Fast initial Covid-19 response means greater caution may be needed later

Background: As the Covid-19 pandemic unfolds it is becoming increas- ingly clear that the strength of the first wave of the epidemic varies signifi- cantly between countries. In this study a simple numerical model is used to illustrate the impact the timing of initial measures against Covid-19 has on the first wave of infection and possible implications this may have for the measures taken as the first wave is ebbing. The results highlight that delay- ing measures by 10 days is sufficient to largely account for the differences seen between countries such as the UK and Germany for the first wave of infections. A pronounced first wave means that a larger fraction of the total population will have been infected and is therefore likely to display immunity. Even if this fraction is far below the level needed for ”herd immunity” the ef- fective reproduction factor Re is decreased compared to a population that had no prior exposure to the virus. Even a small reduction in Re can have major influence on the evolution of the epidemic after the first wave of infections. A large first wave means the resulting value for Re will be lower than if the first wave was mild. Without either vaccine or effective treatment countries that experienced a small first wave should therefore relax measures at a slower pace than countries where the first wave was strong. 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 2 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint 1. introduction24 Around the Globe the Covid-19 (SARS-CoV2) pandemic is currently impacting the daily lives25 of billions of people. After being first reported in late 2019 in the Chinese Province of Hubei,26 the Covid-19 virus has spread to all continents and led to - at the time of writing - about 1/3 of27 the world population being subject to some form of ”lockdown” rules. The paths chosen range28 from strict lockdowns with most people confined to their homes until the peak of the epidemic29 has been clearly passed (e.g. Hubei Province in China, South Korea, Italy, Spain) to more relaxed30 approaches where the emphasis is on minimising the impact on daily life (e.g. Sweden). Many31 nations are somewhere in the middle ground and have opted for various forms of ”soft lockdown”32 where people - whilst strongly encouraged to stay at home - can leave their homes to buy groceries,33 to attend medical appointments or to exercise. In their approaches countries are weighing human34 cost and in particular the capacity of the health system to cope with a surge in the number of cases,35 against the cost of shutting or ramping down many sectors of the economy. Regardless of which36 aspect weighs more heavily on the decision-making, the adopted approaches all have in common37 that they want to prevent an uncontrolled, exponential increase in the number of people infected by38 the virus. Despite debates and in some instances tensions between scientific advice, government39 action and public perception there is concensus that an uncontrolled spread of the virus would40 come at an unacceptable human cost which would overwhelm even the best prepared and efficient41 health system.42 All approaches that have been adopted include various forms of ”social distancing” with the aim43 to reduce the number of direct contacts between people in order to lower the effective reproduction44 factor Re (i.e. the number of people an infected person will infect on average) below a value of45 1. Current estimates for the reproduction factor R0 in a population that had no prior exposure to46 3 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint Covid-19 are between 2 and 3 (e.g. Liu et al. 2020). This makes Covid-19 more contagious than47 for example flu viruses with R0 ≈ 1.3 but less contagious than measles with R0 ≈ 15 in previously48 unexposed populations. In addition to social distancing some countries also prescribe the use of49 face masks when people leave their home - an approach most widely seen in Asia (e.g. China,50 South Korea or Singapore) whereas in most western nations the choice of mask-wearing is left to51 the individual. Social distancing and/or wearing face masks is not a new approach but was widely52 used in earlier pandemics such as the Spanish flu in 1918/1919 (e.g. Martini et al. 2019; Reid et al.53 2001). Such measures are simple and have been shown to be effective in slowing the spread of54 viruses. These low-tech measures are still the backbone of our approach to slow down pandemics.55 However, new technologies like contact tracing using mobile phones are increasingly being tested56 to localise infection hotspots and inform targeted applications of measures.57 As the Covid-19 pandemic unfolds with many countries having passed or are approaching the58 peak of the first wave we can observe marked differences in the number of cases and deaths in59 countries that are broadly comparable in terms of population size, health care systems and overall60 living standards. For example Germany had fewer deaths in the first wave than the UK despite61 having a larger population 83 vs 66 millions. Whilst it will be years until the full extent of the62 human and economic cost of the Covid-19 pandemic is known there are already lessons that can63 be learned - about the initial reactions and measures in future pandemics but also what to look64 out for as nations gradually emerge from the first wave of a pandemic. Analytical and numerical65 models can be powerful tools to understand the evolution of the pandemic so far and to test possible66 scenarios for the evolution of the pandemic in the coming months and years (e.g. Prem et al. 2020;67 Kucharski et al. 2020; Tsang et al. 2020). In this article a very simple model is used to illustrate68 the impact the timing of measures can have on the severity of the first wave of the pandemic and69 the consequences of a weak or a strong first wave once the lockdown rules are gradually relaxed.70 4 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint The model is introduced in section 2, the results presented and discussed in sections 3 and 4 and71

are given in section 5.72 2. Method73 The following introduces the model that will be used to test scenarios in which the timing for74 the imposition and relaxation of measures during an epidemic is varied. The basic assumptions75 for the model are that without imposition of any measures (i.e. daily human contacts as usual) and76 in a population with no prior exposure to the virus the reproduction rate R0 is assumed to be 2.5.77 R0 = 2.5 is at the lower end of the range of estimates forR0 for Covid-19 (e.g. Liu et al. 2020; Wu78 et al. 2020). An incubation time of 5 days is assumed i.e. within 5 days an infected person will on79 average infect 2.5 people.80 The cumulative number of cases C is calculated according to81 C(t0) = 1, (1) C(t1) = C(t0)(1 + R0), (2) ... C(tn) = C(tn−1) + (C(tn−1) −C(tn−2))R0(tn)(sP −C(tn−1)) sP , (3) Re(tn) = R0(tn)(sP −C(tn−1)) sP , (4) where P = 6.6 × 107 is the total population (similar to the UK), s = 0.6 the fraction of the82 population that needs to have been infected for ”herd immunity” to be reached. Since the average83 time between infection and first symptoms to show is about 5 days the assumption is made that84 ∆t = tn − tn−1 =5 days. R0 is the reproduction rate in a population that had no prior exposure to85 the virus. Re is the effective reproduction rate which accounts for the fact that, as the number of86 5 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint infections in the population rise, the ability of the virus to infect people gradually decreases. This87 assumes that people who had the virus will be immune to re-infection and that ”herd immunity”88 can be achieved. A linear relationship is assumed betweenC(tn) and Re. More elaborate functions89 could be used, but for to illustrate possible types of epidemic evolutions a linear relationship is90 sufficient.91 The reproduction rate R0(tn) as used in equation 4 can be considered as indicative of the strin-92 gency of the measures taken to slow the spread of the virus. No measures means R0(tn) = 2.5 and93 R0(tn) = 0 would refer to a situation where every infected person can be isolated before passing94 on the virus to anyone.95 From C(tn) the number of new cases per day is calculated according to:96 ∆C(tn) = C(tn) −C(tn−1) ∆t (5) The total number of fatalities F at time tn is calculated according to:97 F(tn) = m 4 n ∑ i=n−3 C(ti), n ≥ 4, (6) It is not yet clear what the mortality ratem for Covid-19 is. Based on the number of cases reported98 by the World Health Organisation fatalities make about 6.5% of the total number of cases (WHO99 2020). It is estimated that the actual number of people who have been infected is at least one100 order of magnitude higher than the recorded number (e.g. Bendavid et al. 2020; Vardar 2020).101 Therefore, a mortalility rate of m = 0.65% is assumed here. The number of fatalities per day is:102 ∆F(tn) = F(tn) − F(tn−1) ∆t (7) 6 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint a. Experiments103 The goal of measures such as social distancing and lockdowns is to reduce R0 in order to get Re104 below a value of 1 before the number of infected people requiring treatment becomes too large.105 Figure 1 illustrates the evolution of C(tn) if no measures are taken. In this case Re solely reduces106 because the fraction of the population that has been infected increases. In this simple model it takes107 about 120 days for 60% is the population to have been infected, which here will be used as the108 threshold needed to reach herd immunity. From about day 80 onwards the effective reproduction109 rate Re starts to decrease, reaching values close to zero after about 120 days. After that time 60%110 of the population (about 40 Mio people) would have been infected. With the assumed mortality111 rate of 0.65% this would result in 250000 fatalities in a population of 66 million.112 In a set of experiments the model is used to illustrate the sensitivity of the long and short-term113 development of an epidemic to the timing of the initial measures (e.g. social distancing). Focus is114 on the first and potential second wave of infections (experiments A1, A2, B1, B2) and on possible115 long-term evolutions of the epidemic during the years following the first infection (C1, C2, D1,116 D2). The details for the experiments are listed in table 1. All experiments have in common that117 the first measures (reducing R0 from 2.5 to 1.1) start either on day 75 (A1, B1, C1, D1) or 65118 (A2, B2, C2, D2). ”Lockdown” measures which reduce R0 from 1.1 to 0.85 start on day 80 for119 all experiments. The experiments (A, B, C, D) then differ on the timing and type of measures120 following the lockdown on day 80. All experiments are summarised in table 1.121 To illustrate that the model can simulate realistic evolutions of the first wave of the Covid-122 19 epidemic the simulated number of fatalities is aligned with the numbers recorded in the UK123 and Germany. Model and observations are temporally aligned from the time onward when UK,124 German, and simulated total numbers of fatalities first reach or exceed 10. In the model this125 7 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint threshold is reached after 60 days. Data for the UK and Germany are available from Worldometers126 (2020).127 3. Results128 The results shown in Figures 2 and 3 highlight the influence of timing of the first measures on129 the severity of the first wave of an epidemic. A difference of 10 days in the starting time of initial130 measures which reduce R0 from 2.5 to 1.1 (soft lockdown) is sufficient for the model to simulate131 evolutions of the number of deaths and death rate during the first wave which are comparable to the132 numbers recorded in the UK and Germany. If first measures are introduced on day 75 (experiments133 A1, B1, C1, D1) the maximum daily fatalities reach a maximum of just over 1000 deaths a day134 and by day 115 the cumulative fatalities exceed 30000. In contrast if first measures start on day 65135 (experiments A2, B2, C2, D2) the model simulates a peak in daily fatalities of just under 250 and136 a total number of fatalities of under 8000 - even though the lockdown starts on day 80 (R0 = 0.85)137 in all experiments.138 Except for experiments B1 and B2 where a long lockdown allows the number of cases to fall to139 zero, the lockdown measures are relaxed on day 115. In experiments A1 and A2 there is a further140 relaxing of measures on day 165 which allows a second wave to develop. This second wave is141 much more pronounced for experiment A2 (”German” case) than for experiment A1 (”UK” case).142 The respective peaks for daily fatalities are about 750 and 300. By day 280 a similar number143 of cumulative fatalities (≈ 60000) is reached in both cases. The reason for the difference in the144 amplitude of the second wave is the effective transmission rate Re. In A1 the simulated total145 number of cases C is just under 6 milliom people by the end of the lockdown (i.e. just under 10%146 of the total population). However, less than two million people (around 3% of the total population)147 would have been infected by the end of the lockdown in A2. These numbers are in the same order148 8 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint as studies suggest for St Clara County in California (Bendavid et al. 2020) or Spain (Vardar 2020).149 This difference is significant when it comes to the effective transmission rateRe: In neither of the150 two cases do we get close to the 60% level needed for herd immunity, however, the partial herd151 immunity is more pronounced in A1 than A2. When considering measures that aim at getting Re152 close to or ideally below a value of 1 having 3% or 9% of the population who went through the153 infection can be enough to get an effective reproduction rate which is just over or just under the154 critical threshold of 1. This can be clearly seen for experiments A1 and A2 (Figure 2): After the155 lockdown ends on day 115, Re is below 1 for experiment A1 until a further relaxation allows R0156 and Re to increase to 1.7 and about 1.4 in A1 whereas Re increases to about 1.6 in A2 leading157 to a markedly stronger second wave. As mentioned in section 2 R0 does change according to the158 assumed stringency of measures.159 Experiments B1 and B2 (Figure 2) illustrate the evolution for a prolonged lockdown where160 R0 = 0.85 until the number of daily cases ∆C decreases to zero. This point is reached after about161 280 days in B1 and 340 days in B2. The numbers of fatalities plateau at about 37000 and 10000162 cases for B1 and B2, respectively.163 Experiments C1 and C2 show the possible evolution for repeated loosening and tightening of164 the measures if daily fatalities ∆F 75. Rather than a second wave the evolution165 is characterised by a number of ”ripples” as measures are loosed or tightened. The number of166 fatalities gradually increases in both C1 and C2 but the slope flattens as the value of Re decreases.167 This is more pronounced in C1: the stronger first wave leads to a larger difference betweenR0 and168 Re. As mentioned earlier the reproduction rate R0 can be regarded as a measure for how stringent169 measures are: R0 = 2.5 means that daily life is not restricted in any way (as shown in Figure 1170 this comes at a high human cost) and R0 = 0 means that there are no new infections. This is171 only possible if every infected person is completely isolated and is unrealistic once the epidemic is172 9 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint spreading through the population. Experiments D1 and D2 illustrate the case whereR0 is gradually173 allowed to increase starting from R0 = 0.85 during the lockdown to R0 = 2.5. The rate of increase174 in R0 is determined by how large the tendency ofRe to fall is. The large first wave in D1 meansR0175 can increase more quickly than in D2. In D1 R0 = 2.5 after about 5 years whereas it takes about176 13 years in D2. For both D1 and D2 the number of fatalities is about 160000.177 4. Discussion178 The cases shown in Figures 2 and 3 are very idealised. There is little doubt that if A2 (”German”179 case - Figure 2) were to start developing in the real world, measures would be tightened again180 before day 185 therefore avoiding the pronounced second wave. Given thatF and ∆F are recorded,181 authorities would be aware of this development and could act accordingly. Experiments B1 and182 B2 have the lowest number of fatalities but they would require a long lockdown. With lockdowns183 now being gradually eased this is not the path that most countries have chosen.184 The scenarios C1 and C2 Figure 3 are more realistic as the extent of measures can adjust to185 changes in the number of recorded infections and deaths. Here we can see that after the first186 lockdown there are several phases where measures are tightened or loosened for short periods187 resulting in ”ripples” in the number of infections and fatalities but avoiding a strong second wave.188 The thresholds of daily fatalities used to tighten or loosen measures are identical in C1 and C2.189 However, the effective reproduction factor Re is consistently lower in C1 than in C2. In order to190 maintain the advantage of a clearly lower number of fatalities during the first wave the measures191 in C2 would need to be slightly more stringent than in C1 i.e. R0 would need to be consistently192 lower. However, if one assumes that a vaccine (or an effective treatment) becomes available within193 1 to 1.5 years C2 leads to a better outcome than C1. However, C1 would allow a daily life that is194 closer to ”normal” than C2. By specifically targeting ”hotspots” where infections flare up again195 10 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint it may be possible to consistently maintain an overall value of Re < 1 without the need to tighten196 measures everywhere (the latter is the underlying assumption in all experiments). This may lead197 to evolutions of cases and fatalities which fall somewhere between experiments B1/2 and C1/2.198 The scenarios illustrated in Figures 2 and 3 show that both the timing of the first measures as199 well as the choices made once the first wave is ebbing are crucial. Early action is the most effective200 way to reduce the amplitude of a first wave. Even delaying measures by a few days can result in201 many more lives being lost in that first wave. During the Covid-19 pandemic some governments202 chose not to act on initial warnings but only once it became obvious that the pandemic had taken203 a firm foothold. Here, it is also important to acknowledge the difficulty in knowing how far into204 a wave of infection a country actually is. Even in neighbouring countries the wave may be at an205 earlier or later stage and taking identical measures at the same time may lead to very different206 outcomes. If by the time the warnings come in the epidemic is more advanced than expected even207 swift action will not be sufficient to avoid a major first wave. On the other hand if the development208 of the wave lags expectations late action may still be sufficient to largely suppress the first wave.209 The large uncertainty regarding the stage of an epidemic means that a good (or bad) outcome can210 also be down to luck.211 However, luck can no longer be a factor after the first wave. Assuming that the mortality rate212 and level of health care are broadly similar in different countries a large number of deaths in213 proportion to the total population is a strong indicator that a higher percentage of the population214 has been infected than if the number of deaths is low. The results shown in Figures 2 and 3 suggest215 that when gradually easing the lockdown, countries which had a mild first wave (e.g. Germany,216 Austria, Norway, South Korea) may opt for a slightly slower unwinding of measures than countries217 that experienced a major first wave. Experiencing a major first wave means that there is likely to218 be a higher ”partial herd immunity” and that an effective reproduction rateRe < 1 can be achieved219 11 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint with more relaxed measures than in countries where the partial herd immunity is lower. This effect220 can already be significant even if less than 10% of the total population have been infected (e.g.221 Figure 2). Current studies suggest that only 10% or less of the total number of infections have222 been detected and that less than 10% of the population has been infected (Bendavid et al. 2020;223 Vardar 2020).224 At this point it is worth remembering that if one assumes a virus against which a vaccine is years225 away it is likely that the majority of the population will eventually be infected. Furthermore, ”herd226 immunity” can only be achieved if people who had the infection develop long-term immunity.227 Whether this is the case is still subject of ongoing research (e.g. Prompetchara et al. 2020; Shi228 et al. 2020; Grifoni et al. 2020; Braun et al. 2020). The only time when eradication of a virus is229 possible without a vaccine is at the very onset of the outbreak provided the outbreak is localised230 and that infected people can be isolated until they are no longer infectious. However, the window231 of opportunity for this is short and by the time health services and authorities become aware of232 (or acknowledge) the situation it may already be too late. Since people with Covid-19 can be233 infectious before showing any symptoms (or indeed without developing systems) (e.g. Cascella234 et al. 2020; Tindale et al. 2020) and that much international travel carried on as normal in the early235 stages of the pandemic, containment was always going to be difficult.236 5. Conclusions237 A simple model has been used to simulate different scenarios for the Covid-19 epidemic in a238 population of the size of the UK. The findings suggest that:239 • Timing of inital measures is key not just for the first wave of an epidemic but - in the ab-240 sence of either a vaccine or effective treatment - also for the longer term evolutions for years241 following the initial outbreak.242 12 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint • Shifting the implementation time of first measures by 10 days could explain differences in243 the number of recorded fatalities during the Covid-19 pandemic in countries such as the UK244 or Germany.245 • A large first wave means that easing of lockdown measures can occur faster than if the first246 wave was small. The reason for this is a lower effective reproduction factor after a strong first247 wave due to partial ”herd immunity”.248 • Relaxing measures too much after a small first wave risks cancelling out the advantage gained249 by the timely initial response to the pandemic.250 • Whether intial measures can largely suppress a the first wave of an epidemic is a combination251 of timely action and heeding advice as well as luck as at the time when first measures are252 taken it is difficult to know how far into the epidemic a country/region/town has progressed.253 Acknowledgments. Comments by Bablu Sinha are gratefully acknowledged. This research re-254 ceived no specific grant from any funding agency, commercial or not-for-profit sectors. .255 References256 Bendavid, E., and Coauthors, 2020: COVID-19 Antibody Seroprevalence in Santa Clara County,257 California. MedRxiv.258 Braun, J., and Coauthors, 2020: Presence of sars-cov-2 reactive t cells in covid-19 patients and259 healthy donors. medRxiv, doi:10.1101/2020.04.17.20061440, URL https://www.medrxiv.org/260 content/early/2020/04/22/2020.04.17.20061440, https://www.medrxiv.org/content/early/2020/261 04/22/2020.04.17.20061440.full.pdf.262 Cascella, M., M. Rajnik, A. Cuomo, S. C. Dulebohn, and R. Di Napoli, 2020: Features, evaluation263 and treatment coronavirus (COVID-19). Statpearls [internet], StatPearls Publishing.264 13 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint Grifoni, A., and Coauthors, 2020: Targets of T cell responses to SARS-CoV-265 2 coronavirus in humans with COVID-19 disease and unexposed individuals. Cell,266 https://doi.org/10.1016/j.cell.2020.05.015.267 Kucharski, A. J., and Coauthors, 2020: Early dynamics of transmission and control of covid-19: a268 mathematical modelling study. The lancet infectious diseases.269 Liu, Y ., A. A. Gayle, A. Wilder-Smith, and J. Rockl¨ov, 2020: The reproductive number of COVID-270 19 is higher compared to SARS coronavirus. Journal of travel medicine.271 Martini, M., V . Gazzaniga, N. L. Bragazzi, and I. Barberis, 2019: The Spanish Influenza Pandemic:272 a lesson from history 100 years after 1918.Journal of Preventive Medicine and Hygiene, 60 (1),273 E64.274 Prem, K., and Coauthors, 2020: The effect of control strategies to reduce social mixing on out-275 comes of the covid-19 epidemic in wuhan, china: a modelling study. The Lancet Public Health.276 Prompetchara, E., C. Ketloy, and T. Palaga, 2020: Immune responses in COVID-19 and potential277 vaccines: Lessons learned from SARS and MERS epidemic. Asian Pac J Allergy Immunol,278 38 (1), 1–9.279 Reid, A. H., J. K. Taubenberger, and T. G. Fanning, 2001: The 1918 Spanish influenza: integrating280 history and biology. Microbes and infection, 3 (1), 81–87.281 Shi, Y ., and Coauthors, 2020: Covid-19 infection: the perspectives on immune responses. Nature282 Publishing Group.283 Tindale, L., and Coauthors, 2020: Transmission interval estimates suggest pre-symptomatic spread284 of COVID-19. MedRxiv.285 14 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint Tsang, T. K., P. Wu, Y . Lin, E. H. Lau, G. M. Leung, and B. J. Cowling, 2020: Effect of changing286 case definitions for covid-19 on the epidemic curve and transmission parameters in mainland287 china: a modelling study. The Lancet Public Health.288 Vardar, S., 2020: Estudio de seroprevalencia: s ´olo el 5% de los espa ˜noles tiene antic-289 uerpos frente al coronavirus. URL https://www.elmundo.es/ciencia-y-salud/salud/2020/05/13/290 5ebc25ae21efa09e608b45f5.html, 13 May 2020, El Mundo.291 WHO, 2020: WHO Coronavirus Disease (COVID-19) Dashboard. URL https://covid19.who.int,292 World Health Organisation.293 Worldometers, 2020: Coronavirus. URL https://www.worldometers.info/coronavirus/country/294 uk/https://www.worldometers.info/coronavirus/country/germany/.295 Wu, J. T., K. Leung, and G. M. Leung, 2020: Nowcasting and forecasting the potential domestic296 and international spread of the 2019-ncov outbreak originating in wuhan, china: a modelling297 study. The Lancet, 395 (10225), 689–697.298 15 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint LIST OF TABLES299 Table 1. Experiment overview. Measures start either on day 75 or 65 and lockdown300 starts on day 80 in all cases. Lockdown is either relaxed on day 115 (A1, A2,301 C1, C2, D1, D2 - R0 = 1.1 or 1.05) or completely relaxed (R 0 = 2.5) if there302 have been no new daily new cases for 50 days (B1, B2). Further relaxation303 is either on day 165 (A1, A2); if daily fatalities ∆F < 50 (C1, C2); or if the304 effective reproduction rate Re 75 (C1, C2 -306 R0 = 1.05). . . . . . . . . . . . . . . . . . . . . 17307 16 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint Experiment Start measures Lockdown Relax measures Relax further Tighten again [day] [day] [day, ∆C] [day, ∆F, Re] [day, ∆F] A1 75 (R 0 = 1.1) 80 (R 0 = 0.85) 115 (R 0 = 1.1) 165 (R0 = 1.7) 185 (R0 = 1.1) A2 65 (R0 = 1.1) ” ” ” ” B1 75 (R 0 = 1.1) ” If ∑n i=n−10 ∆C(ti) = 0: R0 = 2.5 − − B2 65 (R0 = 1.1) ” ” − − C1 75 (R 0 = 1.1) ” 115 (R0 = 1.05) If ∆F 75: R0 = 1.05 C2 65 (R0 = 1.1) ” ” ” ” D1 75 (R 0 = 1.1) ” ” If Re(tn) < 1: − R0(tn+1) = R0(tn) + (1 − Re(tn)) D2 65 (R0 = 1.1) ” ” ” − TABLE 1. Experiment overview. Measures start either on day 75 or 65 and lockdown starts on day 80 in all cases. Lockdown is either relaxed on day 115 (A1, A2, C1, C2, D1, D2 - R0 = 1.1 or 1.05) or completely relaxed (R0 = 2.5) if there have been no new daily new cases for 50 days (B1, B2). Further relaxation is either on day 165 (A1, A2); if daily fatalities ∆F < 50 (C1, C2); or if the effective reproduction rate Re 75 (C1, C2 - R0 = 1.05). 308 309 310 311 312 313 17 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint LIST OF FIGURES314 Fig. 1. Scenario for the Covid-19 epidemic in a population of the size of the UK (66 million) as-315 suming no measures to stop the spread of the virus are taken. Shown are: cumulative (blue)316 and daily (red) cases (top row), cumulative and daily fatalities (2nd and 3rd row) and the317 reproduction factor R0 (magenta) and ”effective reproduction factor” Re (bottom). . . . . 19318 Fig. 2. As Figure 1 for experiments A1, A2, B1, B2 (see Table 1 for details). Vertical lines show319 the timing when different measures were taken: black dashed - begin of measures (steps320 in the values of R0 (magenta) and Re (blue)), solid black - Lockdown, green dashed - first321 and second easing of lockdown, solid green - 2nd lockdown. For the first wave the model is322 compared to the fatalities reported in the UK (orange line) and Germany (green line). . . . 20323 Fig. 3. As Figure 2 for experiments C1, C2, D1, D2 (see Table 1 for details). Vertical lines show324 the timing when different measures were taken: black dashed - begin of measures (steps325 in the values of R0 (magenta) and Re (blue)), solid black - Lockdown, green dashed. For326 the first wave the model is compared to the fatalities reported in the UK (orange line) and327 Germany (green line). . . . . . . . . . . . . . . . . . . . . 21328 18 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint FIG. 1. Scenario for the Covid-19 epidemic in a population of the size of the UK (66 million) assuming no measures to stop the spread of the virus are taken. Shown are: cumulative (blue) and daily (red) cases (top row), cumulative and daily fatalities (2nd and 3rd row) and the reproduction factor R0 (magenta) and ”effective reproduction factor” Re (bottom). 329 330 331 332 19 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint FI G. 2. As Figure 1 for experiments A1, A2, B1, B2 (see Table 1 for details). Vertical lines show the timing when different measures were taken: black dashed - begin of measures (steps in the values of R0 (magenta) and Re (blue)), solid black - Lockdown, green dashed - first and second easing of lockdown, solid green - 2nd lockdown. For the first wave the model is compared to the fatalities reported in the UK ( orange line) and Germany (green line). 333 334 335 336 337 20 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint FIG. 3. As Figure 2 for experiments C1, C2, D1, D2 (see Table 1 for details). Vertical lines show the timing when different measures were taken: black dashed - begin of measures (steps in the values ofR0 (magenta) and Re (blue)), solid black - Lockdown, green dashed. For the first wave the model is compared to the fatalities reported in the UK (orange line) and Germany (green line). 338 339 340 341 21 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted May 27, 2020. ; https://doi.org/10.1101/2020.05.26.20112680doi: medRxiv preprint