 190 the implication of detecting all symptomatic cases for the pandemic development. 191 192 April 21, 2022 7/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint Testing Model 193 In order to understand the influence of extra testing on infection dynamics, we adopted a model 194 where a fraction of the undetected infected cases ( IX) is detected (IXD) via testing and hence, 195 contained. The newly detected infected ( IXD) contribute to new infections with a frequency 196 reduced by a factor β (β <1) but the infectious period remains unaltered (1/R4) (Testing Model 197 in Fig. 1 and Fig. 3). Li et al. [54] have demonstrated, in the context of COVID-19 transmission 198 in China, that strict control measures (travel restrictions, enhanced testing, self-quarantine, 199 contact precautions, etc.) helped in improving the fraction of all documented infections from 200 14% to 65%,∼ 4−5 fold. For Italy, we estimated that 90% of the infections remained undetected 201 (Table 2). We assumed that enhanced testing reduced this dark figure by daily 2% until reaching 202 60% (assuming similar efficiency as in China, i.e. documented infections increasing 10% to 40%). 203 We introduced a time-dependent fraction µ′ of undetected infections, which, starting from ¯µ, 204 was decreased daily by steps of 2% down to 60%. The asymptomatic fraction was fixed as in the 205

Model (α = 0.4). The undetected portion of symptomatic is instead modified so that 206 the fraction of undetected cases, µ1(t), and the fraction of newly detected cases, µ2(t), satisfies: 207 µ1(t) +µ2(t) = 1−µ , with 208 µ1(t) = µ′(t)−α 1−α , µ2(t) = ¯µ−µ′(t) 1−α . The parameters obtained by fitting the data with the Reference Model were transferred into 209 the Testing Model. This maintains the compartmental flow of the Reference Model and thus 210 ensures that the result reflects the sole effect of isolating a fraction of undetected infections. 211 Correspondingly,R(tk) becomes: 212 R(tk) =R1(tk)S(tk) N(tk) [1−α R3 +βµρ(tk)1−α R6 + α R9 + +βµ(1−ρ(tk))1−α R4 +βµ2(tk)1−α R4 +µ1(tk)1−α R4 ] . Capacity Model 213 To estimate the impact of capacity limitations of the health care system, we implemented time- 214 varying capacity constraints on the hospital (Hlim(t)) and ICU (Ulim(t)) accessibility (Capacity 215 Model in Fig. 1 and Fig. 3 ), using available data for the number of hospital and ICU beds in 216 the different regions. Table 3 reports the pre-pandemic capacity and the increased capacity, 217 specifically allocated to COVID-19 patients, together with the date of accomplished installation. 218 Some regions doubled their capacity and, presumably, this extension of infrastructure has been 219 implemented in a step-wise manner. We assumed a linear increase of the hospital ( Hlim(t)) 220 and ICU (Ulim(t)) capacity from three days before exhaustion until reaching the maximum 221 capacity on the date of accomplished installation. This new capacity was available thereafter. 222 The exhaustion date was determined from the data and refers to the day at which the number of 223 hospitalized and ICU patients became larger than the initial capacity. Before the pandemic, 85% 224 of the hospital beds and 50% of the ICU beds were occupied [55]. In the Capacity Model, 15% 225 and 50% of the pre-pandemic total capacity (Table 3) was considered as the baseline capacity of 226 hospital and ICU beds, i.e. the starting values of Hlim(t) and Ulim(t), respectively. 227 Upon reaching the capacity limit, the influx should be stopped until a vacant bed is available. 228 This could be achieved by introducing a Heaviside step function or any other piecewise method, 229 but this type of function introduces discontinuities and makes solving the ODEs computationally 230 April 21, 2022 8/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint demanding and error-prone. Here, we introduced two functions ( fHlim and fU lim) that behave 231 like a step function but are continuous in nature. fHlim and fU lim return 1 as long as there 232 are free hospital or ICU beds and 0 otherwise. In the Capacity Model , we introduced the 233 compartmentID, to which the flux from IH is directed when the hospital capacity is reached. 234 Then, in a sharp transition, patient access to the hospital or ICU is reduced by the fractions 235 fHlim(t) and fUlim(t), respectively: 236 fHlim = (exp(HR +HU−Hlim))10 (1 + (exp(HR +HU−Hlim))10)10 fUlim = (exp(UR +UD−Ulim))10 (1 + (exp(UR +UD−Ulim))10)10. Both factors increase fatal outcomes of infections when hospital and ICU capacities are 237 reached. We assumed that inaccessibility of hospital or ICU leads to faster and more frequent 238 death. In particular, when the ICU capacity is reached, people in the hospital compartment 239 (HU) die after 1/R7 days which is faster than via the hospital-ICU-dead route ((1 /R7 + 1/R10)). 240 Similarly, when the hospital capacity is reached, people in the infected compartment ( IH) die 241 after 1/R6 + 1/R7 days, satisfying 1/R6 < 1/R6 + 1/R7 < 1/R6 + 1/R7 + 1/R10 (see Reference 242 Model in the Supplementary Material). 243 The MaxCap Model is defined by the same equations as the Capacity Model , but the 244 parameters, Hlim and Ulim were set to the maximum hospital and ICU capacity, respectively, 245 from the beginning of the simulations. 246 Data and code availability 247 Italy COVID-19 data of infected cases, hospitalized and ICU patients and death numbers 248 were provided by the Protezione Civile Italiana [29]. Demographic and mortality data used 249 to estimate IFR, are available from the Italian Institute of Statistics (ISTAT) website [56,57]. 250 ISTAT collects mortality data from the Italian National register office for the resident population 251 (ANPR). An automated method was implemented, and parameter estimation was carried 252 out in Matlab 2019b [58] with a combination of the Data2Dynamics framework [59]. The 253 code is available at https://github.com/arnabbandyopadhyay/COVID-19-in-Italy . For the 254 Bayesian estimation of COVID-19 IFR of Italian regions, see Supplementary Material. 255

256 Region-wise infection fatality rate (IFR) 257 To estimate undetected infections amid the COVID-19 pandemic, we analyzed the mortality rate 258 of previous years and the deaths in 2020. Demographic and death data of the Italian regions 259 have been collected from the Italian Institute of Statistics (ISTAT). The observed mortality of 260 2020 was substantially higher than in previous years in those Italian regions where the pandemic 261 started – e.g. Lombardia, Veneto, Piemonte (Fig. S1). We estimated the total number of 262 infections, including undetected cases, and the associated IFR (defined as the percentage of 263 deaths among all infections, including the undiagnosed infections) for each region with a Bayesian 264 framework by adapting a standard binomial model (see Supplementary Material). Though 265 literature is available on IFR estimates in Italy, the impact of the undetected infections onto the 266 health care facilities and infection dynamics, considering different testing strategies adopted by 267 the regions, were not sufficiently addressed [21,22]. 268 The regional IFR, the estimated total infections, Infection rate (IR) and the undetected 269 fractions were summarised in Table 2. In the northern regions where the outbreak occurred 270 April 21, 2022 9/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint Table 2: Estimation of the total number of infections, the Infection Rate (IR), the Infection fatality rate (IFR) through maximum likelihood in a Bayesian framework based on the data provided by ISTAT up to April 15 th [56,57] (Supplementary Material). Age specific IFRs are reported in Fig. S2. Areas IFR in % (95% CI) Estimated total Infections (Undetected %) IR in % (95% CI) CFR in % Detected Infections Italy 1.58 (1.04 - 1.84) 2627807 (93.73%) 4.37 (3.8 - 6.64) 13.11 165155 Emilia Romagna 1.84 (1.03 - 2.24) 252985 (91.69%) 5.79 (4.84 - 10.22) 13.26 21029 Liguria 2.08 (1.15 - 2.6) 85924 (93.09%) 5.63 (4.57 - 10.01) 13.6 5936 Lombardia 1.66 (1.03 - 1.9) 1390759 (95.53%) 13.83 (12.16 - 22.19) 18.3 62153 Marche 1.88 (0.88 - 2.47) 58555 (90.62%) 3.93 (3.05 - 8.11) 13.56 5503 Piemonte 1.73 (0.78 - 2.12) 258792 (92.94%) 6.1 (5.06 - 13.4) 11.05 18229 Toscana 1.63 (0.69 - 2.36) 62671 (87.77%) 1.43 (0.99 - 3) 7.25 7666 Valle d’Aosta 1.54 (0.73 - 2.34) 9785 (90.19%) 9.74 (6.4 - 17.94) 12.63 958 Veneto 1.3 (0.57 - 1.71) 141466 (89.67%) 2.77 (2.19 - 6.09) 6.43 14624 first – e.g. Emilia Romagna, Piemonte and Veneto – the undetected infections were nearly 10 271 fold more than the reported cases, and in Lombardia, it was more than 21 fold. We observed 272 substantial heterogeneity of the IFR across different age groups (see Fig. S2). For ages below 273 60, it was as low as 0.05%. The IFR was significantly higher in the 81+ age group (9 .5% to 274 20%, Fig. S2). Despite Italy having the highest COVID-19 deaths in Europe, the estimated 275 infection rates (IR) were relatively low (highest in Lombardia ∼ 13% [12.16− 22.19%, 95% CI]) 276 across all regions, and hence the population was far from reaching the herd immunity threshold 277 (∼ 70% with formula 1− 1 R0 , assuming no previous immune memory and considering the lowest 278 mean of reportedR0 for Covid-19 is∼ 3) [60–62]. Our estimated total infections (detected + 279 undetected), IR and IFR are close to the Imperial College London report 20 on Italy [22]. 280 During the early outbreak, different northern regions in Italy adopted different testing 281 strategies, which heavily influenced the infection dynamics. Lombardia and Piemonte followed 282 the World Health Organization (WHO) and central health authority recommendations by mainly 283 testing symptomatic cases, while Veneto implemented a more extensive population testing. 284 Lombardia with ∼ 10 million inhabitants has suffered around 14,000 deaths by the end of 285 April, which is more than half of all COVID-19 deaths in Italy. In comparison, Veneto, with a 286 population of 5 million, has suffered around 1,400 deaths. This difference is also reflected in 287 the CFR and IR, 6.43% and 2.77% in Veneto, while in Lombardia it was 18.30% and 13.83% 288 (Table 2) despite their geographical proximity. 289 To understand whether implementing different testing strategies succeeded in keeping the 290 undetected and the overall infection amount under control, we investigated the association 291 between the tests performed by regions with the total number of infections (detected and 292 undetected, Table 2) in the early phase of the pandemic. According to the null hypothesis, the 293 total number of infections would be uncorrelated with the testing volume, as testing only discovers 294 April 21, 2022 10/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● Abruzzo Bolzano Emilia Romagna Friuli Venezia Giulia ItalyLiguria Lombardia Marche Molise Piemonte Puglia Sardegna Toscana Trento Umbria Valle d'Aosta Veneto Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 Kendall corr.: R = −0.67; p−value = 0 Distance corr. = 0.81; p−value = 0.0099 0.00 0.05 0.10 0.15 20 40 60 Tests per Detected Infected Total Infected per Capita Fig 2: Impact of tests on the total infections. Kendall and distance correlation between the number of tests performed per infection and total infections per capita. Significant negative correlation confirms that the infection dynamics can be controlled by aggressive testing, which is further supported by the infection epidemic curve in Fig. 4A. Data are considered up to April 15th. Light blue line: linear regression fit; gray shaded area: standard error; black dots: region-specific values; red dot: nationwide value; R: correlation coefficient; p: significance. undetected infections and therefore should not impact the total infection. This hypothesis holds 295 when testing does not influence the infection dynamics. We measured the Kendall and distance 296 correlation between total infection per capita and total tests performed (up to April 15 th, 2020) 297 per reported infection. This yielded a significant correlation in both tests (Fig. 2). The negative 298 correlation indicates that testing influenced the infection dynamics by isolation of newly detected 299 cases and subsequent interruption of infection chains. The impact of testing is further supported 300 by the observed infection dynamics. Regions with intense testing, like Veneto and Toscana, 301 flattened the infection curve by the middle of April, while for Lombardia, Liguria and Piemonte 302 with inadequate testing, this was delayed by three weeks (first week of May 2020, Fig. 4A). 303 Influence of undetected cases on Rt 304 To understand the influence of undetected cases and installed NPIs on infection dynamics 305 across different regions in Italy, we used the COVID-19-specific Reference Model to explain the 306 dynamics of infected, hospitalized, ICUs and death numbers provided by the Protezione Civile 307 Italiana [29] (Fig. 4A). As described in the Parametrization section, based on the ensemble of 308 parameters estimated by using the first two weeks of data, we calculated the basic reproduction 309 numberR0 according to equation 1. Estimated behavioral parameters in every window (keeping 310 the physiological parameters constant) were used to calculate the reproduction number Rt 311 (Fig. 4B) according to equation 2. The sudden increase in reported cases resulted in an overshoot 312 in the Rt curve at the beginning. Due to the nationwide NPIs, increased public awareness 313 inducing self-isolation and social distancing, the reproduction number continuously decreased, 314 approaching unity at the end of April. In the regions with many undetected infections, like 315 Emilia Romagna, Lombardia and Piemonte, the reproduction number reached unity in the first 316 April 21, 2022 11/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint week of May, while in Veneto and Toscana it reached unity in the middle of April and was 317 substantially lower by the first week of May. As Rt functionally depends on many factors (see 318 Rt formula in the Methods section), we opted for a sensitivity analysis to find the important 319 factors that regulateRt. It revealed that Rt is highly sensitive to the transmission probability 320 R1 and the dark figure ¯µ (Fig. S9). The influence of installed NPIs, social distancing, awareness 321 etc. are embedded within R1 and therefore, their impact is reflected in the decreasing trend of 322 Rt in all regions. The benefits of testing and the impact of undetected cases on the Rt evolution 323 can as well be inferred by comparison of Rt in the Reference and the Asymptomatic Model with 324 less undetected cases (¯µ =α, µ = 1). 325 In the Asymptomatic Model, all symptomatic infections are detected and, hence, this reduces 326 secondary infections (β <<1). Removal of the highly infectious compartment ( IX), causes a 327 lower turnover from susceptible to exposed. This effect is apparent in the initial phase of the 328 pandemic when Rt in the Asymptomatic Model is much lower than in the Reference Model 329 (iris-blue and red line, respectively, in Fig. 4B). In the long term, the Rt curves from the 330 two models converge, despite the fraction of undetected cases being constant throughout the 331 simulations: ¯µ in the Reference Model and α in the Asymptomatic Model. This is consistent 332 with the effect of the restriction measures, limiting the spreading through undetected cases. The 333 difference in theRt curves of these two models is larger in the pre-lockdown period. As soon as 334 people’s behavior has started changing either by self-awareness or by imposed restrictions, the 335 turnover from susceptible to exposed is reduced. This caused the according adjustment of R1 336 and the merging ofRt in both models. Thus, the influence of undetected infections on Rt wanes 337 (Fig. 4B) because of two reasons, first, restricted contacts due to the nationwide lockdown, and 338 second, enhanced testing strategy adopted by the regions. 339 Increased Test and Isolate (TI) strategy to reduce hospitalizations 340 As the impact of undetected cases on Rt faded with time, we wanted to quantify the benefit of 341 an increased test and isolate (TI) strategy by implementing an early (from March 2 nd, 2020, 342 i.e. one week before lockdown) and late (from March 15 th, 2020) testing strategy. Many countries 343 have implemented a Test, Trace and Isolate (TTI) strategy that has a high detection rate, and 344 several modeling studies indicate that a high proportion of cases would need to isolate to control 345 the pandemic [63, 64]. In our case, an increased test and isolate strategy with a high success 346 rate of detection and isolation (as mentioned in the Methods section) is a phenomenological 347 implementation of a TTI strategy. 348 In the Testing Model we assumed that a fraction (µ2(t)) of the symptomatic undetected cases, 349 IX, was detected by tests (IXD), and hence became less infectious (β <<1 Methods, Fig. 1). We 350 maintained the compartmental flow from the Reference Model by using the same parameter set 351 in order to determine the impact of isolating undetected infections by targeted testing and home 352 quarantine of contact clusters around identified infections. This in silico experiment resulted in 353 a substantial increase in the number of detected infections but reduced the number of required 354 hospitalizations. The early TI scenario resulted in up to ∼ 32% peak reduction of hospital 355 bed occupancy, which reduced death numbers by up to ∼ 44% (Fig. 5A-B) depending on the 356 region. The late TI scenario resulted in a situation similar to reality, namely, an overwhelmed 357 health care system with little decrease in the peak hospital occupancy. However, late TI still 358 reduced death numbers by up to ∼ 24%. Although enhanced testing increased the total number 359 of detected infections in comparison to the real number of detected cases, Rt fell and reached 360 unity three weeks earlier (Fig. S10). In line with previous results [63], this result suggests that 361 TTI-strategies are efficient in decreasing disease propagation. South Korea successfully mounted 362 a targeted testing strategy to contain disease spreading without imposing strict measures, like 363 lockdowns or immigration control [8]. 364 Having established that increased detection and isolation lowers hospitalization rates, we 365 investigated whether the same relation can be inferred from the data directly. We calculated the 366 April 21, 2022 12/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint Step 0 — Parameters set up a.Bayesian estimation of regional IFR b.Literature search Impact of a TTI strategy on the hospitalization and dead number Step 1 — Simulations a.Sim. of Reference Model Step 1 — Simulations a.Sim. of Asymptomatic Model : Results : Input -Physiological parameters estimation -Behavioural parameters estimation Step 4 — MaxCap Model Simulation -Parameters fixed from the Capacity Model -Capacity for Hospital and ICU set to their maximum Excess deaths as obtained by the difference between number of dead in the Capacity Model and MaxCap Model. Impact of a TTI strategy combined with an increased hospital capacity on the hospitalization and dead number -Physiological parameters estimation -Behavioural parameters estimation a. ¯μ ¯μ=α b. α=0.4;Rx,x=2,...,9 -Physiological parameters from two weeks of data -Behavioural parameters ( ) by time- window technique R1,R10,ρ,ϑ,δ -Physiological parameters from two weeks of data -Behavioural parameters ( ) by time- window technique R1,R10,ρ,ϑ,δ calculation and comparisonℛt Step 2 — Testing Model Simulation -Parameters fixed from the Reference Model -Step-wise decrease of μ Step 5 — TestCap Model Simulation -Parameters fixed from the Capacity Model or from the MaxCap Model -Step-wise decrease of μ Step 3 — Capacity Model Simulation -Step-wise functions limiting the access to Hospital and ICU — and , respectivelyfHlim fUlim Fig 3: Flowchart of the study design including features and purposes of the SECIRD models. correlation between the median hospital occupancy and the total number of tests performed per 367 infected up to May 22nd, 2020 (Fig. 5C). Regions with low testing were associated with the health 368 care system hitting its capacity limits, while regions with intense testing kept a functional health 369 care system. The northern regions of Italy faced bottleneck situations in hospitals, which is well 370 reflected by the analysis (Fig. 5C, red color). Especially in Lombardia, where only symptomatic 371 patients were tested, the health care system was overwhelmed. In contrast, Veneto performed 372 ∼ 4 times more tests per infected than Lombardia, which reduced the number of infections and 373 April 21, 2022 13/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint ●●●●●●●●●●●● ●● ●● ● ● ● ● ●●●● ● ● ● ● ● ● ● ● ● ● ●●● ● ●● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●● ●●●●●●●●●●●●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●● ●●●● ● ●● ● ● ● ● ●● ● ● ● ● ● ●● ● ●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●● ●● ●● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ●● ●● ●● ● ● ● ●● ●● ● ● ●● ● ●● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●● ● ●● ● ● ● ●●●●● ● ● ●●●●●●●●● ●● ● ●●● ● ● ●●●●●●●●●●●● ● ● ● ●●●●●●●●●●●●●●●●●●●●●● ●●●● ●● ●● ● ● ●● ●● ● ● ● ● ●● ●●●●● ● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ●●●●● ●●●● ●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●● ●●●●● ●●●●●●●●●●●●●●●● ● ● ●● ●● ● ●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●● ● ●● ●●●●● ● ●●● ●●●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●● ●●●●●●●●●●●●●●●●●●●●● ●● ●●●●●●●●●●●●● ●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●● ● ●●● ● ● ●●●● ●●● ● ● ● ● ● ●● ● ●● ●● ●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●● ● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●● ●●●●●●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●● ●● ●●●●●●●●●●●●●●●●●●● ● ● ● ● ● ● ●● ● ● ●● ●● ● ● ● ●● ●●● ●●●●● ●●●●● ●●●●●●●●●●●●●●●●●●●●●● ● ● ●● ●●● ● ●●●●● ● ● ● ● ●●●●●●●●●●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●● ●●●●●●●●●●●● ● ●● ●●● ●● ● ● ● ● ● ● ●●● ●●● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●● ●●●●● ● ●● ● ● ● ● ● ●●● ●● ● ● ● ● ●●● ● ●●●●●●●● ● ●●●●●●● ●●●● ● ● ●●●●●● ●●● ●●●●●●●●● ●●● ●●●●●● ●●●●●●●●●●●●● ●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●● ●●●●●●●● ●●●●●●●●●●●●● ●●● ●●● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ●●●● ● ●●●● ●●●●●●●●●●●●●●●●●●●●● ● ●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●● ● ●●●● ●●● ●● ● ● ●● ●●● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●● ● ● ●●●●●●●●● ●●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ●● ● ●●● ●● ●● ●●●●●●●●●●●●●●●●●●●●●● ● ●●●● ●● ●● ●● ●● ● ● ●●● ● ● ● ●●●●●● ● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●● ●●● ●●●●●●● ● ●●●●●● ● ●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● Marche Piemonte Veneto Italy Emilia Romagna Lombardia Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22 5000 10000 15000 20000 25000 30000 2000 4000 6000 8000 10000 2000 4000 6000 8000 10000 12000 5000 10000 15000 2e+04 4e+04 6e+04 8e+04 1e+05 500 1000 1500 2000 2500 3000 Cases Legend ● ● ● ● Active Infection Hospitalized ICU Dead A Marche Piemonte Veneto Italy Emilia Romagna Lombardia Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22 1 2 3 4 0 2 4 2 4 6 0 2 4 6 8 1 2 3 4 5 0.0 2.5 5.0 7.5 10.0Reproduction Number Rt Model

Asymptomatic B Fig 4: Reference Model and time-dependent reproduction number Rt in different regions of Italy . (A) Active infections, hospitalized, ICU and death data (nationwide and region-wise) were fitted in a sliding one week time window. Parameter ranges listed in Table 1 were used and the behavioral parameters ( R1, R10, ρ, ϑ, δ) were estimated in each time window (see Methods); dots: data; continuous lines and shaded area: respectively, mean and standard deviation of all dynamics generated by using 100 perturbed parameter sets (see Methods). (B) Dynamics of the time-dependent reproduction-number, Rt, resulting from the fit with the

(red) and the Asymptomatic Model (blue). Statistics of Rt were obtained by fitting the data with 100 perturbed parameter sets; continuous lines and shaded area are, respectively, mean and standard deviation. Vertical lines correspond to the Lockdown implementation (dark red) and release (dark green). Black horizontal line represents Rt = 1. hospitalizations. 374 In summary, the hospitalization and testing data resolved per region suggest a benefit of 375 intense testing strategies to mitigate the load on the health care system. The in silico experiments 376 add evidence that this relationship is induced by the interruption of infection chains, in particular, 377 April 21, 2022 14/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint by the detection of undetected cases. Thus, testing not only improves knowledge on the infection 378 state but also directly impacts the dynamics of the pandemic. 379 Capacity Model and excess dead due to the shortage of hospital beds 380 Table 3: Hospital bed and ICU capacity before and in the course of the pandemic [55, 65]. ICU and normal Beds represent the pre-pandemic total beds. In the simulation we used 50% of ICU and 15% of normal beds as baseline capacity. Added ICU and Added beds represent increased allocation specifically for COVID-19 patients. Date ICU and Date beds is the date when the additional beds and ICUs were in place. AP: autonomous province. Regions ICU Beds Added ICU Date ICU Added beds Date beds Abruzzo 109 4410 67 31/03/2020 537 23/04/2020 Basilicata 49 1861 24 17/03/2020 139 17/03/2020 Calabria 153 5739 60 11/04/2020 126 11/04/2020 Campania 506 17977 104 11/04/2020 773 14/04/2020 Emilia Romagna 449 17295 259 24/03/2020 2189 24/03/2020 Friuli Venezia Giulia 127 4333 102 02/04/2020 358 08/05/2020 Lazio 557 20817 323 24/04/2020 1527 21/04/2020 Liguria 186 5690 127 07/04/2020 1241 01/04/2020 Lombardia 859 37767 939 03/04/2020 11673 12/04/2020 Marche 115 5183 132 31/03/2020 638 06/04/2020 Molise 31 1225 12 28/03/2020 31 07/04/2020 Piemonte 317 16313 500 08/03/2020 4451 16/04/2020 Puglia 302 12531 297 11/04/2020 1027 26/04/2020 Sardegna 123 5739 40 14/04/2020 92 07/04/2020 Sicilia 392 15821 312 23/04/2020 1632 04/05/2020 Toscana 377 12021 247 06/04/2020 1350 05/04/2020 Umbria 70 3259 35 25/03/2020 131 11/04/2020 Valle d’Aosta 12 481 25 03/04/2020 262 03/04/2020 Veneto 487 17512 331 17/03/2020 1910 17/03/2020 Bolzano (AP) 40 2047 66 16/04/2020 442 03/04/2020 Trento (AP) 32 2113 70 02/04/2020 382 07/04/2020 Besides NPIs and promoting social distancing, self-isolation etc., strengthening the health 381 care system is also an inevitable part of the government response. According to the data 382 published by the Italian Ministry of Health, Italy had 3.18 beds per 1000 people with an average 383 occupancy of 75-90% before the pandemic [55]. Between March 1 st and March 11th, 2020, 9-11% 384 of the infected people were admitted to ICU. Out of total ∼ 5200 ICU beds (pre-pandemic) 385 in Italy, 2500 were already occupied by March 20 th. To cope with this critical situation, each 386 region increased the hospital and ICU facilities (Table 3). Despite the considerable increase 387 in hospital and ICU capacity, the unexpected huge wave of patients and the necessary time to 388 adapt the facilities added to the difficulties of crisis management. 389 To investigate the impact of the limited health care capacities, we developed the Capacity 390 and the MaxCap Model (Fig. 1 and Fig. 3). As of May 22 nd, all regions had increased the 391 number of available beds, and the epidemic curves were in a downward phase. Therefore, we 392 investigated a possible impact on the pandemic of hospital overload in the previous months, 393 considering data from February 24 th to May 22 nd. 394 In the Capacity Model, the pre-pandemic occupancy of hospital beds and ICUs was considered 395 85% and 50% [55], and the baseline number of available hospital and ICU beds was set to 396 15% and 50% of the total capacity (Table 3), respectively. The capacity that was increased 397 April 21, 2022 15/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint 31% 7% 29% 6% 22% 2% Italy Lombardia Veneto Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22Aug 6Aug 21 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22Aug 6Aug 21 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22Aug 6Aug 21 500 1000 1500 2000 5000 10000 15000 10000 20000 30000Cases Model

Testing −− Early Testing −− Late A 43% 24% 34% 18% 38% 21% Italy Lombardia Veneto Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22Aug 6Aug 21 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22Aug 6Aug 21 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7Jun 22Jul 7Jul 22Aug 6Aug 21 500 1000 1500 2000 5000 10000 15000 10000 20000 30000 40000Cases Model

Testing −− Early Testing −− Late B ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● Abruzzo Basilicata Bolzano Campania Emilia Romagna Friuli Venezia Giulia Lazio Liguria Lombardia Marche Molise Piemonte Puglia Sardegna Sicilia Toscana Trento Umbria Valle d'Aosta Veneto Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.0099 Kendall corr.: R = −0.55; p−value = 0 Distance corr. = 0.89; p−value = 0.00990 50 100 150 4 8 12 16 Tests per Infected Median Hospital Occupancy (%) Fig 5: Impact of testing and isolation on hospitalization and death. (A & B) Simula- tion results of the Testing Model in two scenarios: undetected cases are decreased from ¯µ = 90% to 60% starting one week before the lockdown (green) and one week post lockdown (blue). (A) Sum of hospitalized including ICU patients. (B) Total deaths. The percentages provided in panels A and B quantify the reduction in peak with respect to the fitted Reference Model (red line). Statistics were performed by fitting the data with 100 perturbed parameter sets (see Methods). Continuous line and shaded region represent the mean and standard deviation, respectively. (C) Kendall and Distance correlations have been performed between the number of tests per infected and the median hospital occupancy, defined as the median of daily hospitalized over the pre-pandemic hospital plus ICU beds. Light blue line: linear regression fit; gray shaded area: standard error; red dots: northern regions; blue dots: southern regions; green dots: central regions. R: correlation coefficient; p: significance. April 21, 2022 16/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint ● ●●● ● ●●●●●● ● ● ●● ● ● ● ● ●● ● ● ● ●● ●●● ● ●●●● ●●●●●●●●●●●● ●● ● ●●● ●●●●● ● ●●●●●●●●●●●●●●●●●●● ●●●●●●●● ●●●● ●●●●●●●● ● ● ●●●● ●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ●● ●●●●●● ●●●●●●●●●●●●●●● ● ●●●●●● ●●●●●●●● ● ●●●●● ● ● ●●●● ● ● ●● ●●●● ● ●●● ●● ●●●● ●●●● ●●●●●●●● ●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●● ● ●● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ●●●● ● ●● ●● ● ●● ●●●●●●●●●●●●●●●●●● ● ● ●●●●● ●●●● ●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●● ● ●● ● ●● ●●● ●● ● ● ● ● ● ● ● ●● ● ●● ● ●●● ●● ●●●●●●●●●●●●●●●●●●● ●● ●●●●●●●●●●●●● ●● ●●●●●●● ●●●●● ●●●●●● ●●● ●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● Marche Piemonte Liguria Lombardia Feb 23 Mar 9 Mar 24 Apr 8 Apr 23 May 8 May 23 Feb 23 Mar 9 Mar 24 Apr 8 Apr 23 May 8 May 23 100 500 5000 10000 15000 100 500 2000 4000 6000 100 500500 1000 1500 2000 100 500500 1000 1500Cases Legend ● ● Hospitalized ICU A 3.97% 26.59% 6.85% 3.84% 50100 200 300400500 1000 2000 3000 4000 5000 6000 7000 Liguria Lombardia Marche Piemonte Excess Dead B Fig 6: Life costs of the limited health care system. (A) Sample Capacity Model fit of hospitalized (red), ICU (iris-blue) data (active infection and death data fitted, but not shown) for the most affected regions. Parameters were fitted as in the Reference Model by considering the first 3 months (February 24 th-May 22nd, 2020) data. Continuous lines: simulation results; round dots: data; Baseline capacity and linear increase in hospital (red) and ICU (iris-blue) capacity (Table 3) are represented as line with respective color. (B) Box plot of the difference in death numbers between the results of the Capacity and the MaxCap Model. Statistics performed over 100 perturbed parameter sets (see Methods) and the box plot shows the median, 25- and 75-percentiles as well as the minimum and the maximum values. We analysed the variation on the excess dead numbers depending on different values of α for the most affected region, Lombardia (Fig. S13). during the crises was described by a region-specific linear function with a daily increment so 398 that the capacity reached its target value at the date indicated in Table 3. We assumed that the 399 unavailability of hospital or ICU beds leads to faster and more frequent death (see Methods). 400 Parameters were determined using the same protocol as for the Reference Model. Capacity Model 401 April 21, 2022 17/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint fit is shown in Fig. 6A and Fig. S11. 402 In the MaxCap Model, the hospital and ICU capacities were fixed to their maximum from 403 the very beginning. The compartmental flow in both models was kept identical by using the 404 same parameter set as for the Capacity Model. We quantified the impact of the limited capacity 405 on COVID-19-associated deaths by subtracting the death numbers in the MaxCap Model from 406 those in the Capacity Model. This difference represents the number of people that would have 407 benefited from a system with a substantially higher capacity at the beginning of the epidemic. 408 The effect of limited health care facilities was dramatic in Lombardia with a ∼ 26% difference in 409 the number of deaths, corresponding to ∼ 4500 people (Fig. 6B). 410 A combined strategy 411 In reality, many regions ramped up facilities to test the immediate contacts of an identified 412 infection, e.g., Veneto [66]) and also strengthen health care facilities to accommodate more 413 patients. Previously we observed the benefits of an early TI strategy that reduces the load upon 414 the health care system, thereby reducing death numbers ( Testing Model, Fig. 5A,B). We also 415 observed a reduction in fatal outcomes in the case of a functional health care system that is not 416 overwhelmed (Capacity Model, Fig. 6A,B). Given these observations, we sought to investigate 417 the combined effects of an improved health care facility with intense testing by considering the 418 following four scenarios: 419 1. linear increase of hospital capacity combined with early TI; 420 2. linear increase of hospital capacity combined with late TI; 421 3. maximum hospital capacity from the beginning combined with early TI; 422 4. maximum hospital capacity from the beginning combined with late TI. 423 Thereby, early/late was assumed one week before/after the lockdown. 424 To simulate scenarios 1 and 2, we transferred the Capacity Model parameters into the 425 TestCap Model (Fig. 3) to keep the compartmental flow intact. To simulate scenarios 3 and 4, 426 we evaluated the TestCap Model assuming the hospital and ICU capacity at their maximum 427 levels from the beginning. In all scenarios, improved TI was simulated as step-wise reduction 428 of undetected cases by 2% per day ( µ′(t), Testing Model in Methods), which is equivalent to 429 ∼ 10-fold increased detection. 430 Fig. 7 reveals several interesting facets. The importance of testing in a realistic situation 431 where the step-wise extension of the health care facility has been installed is depicted in Fig. 7A. 432 It reveals that an early TI strategy brings down hospitalizations close to the pre-pandemic 433 hospital capacity (horizontal black line). An exception is Lombardia, where adopting an early 434 TI strategy led to∼ 10% reduction of the hospitalization peak, while the late TI strategy did 435 not decrease the peak size and led to a situation similar to what happened in reality. Though 436 the peak size remained unchanged in Lombardia in the late TI scenario, simulations showed a 437 reduction in the number of deaths of∼ 17% (Fig. 7A), reaching∼ 40% (Fig. 7B) when combined 438 with an increased hospital capacity. However, adopting an early TI strategy is effective in 439 reducing the death toll across all regions, ranging from ∼ 34% to∼ 52%. 440 Fig. 7B represents the importance of a TI strategy in the settings of a functional health 441 care system. Previously, we estimated a 26% reduction in death numbers in Lombardia by 442 strengthening the hospital infrastructure (Fig. 6B). Improved hospital capacity with early TI 443 further reduced death numbers by a significant amount, which ranged from∼ 35% to 52% across 444 different regions,∼ 52% in Lombardia (Fig. 7B). Early TI with ∼ 5 fold more testing would 445 have reduced the death toll up to ∼ 37% in Lombardia (Fig. S12). In the late TI scenario, it 446 would have decreased ∼ 40% in Lombardia (Fig. 7B), and considering only ∼ 5 times more 447 testing it would have decreased deaths by ∼ 31% (Fig. S12). 448 April 21, 2022 18/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint In summary, this in silico experiment emphasizes the importance of an early TI strategy that 449 could partially compensate for limited health care facilities at the early period (March to May, 450 2020) of the pandemic. However, such an early TI strategy would not be sufficient to contain the 451 hospitalizations within the pre-pandemic hospital limit (horizontal black line, Fig. 7). Therefore 452 extending the hospital infrastructure was mandatory to prevent the overwhelmed health care 453 system. 454 ●●●●●●●●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●●● ●●●●●● ● ●●●● ●●● ● ●● ● ● ● ● ●●● ●● ●● ●●●● ● ●● ●●● ● ● ● ●●●●● ●●●●●●●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●● ● ●●●●●●●●●●●●●●●●● ● ● ● ● ● ●● ● ● ●● ● ●● ● ●●● ● ●● ● ● ●●● ● ● ●● ●●●● ●●●●●●●●●●●● ● ●● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ●● ●●● ● ●●● ●● ●●● ● ●● ● ● ● ● ● ●● ●● ● ●● ●● ● ● ● ●● ●●●● ●● ● ●● ●●● Emilia Romagna Lombardia Piemonte Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23 0 1000 2000 3000 4000 0 5000 10000 0 1000 2000 3000 4000Hospitalized Model Capacity TestCap −− Early TestCap −− Late A ●●●●●●●●●●●●●●●●●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●● 34% 17% ●●●●●●●●●●●●●●●●●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●●● ●● ●●●●●●●●● ●●●● ●●●●●●●●●●●●●● 51% 17% ●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●●●●●●●●●●●●● ●●●●● 46% 24% Emilia Romagna Lombardia Piemonte Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7 0 1000 2000 3000 4000 0 5000 10000 15000 0 1000 2000 3000 4000Dead Model Capacity TestCap −− Early TestCap −− Late ●●●●●●●●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●●● ●●●●●● ● ●●●● ●●● ● ●● ● ● ● ● ●●● ●● ●● ●●●● ● ●● ●●● ● ● ● ●●●●● ●●●●●●●● ●● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ●● ●●●●●●●●●●●●●●●●●● ● ● ● ●● ●● ● ● ●● ● ●● ● ●●●● ●●●● ●●●●●●●●●●● ●●●●●●●●●●●● ● ●● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ●● ●●● ● ●●● ●● ●●● ● ●● ● ● ● ● ● ●● ●● ● ●● ●● ● ● ● ●● ●●●● ●● ● ●● ●●● Emilia Romagna Lombardia Piemonte Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23 0 1000 2000 3000 4000 0 5000 10000 15000 0 1000 2000 3000 4000Hospitalized Model Capacity TestCap −− Early TestCap −− Late B ●● ●●●● ●● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● 35% 17% ●●●●●●●●●●● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● 52%40% ●●●●●●●●●● ●●●● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●● 46% 27% Emilia Romagna Lombardia Piemonte Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7 Feb 23Mar 9Mar 24Apr 8Apr 23May 8May 23Jun 7 1000 2000 3000 4000 5000 10000 15000 20000 1000 2000 3000 4000Dead Model Capacity TestCap −− Early TestCap −− Late Fig 7: A strategy of early TI and extending hospital capacity combined. Simulation

of the TestCap Model. (A) Linear increase of hospital and ICU capacities (scenarios 1 and 2) and (B) maximum capacities from the beginning (scenarios 3 and 4) with early (green) or late testing. Statistics were performed by fitting the data with 100 perturbed parameter sets (see Methods). Line and the shaded region represent the mean and standard deviation, respectively. Hospitalized population is the sum of hospital and ICU patients. The percentage indicates the mean reduction in hospitalized peak and death number with respect to the mean of the Capacity Model. Black dots: data; black horizontal line: capacity (hospital + ICU) before the pandemic. April 21, 2022 19/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint

455 T esting interrupt transmission chains and directly influence infection dynamics 456 Our retrospective study revealed many lessons that can be learned from the COVID-19 situation 457 in Italy. Though containment measures are necessary to reduce the exponential growth of 458 the pandemic and flatten the infection curve as early as possible, prolonged lockdown (mass 459 quarantine) is not a sustainable solution to the pandemic given its socio-economic burden [67]. 460 The power of lockdown lies in restricting the contacts, and reducing the spread mainly from the 461 asymptomatic and pre-symptomatic carriers. This particularly applies to COVID-19 because 462 a substantial part of secondary infections occurs prior to disease onset [31]. Several studies 463 indicate that the silent transmission from pre- and asymptomatic patients was responsible for 464 the majority of new infections [54, 68, 69]. Although a recent study has found that there is a 465 lower risk of transmission from asymptomatic people [70,71], asymptomatic cases still present a 466 significant public-health risk, as they are usually unaware of their infection and do not take any 467 increased self-isolation measures. In Fig. 2 we showed that testing not only reduces the dark 468 figure but also interrupts subsequent transmission chains from undetected cases and thereby 469 directly influences the infection dynamics. This emphasizes the importance of a massive testing 470 strategy to control the pandemic. 471 Regional health care facilities were less overwhelmed with more testing 472 With the help of a mathematical analysis of the different regions of Italy, we have provided 473 evidence for a general relation between intense testing and reduced burden on the health care 474 system. To interrupt virus transmission chains, the Veneto Region developed a comprehensive 475 public health strategy focusing on case finding, contact tracing and quarantining close and occa- 476 sional case contacts [72]. Also, testing was extended to all, symptomatic and non-symptomatic 477 case contacts. Toscana followed a very similar strategy as Veneto, whereas Lombardia was 478 testing only the symptomatic cases. Lombardia has twice the population of Veneto (10M vs 5M). 479 Tests performed per capita in Veneto were almost twice as high than in Lombardia [73]. The 480 epidemiological outcomes of the testing strategy adopted by Veneto and Lombardia are very 481 different in terms of incidence number, evolution of the pandemic and the bottleneck situation of 482 the health care system. Veneto and Toscana managed to flatten the infection curve one month 483 earlier than Lombardia and Piemonte. In Fig. 2, Lombardia, Emilia, and Piemonte are placed in 484 the low test, high infection regime whereas Veneto is in the high test and low infection regime. 485 Therefore the pandemic situation of different Italian regions must be addressed in the light of 486 their testing strategy. Different testing strategies and their implications for the reproduction 487 number have been studied [68,74]. Several other studies emphasize the combination of contact 488 tracing with testing and its implication on the incidence number [63,75]. Our results suggest, 489 that the bottleneck in the health care system of northern Italy regions was a consequence of 490 their TTI strategy. In particular, testing of symptomatic individuals alone appears inefficient. 491 Early TTI could mitigate but not avoid the overload of the health care in Italy 492 In the middle of the crisis, many health care workers were infected with COVID-19 while treating 493 COVID-19 patients, and the voluntary participation of interns and retired personnel was required. 494 Moreover, delays in the testing of health care personnel led to the spread of infection through 495 health care workers. The shortage of health care workers together with limited hospital beds led 496 to a bottleneck situation in the health care system. A study revealed that a weekly screening of 497 the health care workers and other high-risk groups irrespective of their symptoms would reduce 498 transmission by 23% [74]. We quantified the impact of the overwhelmed health care system 499 on the death toll and studied how such a bottleneck situation could be avoided. We showed 500 that a substantial portion of the death toll, ∼ 35% in Lombardia, could be prevented by testing 501 and this could have mitigated the shortage of health care facilities at the early stage of the 502 pandemic, though it would not have contained the hospitalization within its pre-pandemic limit 503 in all cases. Hence, given the capacities, the bottleneck of health care facilities could not be 504 April 21, 2022 20/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint completely avoided by adopting massive testing alone. 505 An early TTI strategy can replace mass testing strategies 506 A∼ 10 fold increased testing demands huge testing facilities and is not an economic strategy. 507 Moreover, successful detection depends on the subjects getting tested and their previous travel 508 and contact history. Alternatively, tracking and targeted testing with home quarantine of 509 possible cases significantly reduce infection transmission and could be adopted instead of rapid 510 mass testing due to the higher chance of successful detection. However, manual contact tracing 511 is infeasible at higher incidences and contact tracing apps require ethical clearance in accessing 512 the location data, transparency and protection of personal data [68]. In this context, it has to 513 be emphasized that, in the framework of our mathematical model, the impact of tests on the 514 spreading of infections is based on the isolation of positively tested individuals regardless of their 515 symptoms, which is in line with the previous observations [63, 69]. This implies that contact 516 tracing and quarantine without testing would have a similar effect and might be an efficient 517 strategy when sufficient test capacities are not available. Thus, an effective contact tracing and 518 quarantine mechanism monitored through modern technologies, together with improved health 519 care facilities could reduce mortality in the possible future waves or other pandemics. 520

521 Our modelling study has several limitations. During the first wave in Italy, there was a high 522 degree of uncertainty regarding the fraction of pre-symptomatic and asymptomatic cases and 523 their associated transmission. These fractions were also subject to the regional testing strategy, 524 and their dynamic nature is observed in the weekly reports published by ISS. In our analysis, we 525 set the asymptomatic fraction, α, to the national average, 0.4. In our simulation, we considered 526 a fixed incubation period. We performed a sensitivity analysis of R3 upon theRt within the 527 range provided in Table 1, and we found that Rt is less sensitive towards the variations of R3. 528 As mentioned in the Parameterization section, we determined the range of parameter values 529 that constrained the fit of the physiological parameters by the information available in the 530 literature on the virus characteristics. Some of the physiological parameters in the model may be 531 internally linked. For example, hospitalization and ICU cases increase with infection cases. Here, 532 we assumed that the nature of the virus did not change significantly during the investigation 533 period, and, therefore, we kept the physiological parameters, and hence the internal relations, 534 constant throughout the investigation period. The behavioral adjustments (through NPIs and 535 awareness) caused the breakdown of such relationships and shaped the pandemic. As the 536 behavioral parameters reflect the public behavior which evolved with time, they depend upon 537 several factors and are region-specific. Therefore, it is difficult to infer a proper distribution of 538 such parameters. Nevertheless, as more precise parameter distribution would become available, 539 sampling from a different distribution might improve the quality of the model. 540 For the present analysis, we did not use an age-stratified version of the Reference model due 541 to the lack of knowledge of age-stratified model parameters and incomplete age-stratified data 542 during the first wave. However, the age-dependence is phenomenologically included in the model 543 by using a time-dependent hospitalization rate, which reflects the demography of the infected 544 people and other contingent factors that might alter the outcome of the pandemic. We also 545 did not include co-morbidities or pre-existing medical conditions of a sub-population and did 546 not explicitly consider the potential changes in viral transmissibility due to the environmental 547 factors, such as temperature and humidity. Further, cross-regional movements and the potential 548 for imported or exported infections, which might hamper the testing strategy based on contact 549 tracing, were not considered. Lastly, a delay in testing results might hamper outcomes in a 550 contact tracing-based testing strategy [76]. In our simulation, we did not explicitly consider 551 delays in isolation and its impact on the daily cases. Instead of addressing above limitations 552 explicitly, we perturbed our behavioral parameter sets up to 10% of its base value to ensure the 553 robustness of our results in a plausible range of parameter values. 554 April 21, 2022 21/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint

555 During the first wave of COVID-19 hospital and intensive care unit beds got overwhelmed in 556 Italy. There are potentially many factors, such as infections from undetected index cases, early 557 vs late testing strategies, limited health care facilities, etc., that might have aggravated the 558 COVID-19 situation in Italy. In this paper, we developed a COVID-19 specific infection epidemic 559 model to address the bottleneck situation of the health care system that most of the northern 560 regions of Italy, particularly Lombardia have faced during the first wave of the pandemic. As 561 the testing was limited at the beginning of the pandemic, a large portion of cases remained 562 undetected, which was a major driver of new infections. We first estimated the dark figure for 563 different regions of Italy through a Bayesian Markov Chain Monte Carlo (MCMC) framework. 564 With an adaptive methodology, we estimated the model parameters by fitting the active cases, 565 hospitalized, ICU, and death data published by the Civil Protection Department, Italy. We 566 showed that testing directly influences the infection dynamics by interrupting transmission from 567 undetected cases. We showed that intense testing is associated with the reduced burden of the 568 health care facility and in reality, regional hospitals were less overwhelmed with more testing. 569 By considering regional pre- and post-pandemic hospital and ICU beds we quantify the impact 570 of the overwhelmed health care system upon the death amount. The impact was highest in 571 Lombardia, which affected∼ 4000 people. Implementing an early TTI strategy in Lombardia 572 would have decreased overall hospital occupancy that would have reduced the death toll by 573 ∼ 45%. However, such a strategy would not have kept the hospitalization amount within the 574 pre-pandemic hospital limit. In this context, it is important to keep in mind that the effectiveness 575 of such strategy lies in the isolation of positively tested individuals regardless of their symptoms. 576 Therefore contact tracing and quarantine without testing would have a similar effect and might 577 be an efficient strategy when sufficient test capacities are not available. 578 Declarations 579

580 Our sincere thank to Dr. Luciano D’Alfonso, Senatore della Repubblica Italiana, Dr. Angelo 581 Borrelli, capo del Dipartimento della Protezione Civile Italiana e commissario per l’emergenza 582 Covid-19, Dr.ssa Eliana Mazzaro, Dip. della Protezione Civile Italiana, Dott. Stefano Marro, 583 Prevenzione Sanitaria presso Ministero della Salute, for responding to our requests in time and 584 for sharing data of hospital and ICU capacities. We thank Rebecca Ludwig for thoughtful 585

and comments on the manuscript. 586 Consent for Publication 587 Not applicable. 588 Funding 589 This project has received funding from the European Union’s Horizon 2020 research and 590 innovation programme under grant agreement No 101003480 and the Initiative and Networking 591 Fund of the Helmholtz Association. It was supported by German Federal Ministry of Education 592 and Research for the project CoViDec (FKZ: 01KI20102). The funding bodies had no role in 593 the design of the study, collection, analysis, and interpretation of the results, or writing the 594 manuscript. 595 Availability of the code 596 The code is available at https://github.com/arnabbandyopadhyay/COVID-19-in-Italy. 597 April 21, 2022 22/28 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 22, 2022. ; https://doi.org/10.1101/2020.10.12.20211169doi: medRxiv preprint Author’s contributions 598 AB and MS acquired and pre-processed the data, coded the simulation, automated the analysis 599 of the data, analyzed simulation results and led the work. TM and MMH developed the reference 600 SECIRD model. AB, MS and TM designed the capacity model and protocols for parameter 601 estimation of SECIRD models. AB and MS developed other versions of the SECIRD model. TM 602 derived the literature based parameter sets. TM and SK provided insights through discussion. 603 AB wrote the paper. AB, MMH, MS and SB revised the paper. MMH supervised the study. 604 Competing interests 605 The authors declare that they have no competing interests. 606 Ethics Approval and Consent to Participate. 607 Not applicable. 608

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