{"paper_id":"27286b89-6d9b-4ae0-b947-946c4a629a66","body_text":"Mohammadi et al.\n,\nRESEARCH\nHuman behaviour, NPI and mobility\nreduction effects on COVID-19\ntransmission in different countries of the\nworld\nZahra Mohammadi 1* †, Monica Gabriela Cojocaru 1† and Edward Wolfgang Thommes 1,2†\n*Correspondence:\nzahram@uoguelph.ca\n1Department of Mathematics &\nStatistics, University of Guelph, 50\nStone Road E., N1G 2W1, Guelph,\nCanada\nFull list of author information is\navailable at the end of the article\n†Equal contributor\n1Department of Mathematics & Statistics, University of Guelph, Guelph, ON Canada\n2Modeling, Epidemiology and Data Science, Sanofi Pasteur Global, Toronto, Canada\nAbstract\nBackground: The outbreak of Coronavirus disease, which originated in Wuhan, China\nin 2019, has affected the lives of billions of people globally. Throughout 2020, the\nreproduction number of COVID-19 was widely used by decision-makers to explain their\nstrategies to control the pandemic.\nMethods: In this work, we deduce and analyze both initial and effective reproduction\nnumbers for 12 diverse world regions between February and December of 2020. We\nconsider mobility reductions, mask wearing and compliance with masks, mask efficacy\nvalues alongside other non-pharmaceutical interventions (NPIs) in each region to get\nfurther insights in how each of the above factored into each region’s SARS-COV-2\ntransmission dynamic.\nResults: We quantify in each region the following reductions in the observed effective\nreproduction numbers of the pandemic: i) reduction due to decrease in mobility (as\ncaptured in Google mobility reports); ii) reduction due to mask wearing and mask\ncompliance; iii) reduction due to other NPI’s, over and above the ones identified in i) and\nii).\nConclusion: In most cases mobility reduction coming from nationwide lockdown\nmeasures has helped stave off the initial wave in countries who took these types of\nmeasures. Beyond the first waves, mask mandates and compliance, together with\nsocial-distancing measures (which we refer to as other NPI’s) have allowed some control\nof subsequent disease spread. The methodology we propose here is novel and can be\napplied to other respiratory diseases such as influenza or RSV.\nKeywords: SEIRL model; Initial and Effective Reproduction number; Mobility; Mask:\nadoption, compliance & efficacy; Pandemic control\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \nNOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.\n\nMohammadi et al. Page 2 of 24\n1 Background\nThe first known case of disease caused by SARS-CoV-2 was identified in Wuhan, China, in December 2019.\nThe disease spread worldwide in a few weeks, leading to a pandemic still ongoing as of the winter of 2022. Since\nDecember 2019, the basic and effective reproduction number of COVID-19 have been continuously discussed\nby scientists, political decision-makers and the media (regular and social). The basic reproduction number\nof an infectious disease, denoted by R0, represents the expected number of new cases generated by a single\ninfectious individual in a fully susceptible population. In epidemiology, a pandemic will be under control and\nthe transmission will die out when R0 < 1. Estimating the basic reproduction number for COVID-19 was\nchallenging since it was depending on the behavioural activity in local populations. The basic reproduction\nnumber for COVID-19 was reported to take values from 2.2 [1] to 6.33 [2] in different countries. In general,\nalthough whole populations started with being susceptible to virus, the progression of the pandemic steadily\ndecreased the number of susceptibles in each region. Consequently, the average number of secondary cases per\ninfectious case changed as the population became immunized (by recovering or dying). Thus as the pandemic\nprogressed, R0 gives way to the effective reproductive number, denoted by Reff , which measures the average\nnumber of secondary cases per infectious case in a population at any specific time (where only a fraction is\nsusceptible) [3]. In epidemiology, Reff is a monitoring indicator of progress in controlling a pandemic. It can\nalso be a way to monitor the effectiveness of interventions (both the effect of immunity and of additional\nnon-pharmaceutical interventions) during a pandemic.\nTransmission of SARS-COV-2 depends on the rate of person-to-person contact and on the probability of\ntransmission given one meaningful contact between an infected and a susceptible individual. While the proba-\nbility of transmission per contact is reduced by NPI’s, principally the wearing of masks [4, 5], the effectiveness\nof mask-wearing in preventing transmission of SARS-CoV-2 was not recognized in some world regions during\nthe first several months of the pandemic, despite the effectiveness of public mask use in controlling the spread\nof the 2003 SARS [6, 7].\nAnother critical non-pharmaceutical intervention for slowing epidemic growth is social distancing which in-\ncludes shelter-in-place requirements, prohibition of indoor gatherings, imposition of travel restrictions, school\nclosures and workplace closures. Previous studies investigated the quantitative relationships between the\nCOVID-19 epidemic parameters (for instance the total death toll) and social distancing efforts [8, 9, 10, 11].\nMobile data provide a unique opportunity to investigate to some degree the effectiveness of social distanc-\ning measures in reducing the effective reproduction number of COVID-19 [12, 13, 14]. Mobile data can be\ninterpreted as a proxy of person-to-person contact reduction as a consequence of social distancing measures,\nalthough it generally does not capture short-range behavioral changes, such as maintaining a 6 foot spacing be-\ntween individuals in public settings. The publicly available data on human mobility that is provided by Google,\nApple, Facebook, etc have been used in several articles to evaluate the effectiveness of non-pharmaceutical\ninterventions (NPIs) on the spread of COVID-19 [15, 16, 17, 18, 19, 20].\nExisting pre-pandemic work, such as [21, 22, 23], represents the effect of the population-level contact patterns\non the infection transmission dynamics. The infection transmission rate varies in different countries as a result\nof the different social and economic structures and different contact patterns. Mistry et al [22] used the derived\ncontact matrices to model the spread of airborne infectious diseases. The transmission rate of COVID-19\nfundamentally depends on interpersonal interaction rates. Most countries considered different strategies for\nreducing the contact rate in order to control the spread of the virus. Feehan and Mahmud calculated age-\nstructured contact matrices to quantify how much interpersonal contact has changed during the pandemic\nin the United States [24]. They estimated about 82% decline in interpersonal contact between March 22nd\nand April 8-th, 2020 (known as wave 0) and an increase in daily average contact rates over the subsequent\nwaves. Other studies observed the decline in contact rates in China [25], United Kingdom [26], Luxembourg\n[27], Italy, Belgium, France, and the Netherlands [28] throughout the pandemic. Prem et al. created synthetic\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 3 of 24\ncontact matrices to represent the effect of intervention measures to reduce social mixing on outcomes of the\nCOVID-19 epidemic in Wuhan, China [29,30]. The age-specific social contact characterization also supports the\npossibility of suspecting differences in transmission patterns of COVID-19 outbreak among different age-groups\n[31, 32, 33, 20]. In this work, projected contact matrices provided by Prem et al. [21] are used.\nThis work presents a SEIRL (Susceptible, Exposed, Infectious, Recovered and isoLated) model that uses inci-\ndence data, Google mobility data (as a modifier of effective contact rates), mask efficacy and mask compliance\ndata to provide insight into the strategies employed for controlling the pandemic in each country under consid-\neration. It explores and quantifies the effectiveness of non-pharmaceutical policy interventions across 12 diverse\ncountries/regions, using their effective reproduction number Reff . To accomplish these goals we estimate the\nR0 values of each region (using the classic next-generation matrix analysis [34]) and then a time-dependent ef-\nfective reproduction number, denoted byReff−data, using known repositories of incidence data for each country\n[35]. Using the projected contact rates from [21] extrapolated to each country of interest with publicly available\ndemographic data, we also infer the time-dependent effective contact rates, and hence the time-dependent ef-\nfective reproduction number of each country as a function of multiple Google mobility indices. We denote this\nbyReff−mobil.\nComparing the two estimates of Reff we investigate the effect of NPI’s, over and above changes in contact\nrates due to mobility and mask mandates, in each country’s epidemiology throughout the year 2020 [1]. It is\nconcluded in most cases that mobility reduction coming from stringent lockdown measures helped stave off\nthe initial wave in countries which took these types of measures (see for instance Figure 2). While mobility\nincreased in the second part of 2020 (see Figure 7), mask mandates together with all other NPI measures (for\ninstance social-distancing) have allowed some “control” of subsequent waves, in the sense that countries were\nable to maintain their effective reproduction numbers around 1.\nThe structure of the paper is as follows: Section 2 presents the setup and methodology employed in the\nanalyses of each of the twelve regions. Section 3 presents the results and discussion on quantification of the\nreduction in the effective reproduction numbers Reff−mobile and Reff−mobilemask, as well as the estimated\neffective reproduction numbers based on incidence data Reff−data. The paper closes with a discussion of the\nresults and a few directions for future work.\n2 Methods and model setup\nWe chose 10 countries around the world, one U.S. state (Florida) and one province of Canada (Ontario), based\non a diversity of characteristics: population density, median age, urbanization of population and gross domestic\nproduct (GDP) in 2020 (theses various characteristics are presented in Table 1 below:\nRegions Population Den-\nsity\nGDP Median Age Urbanization\n1 Ontario 37.9/sq mi 710 40.4 86.2\n2 Florida 384.3/sq mi 1095.9 42.5 91.2\n3 Romania 218.6/sq mi 248.6 42.5 56.4\n4 Sweden 64.7/sq mi 529.1 41.1 88\n5 Italy 521.4/sq mi 1848.2 46.5 71\n6 Ghana 262.9/sq mi 67.3 21.4 57.3\n7 South Africa 109.8/sq mi 282.6 28 67.4\n8 Saudi Arabia 38.8/sq mi 680.9 30.8 84.3\n9 Indonesia 357.4/sq mi 1089 31.1 56.6\n10 Nepal 466.2/sq mi 32.2 25.3 20.6\n11 Brazil 64.7/sq mi 1363.8 33.2 87.1\n12 Argentina 37.3/sq mi 382.8 32.4 92.1\nTable 1: Countries under consideration.\n[1]We chose to concentrate on the year 2020 specifically because there were no preventative or antiviral treat-\nments known against this virus at that time, and countries had to rely on some combination of NPI’s to fight\nits spread.\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 4 of 24\nThe data are collected from IndexMundi . In each of these regions we are interested to model the pandemic\nevolution during the year 2020 via a SEIRL model described below.\nSusceptible individuals (denoted by S and considered to be the entire population initially) exposed to the\nvirus enter the exposed (E) compartment for an average of 1/σ days before they become contagious, at which\npoint they move into the I (infected) compartment. In general, there is an a proportion of infected individuals\nwho will not develop symptoms (so-called asymptomatic, denoted by IA), while the remaining 1−a percentage\nmake up the infected symptomatic individuals, denoted by IS. Thus here :\nI(t) =IA(t) +IS(t) =aI(t) + (1−a)I(t). (1)\nAnϵ proportion ofIS(t) will self-isolate into theL (isolated) compartment. They do so with a delay of 1/κ days,\naccounting for a test result wait time and/or individuals who may disregard minor symptoms initially. After 1/γ\ndays, individuals recover from (or succumb to) their infection and move into the R (recovered) compartment.\nA diagram of the process we model is as follows 1:\nFigure 1: Transmission model in diagram form.\nUsing the expressions in (1) and model diagram (1), we obtain the following equations:\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\ndS\ndt =−βS(t) I(t)\nNtotal\n,\ndE\ndt =βS(t) I(t)\nNtotal\n−σE(t),\ndI\ndt =σE(t)−γI(t) +ϵ(γ−κ)(1−a)I(t)\ndL\ndt =ϵκ(1−a)I(t)−γL(t).\ndR\ndt =γ(1−ϵ(1−a))I(t) +γL(t).\n(2)\nOur model parameters have been taken from literature (as can be seen in Table 2), with the exception of the\nrate of isolation ϵ, which we assume to be equal to 95%.\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 5 of 24\nSymbol Definition Initial Value Reference\nNtotal Population size Table 4\nσ Rate at which exposed become infectious (days −1) 1/2.5 [36]\na Proportion of permanently asymptomatic cases 0.5 [37],[38],[39]\nϵ Proportion of compliance with isolation 0.95 assumed\nκ Isolation delay 1 assumed\nγ Recovery/removal rate 1/7 [40]\nTable 2: Parameter values for our model 2.\n2.1 Time series of effective reproduction numbers using a near-disease-free equilibrium estimate and\nincidence data\nThe Jacobian analysis near the disease-free equilibrium (DFE) which consists ofS(0) =N andI(0) = 0) for the\nsystem (2) and the next generation matrix method ([34]) for computing the initial R0 are given in Appendix.\nWe have employed a similar type of approach on our papers [41, 42], where the compartmental models were\nslightly different. We obtain its closed form expression:\nR0 = β\n(ϵγa−ϵκa−ϵγ +ϵκ +γ). (3)\nWe can also estimate R0 as a function of the growth factor near the DFE in each region using (9) (see more\ndetails in Appendix):\nR0(ρ) = ϵγaρ +ϵγaσ−ϵκaρ−ϵκaσ−ϵγρ−ϵγσ +ϵκρ +ϵκσ +γρ +γσ +ρ2 +ρσ\nσ((ϵγa−ϵκa−ϵγ +ϵκ +γ)) . (4)\nTo estimate the exponential growth factor for each region as a time series, we rely on weekly case incidence\ndata (which we denote by inc(t)) for each region. We assume that inc(t) is given by an exponential curve of\nthe type:\ninc(t) =inc(0)eρt.\nIn this case, we can compute a time-series of the exponential growth factor:\nρ(t) = lninc(t + 1)\ninc(t) , with inc(t)̸= 0.\nUsing this time series of ρ(t) in equation (10) we obtain a time series for the effective reproduction number:\nReff−data(t) =R0(ρ(t))s(t), where s(t) represents the remaining fraction of susceptibles at each t, (5)\ni.e. the difference between the entire population and the current cumulative number of infected individuals:\ns(t) = 1−\n∑\nτ∈[0,t]\ninc(τ).\nFigure 2 represents the weekly changes in the effective reproduction numbers of incidence data, Reff−data\nthat is explained in section (2.1), throughout 2020 for each geographical location under study. The vertical\nlines in each panel represent the dates in which local governments have introduced nationwide measures: in\nmost countries lockdown measures took effect, while in Sweden and Indonesia partial lockdown measures were\nin place. In Sweden, nationwide lockdown was considered to be a violation of people’s freedom of movement.\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 6 of 24\nThe government strategy was based on individual responsibility. Measures included were: border closures,\nrecommendations about social distancing, and traveling. Local reports show a 50% drop in public transport\nusage in April for the Swedish counties [43],[44] . In Stockholm, a 30% drop in the number of cars [45], and\n70% fewer pedestrians [46] was reported in April 2020. Later in November, the Swedish government imposed\nmandatory restrictions as well (e.g. all gatherings of more than eight people were banned).Italy had one of the\nearliest implementations of lockdown, as early as February 23, 2020. We showcase all dates for all locations in\nTable 3.\nRegions Hard/partial Lockdown order Mask Mandate\n1 Ontario 17 March 17 July\n2 Florida 17 March 25 June\n3 Romania 16 March 1 August\n4 Sweden* 11 March 7 December\n5 Italy 22 February 7 October\n6 Ghana 15 March 15 June\n7 South Africa 27 March 1 May\n8 Saudi Arabia 15 March 22 May\n9 Indonesia 30 March 5 April\n10 Nepal 24 March 31 July\n11 Brazil 24 March 2 July\n12 Argentina 19 March 29 August\nTable 3: Nonpharmaceutical Interventions (NPIs) measures\n2.2 Data sources\nIn the remainder of the paper we use various sources of publicly-available data. First we use Google data\nmobility [47] for each region of interest. Then we use Johns Hopkins data for case incidence: incidence [35] and\nwe use the Prem et al. [21] paper and their contact data projections (where projections for provinces or states\nin Canada and the US were obtained by using the projections weighted with population data for such provinces\nor states. Lockdown measures start dates have been taken from the ascent of the Oxford stringency index at\nFinancial Times.\nPopulation data were obtained from Stats Canada [48], US Census data [49], whereas for other countries we\nused the online repository: World age distribution [50]. For obtaining data on mask wearing compliance we\nused Mask Compliance [51] and European-countries [52].\n2.3 Time-series of effective reproduction numbers accounting for mobility data and projected contact\nrates\nWe first devise a mechanism to mix the daily average contact rates in each region’s population with the\nbehavioural activity in that population. In Prem et. al. [21] the authors compute projected daily average\ncontact rates for 157 countries. Specifically, they estimate the average contacts for categories of activities during\na typical day, such as: home, work and other locations. They present their results for a population stratified by\nage, and divided into 16 age subgroups (See Appendix for the details). We amalgamated the average contact\nrate in home, work, and other locations, then we computed the weighted average of a given projected contact\nmatrix in a region with the corresponding proportions of 5-year age population groups in 2020 to determine\none single average contact rate. We consider this last value as the average baseline (pre-lockdown) contact rate\nin that region (for instance, for Ontario it was computed to be: contactav≈ 11.04). All regions’ contacts are\nreported below in Table 4.\nGoogle reports contain changes in movement over time, compared to baseline (pre-lockdown) activity in six\ncategories: retail/recreation, groceries/pharmacies, parks, transit stations, workplaces, and domiciles (COVID-\n19 Community Mobility Reports) [47]. We have used the Google index data in other works, see [20, 53]. To find\nthe mobility-influenced, time-dependent contact rates post-lockdown, we considered the average contacts rate\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 7 of 24\n(a) Ontario\n (b) Florida\n (c) Romania\n(d) Sweden\n (e) Italy\n (f) Ghana\n(g) South Africa\n (h) Saudi Arabia\n (i) Indonesia\n(j) Nepal\n (k) Brazil\n (l) Argentina\nFigure 2: Weekly effective reproduction numbers based on incidence data. The yellow curve represents the\noutcome of equation (10), while the vertical pink dash line represents the start of nationwide social distancing\norders in each region under consideration.\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 8 of 24\nfor the home, work, and other location categories (comprising retail/recreation and groceries/pharmacies) from\nPrem et al. [21] for each region. Next, we used these category rates to modify the same categories of mobility\ndata as follows:\ncontactm\nav(t) =contactm\nav·gm(t) where m∈{ Home, Work, Other location}, t=1 week\nand where gm(t) is the percentage increase or decrease in the category m of mobility as compared to Google’s\nbaseline values per category. Finally, we amalgamated the Google mobility-influenced contact rates of these\ncategories to compute the weekly mobility-influenced contact rate by considering an average number of weekly\nhours hrm in each category:\ncontactav(t) =\n∑\nm\nhrmcontactm\nav(t) where m∈{ Home, Work, Other location}\nLet us now refine our view of the effective reproduction number Reff = R0s(t) from the perspec-\ntive of the changes in contact rates due to mobility reduction. From the last section we know that\nR0 = β\n(ϵγa−ϵκa−ϵγ +ϵκ +γ), however now we have\nβ(t) =contactav(t)·p =⇒ Reff−mobil = contactav(t)·p\n(ϵγa−ϵκa−ϵγ +ϵκ +γ)(1−\n∑\nτ∈[0,t]\ninc(τ)), (6)\nwhere p is the probability of transmission per meaningful contact. To estimate p, we need to have a handle on\nthe values of R0 from incidence data as well. To estimate R0 from incidence data we used equation (10). The\ngrowth factorρ is computed from the initial phase of (close to) exponential growth in the neighbourhood of the\nDFE, which corresponds to a phase of linear growth in log(inc), with slope ρ. We identify the initial, fastest\nphase of nearly unchecked growth in any given region with the help of a piecewise linear fit to the log of the\nincidence. We utilize the R function dpseg(), which is a part of the dpseg package, https://cran.r-project.\norg/web/packages/dpseg/index.html. This function uses a dynamic programming algorithm to generate an\noptimal piecewise linear fit to a time series, which balances goodness of fit against an (adjustable) penalty for\neach additional segment. We then identify the earliest segment with the steepest positive slope (largest ρ) as\ncorresponding to the initial near-unchecked exponential growth phase. We report the values we obtain in Table\n2.[2]\n[2]The last column in Table 2 highlights the number of weeks that dpseg is assigning for the steepest slope. The\nweeks are numbered from the first week with positive cases in each location, so near disease-free.\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 9 of 24\nRegion Population\nNtotal\ncontactav R0 ρ # of\nweeks (ρ)\n1 Ontario 14,734,014 11.04531438 1.856251 1.239646 5\n2 Florida 21,477,737 10.50481103 2.547635 2.044037 2\n3 Romania 19,237,682 10.53032815 2.183026 1.63537 3\n4 Sweden 10,099,270 11.09614737 2.372179 1.851232 4\n5 Italy 60,461,828 12.38928992 4.054303 3.485834 2\n6 Ghana 31,072,945 16.04056691 2.373496 1.852704 2\n7 South Africa 59,308,690 13.21954859 3.143281 2.654134 2\n8 Saudi Arabia 34,813,867 13.26255761 2.533263 2.028494 2\n9 Indonesia 273,523,621 12.54859287 2.733693 2.241501 2\n10 Nepal 29,136,808 16.09865556 2.025042 1.447956 2\n11 Brazil 212,559,409 12.72484009 2.680081 2.185299 2\n12 Argentina 45,195,777 12.13054343 1.998173 1.415379 3\nTable 4: The basic reproduction number,R0, at the beginning of the COVID-19 pandemic and contact average\nrate, contactav, before the COVID-19 outbreak for each geographical location under study. The table also\ncontains total population numbers and an estimated level of mask compliance in each population - data sources\nhighlighted in Section 2.2.\nTable 4 summarizes the basic reproduction number R0 at the beginning of the COVID-19 outbreak and the\naverage contact rate (before pandemic) and mask compliance level ( compliancem). The basic reproduction\nnumberR0 has maximum values in Italy and South Africa with 4.05 and 3.14, and minimum values in Ontario\nand Argentina with 1.85 and 1.99. We retrieve different mask compliance levels for each region from different\nsources (see Section 2.2).\n3 Results and Discussion\n3.1 Quantifying the effective reproduction number using incidence data\nTo quantify the overall relative status of the pandemic at the various locations, we show in Figure3 the evolution\nof Reff−data in each region using a heatmap plot and depicting values of Reff−data(t)∈ [0, 4].\nFigure 3: The effective reproduction numbers from incidence data plotted per range of values ( Reff ∈\n{[0, 0.5], [0.5−1],..., [2.5−3]}) from February 15 to December 31, 2020. Lightest color patches signify biggest\nreductions in values of Reff . In the second panel we see the cumulative incidence for the same regions\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 10 of 24\nThe color gradient signifies lowest values of the effective reproduction numbers in lightest color zones, and\nhighest values in darkest zones. Figure 3 showcases a comparison of the Reff−data between locations. We can\nimmediately see the effect of the reduction in Reff−data, across the board, in all countries between March and\nApril, and the rest of the year. It is clear the drop achieved by initial lockdowns and mobility reduction allowed\nall countries to drop their Reff−data to around 1, and interestingly most remained around this value for the\nrest of 2020. We include here (Table 5) the average Reff−data at each location after the initial drop.\nOntario Florida Sweden Italy Romania Saudi Arabia Indonesia Nepal South Africa Ghana Brazil Argentina\n1.027 1.064 1.05 1.07 1.04 1.02 1.075 1.07 1.09 1.04 1.07\nTable 5: Average Reff−data at each location after the initial drop\nQualitatively, we can understand why Reff−data has generally fluctuated in the vicinity of 1: On the one\nhand, rapid growth of incidence causes alarm at both the policymaker and individual level, and typically leads\nto increased NPI directives as well as compliance. On the other hand, because these measures are hard to\nmaintain and economically taxing, NPIs are generally relaxed not long after incidence starts to drop. In other\nwords, it is the human behavioural element that we do not model here, but that we glimpse.\n3.2 Quantifying the effective reproduction numbers accounting for mobility data\nWe observe that the initial sharp reduction in contact rate due to mobility happened in the middle of March\nin most regions under study, when initial lockdown was in effect, except in Sweden. The contact rate gradu-\nally increased from early May when partial reopening was implemented by governments. The results of these\nmeasures are noticeable in the figure 4 and 7 upper right panels.\nFigure 4: Weekly amalgamated Google Mobility Index in the Home, work and other activities respect to the\nbaseline (pre-lockdown) influenced by average contact rates, from Feb 15 to Dec 31, 2020. Baseline rates\nwere computed from Google mobility reports over a 6week interval of January-February 2020.\nThe effect of mobility restrictions throughout 2020 for each geographical location under study is presented in\nFigure 5 below. We plot the theoretically estimate Reff−mobile numbers together with the Reff−data effective\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 11 of 24\nnumbers at each location. Overall, under Google mobility reductions using formula 6, the mobility reduction\neffect is not enough, on its own, to explain the values Reff−data. This is not surprising, as each location had a\nvarying combination of NPI measures.\n(a) Ontario\n (b) Florida\n (c) Romania\n(d) Sweden\n (e) Italy\n (f) Ghana\n(g) South Africa\n (h) Saudi Arabia\n (i) Indonesia\n(j) Nepal\n (k) Brazil\n (l) Argentina\nFigure 5: Effective reproduction numbers from the mobility data influenced by contact rate. In\neach panel, the red vertical dash line represents the lockdown measures date and the pink curve shows the\nweekly effective reproduction numbers from the mobility affected by average contact rate in that region.\nFigures 5 (and 6 in an ensemble view) reveal the reduction in mobility in each region. It seems that the\nmobility decreased 51% and 54% in Nepal and Italy with respect to the baseline in the first and second weeks\nof April 2020, respectively. The mobility fell about 20% percent in Indonesia and Sweden. Large-scale social\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 12 of 24\nrestrictions (sometimes called partial lockdown) were introduced by the Indonesian government in place of\nnationwide lockdown at the end of March 2020 while the Swedish authorities imposed some restrictions on\ngatherings in late November.\nFigure 6: Reduction in mobility influenced by contact rate throughout 2020. The week that reduction hap-\npened is highlighted by ”month/day” in each bar.\n3.3 Human behaviour and its impact on disease transmission\n3.3.1 The effects of mask mandates and mask compliance on further reduction of the effective\nreproduction numbers\nWe will be looking at two main tools that populations can use to control the pandemic: social distancing and\nmask wearing. In our framework here, each one of these directly influences the transmission rate β. Denoting\nby maskeff the efficacy of an average mask at preventing transmission and by compliancem the compliance\nwith mask wearing let us imagine a meaningful contact between an infected and a susceptible individual: If\nan individual wears a mask and maskeff = 0.3, then he/she has an increased protection against transmission.\nIf the individual complies with mask wearing 50% of the time, then their protection due to mask wearing is,\non average maskeff·compliancem = 0.15 which implies that the per-contact transmission probability p will\ndecrease with mask wearing:\np′ = (1−maskeff·compliancem)·p.\nRecalling that the level of mask-wearing and social distancing both change over time, we estimate that\nβ(t) =contactav(1−maskeff·compliancem(t))·p. (7)\nLet us consider only mask-wearing for the time being. In this paper we use a value of maskeff = 50%, as\naveraged based on estimates in [54] (see a more detailed discussion in Appendix. and the values of mask\ncompliance from IHME (details of data sources in Data sources section above. ). Using (7) in the estimate (6)\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 13 of 24\nleads to:\nReff−mobilemask = (1−maskeff·compliancem(t))contactav(t)·p\n−ϵκ·a +ϵκ +γ (1−\n∑\nτ∈[0,t]\ni(τ)) (8)\nwith data from Table 4.\nFigure 7 shows the effective reproduction numbers as obtained from the incidence data (yellow curves) from\nFigure 2, together with our theoretical estimates from Figure 5 (solid pink curves) using mobility data, to which\nnow we add a new theoretically estimated Reff−mobilemask number reflecting mask wearing data and formula\n8 above. The red and black dashed lines in each panel show the lockdown and mask-wearing mandate dates,\nrespectively, in each region as publicly available.\nWe observe that the theoretically-estimated curve using both mobility reductions and mask wearing data\n(which we will now denote by Reff−mobilemask) is accounting for more of the reduction in transmission than\nthe estimated Reff−mobile curves of Figure 5. Evidently, in some regions (Ontario and Argentina) we observe\nwhat it looks like an over-reduction in the values of Reff−mobilemask as compared to Reff−data, while in other\ncountries, most notably Sweden, we notice essentially no contribution in further reduction from Reff−mobile\nto Reff−mobilemask. In Sweden’s case, this is not surprising, as the mask wearing levels in the IHME data\nwe used hover between 1% − 2% throughout 2020. Last but not least, this assumes a values of mask efficacy\nmaskeff = 50%. If this value is decreased, the Reff−mobilemask curves will shift upwards, i.e. the reduction of\nReff mobile due to mask wearing will be smaller.\n3.3.2 Effects of other social distancing measures on further reduction of disease spread\nAs we highlighted in previous section, a host of other NPI’s have been employed, at different strengths, across\nthe regions. While it is clear from our investigations thus far that the mobility reduction (as reflected in Google\nmobility data), along with mask wearing and mask compliance helped tremendously in the de-escalation of the\nReff curves, we wish to further analyze the data to extract more information on the strength of other NPI’s.\nLet us denote by complianceoNPI the compliance level in the local population with other NPI measures (by\nother we mean other than mobility and mask wearing). With this in mind, an average individual in a local\npopulation is protected over the course of their contacts proportional to what fraction of the time they also\ncomply with other NPI measures:\ncontact′\nav = (1−complianceoNPI (t))·contactav\nwhich then means that\nReff−data = (1−complianceoNPI (t))Reff−mobilemask =⇒ Reff−data\nReff−mobilemask\n= 1−complianceoNPI (t)\nThis means that to quantify the effects of other NPI measures per region, we further look at the ratio:\nReff−data(t)\nReff−mobilmask(t)\n. We present these plots in Figure 8 below. Clearly when the ratio is less than 1, then\nthe reduction in the Reff that we quantified from observed data is stronger than the reduction of Reff based\non mobility and mask wearing and viceversa. Specifically we obtain the following:\nReff−data\nReff−mobil\n≤ 1 =⇒ 1−complianceoNPI (t)≤ 1 =⇒ complianceoNPI (t)≥ 0\nIn the other case, under our assumptions, we get\nReff−data\nReff−mobil\n> 1 =⇒ complianceoNPI < 0.\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 14 of 24\n(a) Ontario\n (b) Florida\n (c) Romania\n(d) Sweden\n (e) Italy\n (f) Ghana\n(g) South Africa\n (h) Saudi Arabia\n (i) Indonesia\n(j) Nepal\n (k) Brazil\n (l) Argentina\nFigure 7: A comparison of the effective reproduction number as obtained from the incidence data (yellow\ncurves), to our theoretical estimate from Section 3.1 (solid pink curves) using mobility data. Beyond the\ndate of mask mandate enactment in each region, we show the theoretically-estimated incidence both with\n(solid pink) and without (dashed pink) the added effect of mask-wearing. The red and black dashed lines\nin each panel show the lockdown and mask-wearing mandate dates, respectively, in each region as publicly\navailable.\nIn cases where complianceoNPI < 0 we interpret it to mean that while the local population has been very\ncompliant with mask wearing (assumed to be at 50% efficacy in all regions), they may not have been as\nobservant towards other measures.\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 15 of 24\nOne remark is worth to be made at this point: if one decreases the mask efficacy maskeff to an average\nof 40%, respectively even lower to 30% (as in [54]), then the Reff−mobilemask curves of Figure 5 would scale\nequivalently upward by a constant, thus implying that the mask wearing effect is less effective and therefore\nthat the ratio Ref f−data\nRef f−mobil\nwould be less than 1 (i.e., complianceoNPI (t)> 0) for most (respectively all) regions.\n(a) Ontario\n (b) Florida\n (c) Romania\n(d) Sweden\n (e) Italy\n (f) Ghana\n(g) South Africa\n (h) Saudi Arabia\n (i) Indonesia\n(j) Nepal\n (k) Brazil\n (l) Argentina\nFigure 8: Effect of other NPI measures (e.g. 6 feet (2m) social distancing, hand washing, etc.). Mandatory\nmasks were introduced at dates represented by the vertical dashed line in each panel.\nResults in Sweden in particular stand out (see Figure 9). They indicate that other NPI measures were\nextremely effective in reducing the transmission rate of disease, in the absence of mandated lockdown periods\nand nearly 0 mask wearing. In the case of Sweden for instance (upper panel of Figure 9), complianceoNPI (t)\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 16 of 24\nis large starting in April 2020. Here complianceoNPI (t)> 0 at and over 50% in Sweden. In case of Indonesia,\nwe estimate that complianceoNPI (t) at and over 30-40% in Indonesia. Both these ranges assume an average of\nmaskeff = 50% over the time period May-December 2020.\n(a) Sweden\n(b) Indonesia\nFigure 9: Effect of other NPI measures in Sweden and Indonesia. Mandatory masks were never introduced\nin Sweden until November 2020, but they are present earlier in Indonesia. Nationwide lockdown was never\nused in these countries in 2020.\nAt the other end of the spectrum, Ontario (upper left corner panel in Figure 8) seems to display a ratio\nof Ref f−data\nRef f−mobil\n≈ 1 after the mask mandate date (vertical black dash line). Moreover, we have periods of time\nwhere the ration is larger than 1 somewhat, so then complianceoNPI might have been negative (in the case\nwheremaskeff = 50%). This seems to indicate that, under our assumptions, the mobility reductions captured\nvia Google indexes and the mask compliance levels have essentially captured the full picture of the pandemic\nevolution in this region. Similar trends can be seen in Argentina and Nepal (see Figure 8 and Figure 10).\n3.3.3 Further investigations into mask efficacy and its impact on transmission\nIn the sections above, we have considered a fixed value of maskeff = 50% across all regions, and we have\ncommented on how a decrease of this value may affect the reductions of Reff−mobile values. From formula 6\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 17 of 24\n(a) Ontario\n(b) Argentina\nFigure 10: Effect of other NPI measures in Ontario and Argentina. Mandatory masks were introduced at\ndates represented by the vertical dashed line in each panel.\nwe have\nReff−data = (1−maskeff·compliancem(t))Reff−mobile\nfor each region. Here, we perform a maximum-likelihood estimate of maskeff for each region, such that the fit\nofReff−mobile toReff−data is optimized. In other words, if we considered NPIs to consist only of mask-wearing,\nwhat mask efficacy would best reproduce the observed time series of effective reproduction number in a given\nregion? We present our results in a new plot with a small Table 6:\nOntario Florida Sweden Italy Romania Saudi Arabia Indonesia Nepal South Africa Ghana Brazil Argentina\n39% 75% 100% 83% 52% 80% 82% 45% 85% 98% 88% 44%\nTable 6: Maximum likelihood best fit values for maskeff per country\nThe graphs of the new Reff−mobilemask time series are presented in Figure 11 (dark pink curves). Here we\nsee again that Sweden stands out simply because mask wearing was not a policy the population had adopted\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 18 of 24\nin 2020; even at a 100% efficacy, an adoption of 1-2% has negligible effect. Thus other NPI factors must have\nbeen in play.\nAmong all the other countries, we see that high levels of mask wearing (for instance in Ontario, and similarly\nRomania and Argentina) correlates to realistic mask efficacy values (in [54] a realistic expected protection\nfrom the mostly cloth-type masks available widely in 2020 is between 30% to 50%) In regions such as Florida,\nItaly, Indonesia, South Africa, Ghana and Brazil the lower mask wearing levels would have needed to be\ncompensated by higher mask efficacy levels. Since such levels of mask efficacy were not possible in 2020 for an\naverage individual in any of these countries, then other NPI factors had to have been in play.\nThis analysis furthers the importance of our analysis in the last subsection (Subsection 3.3.2) where we\nmanage to quantify the effect of other NPI factors ( oNPI ) in reductions of transmission in each of the 12\nregions.\n4 Conclusion\nThis paper shows that estimated epidemiological parameters of an underlying SEIR(L) model can be used to\ncompute a time series of effective reproduction numbers accounting for mobility and mask wearing (explicitly\nusing available free data), which are then used to highlight differing pandemic trajectories in very different\nparts of the world. Our sample consisted of 12 regions (10 countries, 1 Canadian province and 1 US state)\nchosen based on diversity of population density, median age, urbanization of the population, projected average\ncontact rates, and gross domestic product (GDP) as in Table 1. We used a SEIR(L) epidemiological model\n(with parameter values from existing literature) and we used it to compute the near disease-free mathematical\nexpressions of the effective reproduction numbers in terms of initial exponential growth of infection. While we\nmade some specific choices on the structure of the compartments and the flow rates between them, we note that\nthe mathematical methodology we applied is universally applicable to other forms of SIR and SEIR models,\nand not just to ours. This makes our results applicable to many other variants of compartments models for\ninfectious disease transmission, not just for SARS-Cov-2 (for instance the next concern in the wake of the\npandemic are the next flu seasons and the possible mitigation measures in case high;y infectious flu variants\nwill make an appearance).\nWe were able to highlight quantitative relationships between the inferred weekly effective reproduction num-\nbers and the estimated weekly effective numbers based on mobility reduction (as captured by Google mobility\nindex) and mask-wearing (as captured from existing data).\nFigures 2 and 3 show that there is a sharp drop inReff−data at the initial lockdown, then most countries have\nmaintained their effective reproduction numbers around 1 by a combination of reduced mobility, mask-wearing\nand some additional other NPI’s not. Figure 7 shows a mobility-induced decrease of Reff−mobil with a further\ndecrease when we add mask wearing levels in each region.\nFurther, our modeling analyses provide direct illustrations of the effectiveness of other NPI’s in controlling\ntransmission in each region. Figures 7 and 8 show that effective reproduction numbers in all regions have\nbeen helped by population adherence and practice of NPI’s over and above reductions in mobility and mask\nprotection. This is also obvious by comparing the values of the effective reproductions numbers inferred from\ndata versus (in Figure 7 most regions maintain their values in the neighborhood of 1), while mobility reduction\nalone (as illustrated from Google mobility reports and in Figure 4) has steadily decrease beyond May 2020 in\nall locations.\nThere are several assumptions underlying our study. Clearly, the mobility reduction as reflected in Google\nmobility reports is used here as representative across each of the populations, however that may not be quite\naccurate and it depends on the percentage of cellphone usage in a region and whether or not that percentage can\nbe considered representative of an average individual. At the same time, the pre-pandemic projected contact\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 19 of 24\nFigure 11: Maximum-likelihood estimate of maskeff for each region so that the fit of Reff−mobile to\nReff−data is optimized. Curves in dark pink color are the new Reff−mobilemask estimates, where for each\ncountry we use the deduced value of maskeff listed.\nrates from [21] are themselves estimates, thus subject to further change or calibration, given the wealth of data\nfrom last year studies.\nNevertheless, the overall ideas we followed are fairly straightforward and the quantification of the control on\nthe pandemic via time series of effective reproduction numbers can be done as shown by using parameter values\nand data, without the need to model and fit SEIR model curves. Even if some of the assumptions/values in\nour analysis change, the methodology we propose is flexible, novel and easy to follow and implementing any\nnew or updated piece of data available is straightforward. As future directions of research we are interested in\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 20 of 24\nusing differing data sources for contact rates in some regions and differing estimates for mobility reductions to\nreplace the Google mobility reports. We can also us differing S(E)IR models and more data on socio-economic\nand demographic factors that may lead to further insights into accounting for differences in pandemic evolution\nin diverse countries around the world.\nDeclarations\nAcknowledgements\nNot applicable.\nFunding\nThis research was funded by a Natural Sciences and Engineering Research Council of Canada Accelerator Supplement #401285 (Cojocaru, M. G. - PI).\nThe first author’s salary was supported from this grant as well.\nAbbreviations\nNot applicable.\nAvailability of data and materials\nThe data used and/or analyzed during the current study are derived from public domain resources. The datasets are available in the [COVID-19\nCommunity Mobility Reports] repository, https://www.google.com/covid19/mobility/, the [COVID-19 Data Repository by the Center for Systems Science\nand Engineering (CSSE) at Johns Hopkins University], https://github.com/CSSEGISandData/COVID-19. We used the [Prem et al. contact data],\nhttps://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005697sec020. Population data were obtained from Stats Canada\nhttps://www.statcan.gc.ca/eng/start, US Census data https://data.census.gov/cedsci/table?q=Floridatid=ACSST1Y2019.S0101hidePreview=false, and\nhttps://population.un.org/wpp/Download/Standard/Population/ for other countries. The data related to mask wearing compliance are available on\ncovid19.healthdata.org and https://www.statista.com/statistics/1114375/wearing-a-face-mask-outside-in-european-countries/.\nEthics approval and consent to participate\nThis study does not require ethical approval. All data used or analyzed in this study are freely available in the public domain, and all methods are obtained\ndirectly from cited researchers. There is no direct interaction between the researchers and any individual or group in this study.\nCompeting interests\nThe authors declare that they have no competing interests.\nConsent for publication\nNot applicable.\nAuthors’ contributions\nAll authors contributed equally to the design and implementation of the research, analysis of the results, and writing of the manuscript.\nAuthor details\n1Department of Mathematics & Statistics, University of Guelph, 50 Stone Road E., N1G 2W1, Guelph, Canada. 2Modeling, Epidemiology and Data\nScience, Sanofi Pasteur, Toronto, Canada.\nReferences\n1. Li, Q., Guan, X., Wu, P., Wang, X., ..., Feng, Z.: Early transmission dynamics in wuhan, china, of novel coronavirus-infected pneumonia. (2020).\ndoi:10.1056/NEJMoa2001316\n2. Liu, Y., Gayle, A.A., Wilder-Smith, A., Rockl¨ ov., J.: The reproductive number of covid-19 is higher compared to sars coronavirus (2020).\ndoi:10.1093/jtm/taaa021\n3. Cauchemez, S., Bo¨ elle, P.-Y., Thomas, G., Valleron, A.-J.: Estimating in real time the efficacy of measures to control emerging communicable\ndiseases. Am J Epidemiol 164(6), 591–597 (2006). doi:10.1093/aje/kwj274\n4. Stutt, R.O.J.H., Retkute, R., Bradley, M., Gilligan, C.A., Colvin, J.: A modelling framework to assess the likely effectiveness of facemasks in\ncombination with ‘lock-down’ in managing the covid-19 pandemic 476(2238) (2021). doi:10.1098/rspa.2020.0376\n5. Eikenberry, S.E., Mancuso, M., Iboi, E., Phan, T., Eikenberry, K., Kuang, Y., Kostelich, E., Gumel, A.B.: To mask or not to mask: Modeling the\npotential for face mask use by the general public to curtail the covid-19 pandemic 5, 293–308 (2020). doi:10.1016/j.idm.2020.04.001\n6. Lau, J.T.F., Tsui, H., Lau, M., Yang, X.: Sars transmission, risk factors, and prevention in hong kong. 10(4), 587–592 (2004)\n7. Wu, J., Xu, F., Zhou, W., Feikin, D.R., Lin, C.-Y., He, X., Zhu, Z., Liang, W., Chin †, D.P., Schuchat, A.: Risk factors for sars among persons without\nknown contact with sars patients, beijing, china. 10(2), 210–216 (2004)\n8. Giordano, G., Blanchini, F., Bruno, R., Colaneri, P., Filippo, A.D., Matteo, A.D., Colaneri, M.: Modelling the covid-19 epidemic and implementation\nof population-wide interventions in italy 26, 855–860 (2020). doi:10.1038/s41591-020-0883-7\n9. Kucharski, A.J., Russell, T.W., Diamond, C., Liu, Y., Edmunds, J., Funk, S., et al: Early dynamics of transmission and control of covid-19: a\nmathematical modelling study. 20(5), 553–558 (2020). doi:10.1016/S1473-3099(20)30144-4\n10. Zoltan Neufeld, H.K., Czirok, A.: Targeted adaptive isolation strategy for covid-19 pandemic 5, 357–361 (2020). doi:10.1016/j.idm.2020.04.003\n11. Dandekar, R., Henderson, S.G., Jansen, M., Moka, S., Nazarathy, Y., Rackauckas, C., Taylor, P.G., Vuorinen, A.: Safe blues: A method for estimation\nand control in the fight against covid-19 (2020). doi:10.1101/2020.05.04.20090258\n12. Khataee, H., Scheuring, I., Czirok, A., Neufeld, Z.: Effects of social distancing on the spreading of covid-19 inferred from mobile phone data 11(1661)\n(2021). doi:10.1038/s41598-021-81308-2\n13. Kain, M.P., Childs, M.L., Becker, A.D., Mordecai, E.A.: Chopping the tail: how preventing superspreading can help to maintain covid-19 control 34\n(2021). doi:10.1016/j.epidem.2020.100430\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 21 of 24\n14. de Oliveira, S.B., Pˆ orto, V.B.G., Ganem, F., Mendes, F.M., Almiron, M., de Oliveira, W.K., Fantinato, F.F.S.T., de Almeida, W.A.F., de Macedo\nBorges Junior, A.P., Pinheiro, H.N.B., dos Santos Oliveira, R., Andrews, J.R., Faria, N.R., Lopes, M.B., de Ara´ ujo, W.N., DiazQuijano, F.A., Nakaya,\nH.I., Croda, J.: Monitoring social distancing and sars-cov-2 transmission in brazil using cell phone mobility data (2020).\ndoi:10.1101/2020.04.30.20082172\n15. Basellini, U., Alburez-Gutierrez, D., Fava, E.D., Perrotta, D., Bonetti, M., Camarda, C.G., Zagheni, E.: Linking excess mortality to mobility data\nduring the first wave of covid-19 in england and wales. SSM - Population Health 14, 100799 (2021). doi:10.1016/j.ssmph.2021.100799\n16. Kartal, M.T., Depren, ¨Ozer., Depren, S.K.: The relationship between mobility and covid-19 pandemic: Daily evidence from an emerging country by\ncausality analysis. Transportation Research Interdisciplinary Perspectives 10, 100366 (2021). doi:10.1016/j.trip.2021.100366\n17. Ilin, C., Annan-Phan, S., Xiao HuiTai and, S.M., Hsiang, S., Blumenstock, J.E.: Public mobility data enables covid-19 forecasting and management at\nlocal and global scales. Scientific Reports 11(13531) (2021). doi:10.1038/s41598-021-92892-8\n18. Sadowski, A., Galar, Z., Walasek, R., Zimon, G., Engelseth, P.: Big data insight on global mobility during the covid-19 pandemic lockdown. Journal of\nBig Data 8(78) (2021). doi:10.1186/s40537-021-00474-2\n19. Cot, C., Cacciapaglia, G., Sannino, F.: Mining google and apple mobility data: temporal anatomy for covid-19 social distancing. Scientific Reports\n11(4150) (2021). doi:10.1038/s41598-021-83441-4\n20. Fields, R., Humphrey, L., Flynn-Primrose, D., Mohammadi, Z., Nahirniak, M., Thommes, E., Cojocaru, M.: Age-stratified transmission model of\ncovid-19 in ontario with human mobility during pandemic’s first wave. Heliyon 7(9), 07905 (2021)\n21. Prem, K., Cook, A.R., Jit, M.: Projecting social contact matrices in 152 countries using contact surveys and demographic data. PLoS computational\nbiology 13(9), 1005697 (2017)\n22. Mistry, D., Litvinova, M., y Piontti, A.P., Chinazzi, M., Fumanelli, L., Gomes, M.F.C., Haque, S.A., Liu, Q.-H., Mu, K., Xiong, X., Halloran, M.E.,\nJr., I.M.L., Merler, S., Ajelliy, M., Vespignani, A.: Inferring high-resolution human mixing patterns for disease modeling 323(12) (2021).\ndoi:10.1038/s41467-020-20544-y\n23. Mossong, J., Hens, N., Jit, M., Beutels, P., Auranen, K., Mikolajczyk, R., Massari, M., Salmaso, S., Tomba, G.S., Wallinga, J., et al.: Social contacts\nand mixing patterns relevant to the spread of infectious diseases. PLoS Med 5(3), 74 (2008)\n24. Feehan, D.M., Mahmud, A.S.: Quantifying population contact patterns in the united states during the covid-19 pandemic 12(893) (2021).\ndoi:10.1038/s41467-021-20990-2\n25. Zhang, J., Litvinova, M., Liang, Y., Wang, Y., Wang, W., Zhao, S., Wu, Q., Merler, S., Viboud, C., Vespignani, A., Ajelli, M., Yu1, H.: Changes in\ncontact patterns shape the dynamics of the covid-19 outbreak in china 368(6498), 1481–1486 (2020). doi:10.1126/science.abb8001\n26. Jarvis, C.I., Zandvoort, K.V., Gimma, A., Prem, K., Klepac, P., Rubin, G.J., and, W.J.E.: Quantifying the impact of physical distance measures on the\ntransmission of COVID-19 in the UK (2020). doi:10.1101/2020.03.31.20049023\n27. Latsuzbaia, A., Herold, M., Bertemes, J.-P., Mossong, J.: Evolving social contact patterns during the covid-19 crisis in luxembourg 15(e0237128)\n(2020). doi:10.1371/journal.pone.0237128\n28. Fava, E.D., Cimentada, J., Perrotta, D., Andr´ e Grow, F.R., Gil-Clavel, S., Zagheni, E.: The differential impact of physical distancing strategies on\nsocial contacts relevant for the spread of covid-19 (2020). doi:10.1101/2020.05.15.20102657\n29. Prem, K., Liu, Y., Kucharski, T.W.R.A.J., Eggo, R.M., Davies, N., for the Mathematical Modelling of Infectious Diseases COVID-19 Working Group,\nC., Jit, M., Klepac, P.: The effect of control strategies to reduce social mixing on outcomes of the covid-19 epidemic in wuhan, china: a modelling\nstudy 5(5), 261–270 (2020). doi:10.1016/S2468-2667(20)30073-6\n30. Prem, K., van Zandvoort, K., Klepac, P., Eggo1, R.M., Davies, N.G., for the Mathematical Modelling of Infectious Diseases COVID-19\nWorking Group, C., Cook, A.R., Jit, M.: Projecting contact matrices in 177 geographical regions: an update and comparison with empirical data for\nthe covid-19 era (2020). doi: 10.1101/2020.07.22.20159772\n31. Spouge, J.L.: A comprehensive estimation of country-level basic reproduction numbers r0 for covid-19: Regime regression can automatically estimate\nthe end of the exponential phase in epidemic data 16(7) (2021). doi:10.1371/journal.pone.0254145\n32. Liua, Y., Gua, Z., Xiab, S., Shib, B., Zhoub, X.-N., Shig, Y., Liu, J.: What are the underlying transmission patterns of covid-19 outbreak? an\nage-specific social contact characterization 22 (2020). doi:10.1016/j.eclinm.2020.100354\n33. Brankston, G., Merkley, E., Fisman, D.N., Tuite, A.R., Poljak, Z., Loewen, P.J., Greer, A.L.: Quantifying contact patterns in response to covid-19\npublic health measures in canada running title: Contact patterns during covid-19 in canada (2021). doi:10.1101/2021.03.11.21253301\n34. van den Driessche, P.: Reproduction numbers of infectious disease models. Infectious Disease Modelling 2(3), 288–303 (2017)\n35. COVID-19 Dashboard by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University. Johns Hopkins University Medicine —\nCoronavirus Resource Center. https://coronavirus.jhu.edu/map.html\n36. Tuite, A.R., Fisman, D.N., Greer, A.L.: Mathematical modelling of covid-19 transmission and mitigation strategies in the population of ontario,\ncanada. CMAJ 192(19), 497–505 (2020)\n37. Mizumoto, K., Kagaya, K., Zarebski, A., Chowell, G.: Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on\nboard the diamond princess cruise ship, yokohama, japan, 2020. Eurosurveillance 25(10) (2020). doi:10.2807/1560-7917.es.2020.25.10.2000180\n38. He, W., Yi, G.Y., Zhu, Y.: Estimation of the basic reproduction number, average incubation time, asymptomatic infection rate, and case fatality rate\nfor COVID-19: Meta-analysis and sensitivity analysis. Journal of Medical Virology (2020). doi:10.1002/jmv.26041\n39. Ontario, P.H.: COVID-19 – What We Know So Far About. . . Asymptomatic Infection and Asymptomatic Transmission.\nhttps://www.publichealthontario.ca/-/media/documents/ncov/what-we-know-jan-30-2020.pdf?la=en Accessed 2020-06-19\n40. Wu, J., Tang, B., Bragazzi, N.L., Nah, K., McCarthy, Z.: Quantifying the role of social distancing, personal protection and case detection in\nmitigating COVID-19 outbreak in ontario, canada. Journal of Mathematics in Industry 10(1) (2020). doi:10.1186/s13362-020-00083-3\n41. Asgary, A., Cojocaru, M.G., Najafabadi, M.M., Wu, J.: Simulating preventative testing of sars-cov-2 in schools: policy implications. BMC Public\nHealth 21(1), 1–18 (2021)\n42. Humphrey, L., Thommes, E.W., Fields, R., Hakim, N., Chit, A., Cojocaru, M.G.: A path out of covid-19 quarantine: an analysis of policy scenarios.\nmedRxiv (2020). doi:10.1101/2020.04.23.20077503. https://www.medrxiv.org/content/early/2020/04/29/2020.04.23.20077503.full.pdf\n43. COVID-19 Pandemic in Sweden. https://en.wikipedia.org/wiki/COVID-19_pandemic_in_Sweden#cite_ref-170\n44. Jenelius, E., Cebecauer, M.: Impacts of covid-19 on public transport ridership in sweden: Analysis of ticket validations, sales and passenger counts.\nTransportation Research Interdisciplinary Perspectives 8, 100242 (2020)\n45. Hovne, A.: N¨ ara Var Tredje Bil Borta Fr˚ an Stockholms Gator”. Omni (in Swedish).\nhttps://omni.se/nara-var-tredje-bil-borta-fran-stockholms-gator/a/awQ7jL Accessed 2020-03-31\n46. Henley: Critics Question Swedish Approach as Coronavirus Death Toll Reaches 1,000. The Guardian.\nhttps://www.theguardian.com/world/2020/apr/15/sweden-coronavirus-death-toll-reaches-1000 Accessed 2020-04-15\n47. Google: COVID-19 Community Mobility Reports (2020). https://www.google.com/covid19/mobility/ Accessed 15 Feb 2020\n48. Statistics Canada: Population Estimates. https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=1710000501&pickMembers%5B0%5D=1.1&\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 22 of 24\npickMembers%5B1%5D=2.1&cubeTimeFrame.startYear=2016&cubeTimeFrame.endYear=2020&referencePeriods=20160101%2C20200101 Accessed\nJuly 2020\n49. United States Census. https://data.census.gov/cedsci/table?q=Florida&tid=ACSST1Y2019.S0101&hidePreview=false Accessed 2019\n50. United Nations: World age distribution (2019). https://population.un.org/wpp/Download/Standard/Population/ Accessed 2019\n51. The Institute for Health Metrics and Evaluation , Compliance with Mask. https://covid19.healthdata.org/ Accessed June 4, 2021\n52. London, Y.I.C.: How Often Have You Worn a Face Mask Outside Your Home to Protect Yourself or Others from Coronavirus (COVID-19)?\nhttps://www.statista.com/statistics/1114375/wearing-a-face-mask-outside-in-european-countries/ Accessed January 10, 2021\n53. Fields, R., Humphrey, L., Thommes, E.W., Cojocaru, M.G.: Covid-19 in ontario: Modelling the pandemic by age groups incorporating preventative\nrapid-testing. Mathematics of Public Health, 67–83 (2022)\n54. Wilson, A.M., Abney, S.E., King, M.-F., Weir, M.H., L´ opez-Garc ´ ıa, M., Sexton, J.D., Dancer, S.J., Proctor, J., Noakes, C.J., Reynolds, K.A.:\nCovid-19 and use of non-traditional masks: how do various materials compare in reducing the risk of infection for mask wearers? Journal of Hospital\nInfection 105(4), 640–642 (2020)\n55. Junling, M.: Estimating epidemic exponential growth rate and basic reproduction number. Infectious Disease Modelling (2020)\n56. Fields, R., Humphrey, L., Flynn-Primrose, D., Nahirniak, M., Mohammadi, Z., Thommes, E.W., Cojocaru, M.G.: Age-stratified transmission model of\ncovid-19 in ontario with human mobility. submitted to: Helyion Mathematics (2020)\n57. Chu, D.K., Akl, E.A., Duda, S., Solo, K., Yaacoub, S., Sch¨ unemann, H.J., et al.: Physical distancing, face masks, and eye protection to prevent\nperson-to-person transmission of sars-cov-2 and covid-19: a systematic review and meta-analysis 395(10242), 1973–1987 (2020).\ndoi:10.1016/S0140-6736(20)31142-9\n58. Brenan, M.: Americans’ Face Mask Usage Varies Greatly by Demographics.\nhttps://news.gallup.com/poll/315590/americans-face-mask-usage-varies-greatly-demographics.aspx Accessed July 13, 2020\nFigure Captions\n1 Transmission model in diagram form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4\n2 Weekly effective reproduction numbers based on incidence data. The yellow curve represents the outcome of equation (10), while the vertical\npink dash line represents the start of nationwide social distancing orders in each region under consideration. . . . . . . . . . . . . . . . . . 7\n3 The effective reproduction numbers from incidence data plotted per range of values ( Ref f ∈{[0, 0.5], [0.5− 1],..., [2.5− 3]}) from\nFebruary 15 to December 31, 2020. Lightest color patches signify biggest reductions in values of Ref f. In the second panel we see the\ncumulative incidence for the same regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9\n4 Weekly amalgamated Google Mobility Index in the Home, work and other activities respect to the baseline (pre-lockdown) influenced by\naverage contact rates, from Feb 15 to Dec 31, 2020. Baseline rates were computed from Google mobility reports over a 6week interval of\nJanuary-February 2020. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10\n5 Effective reproduction numbers from the mobility data influenced by contact rate. In each panel, the red vertical dash line represents the\nlockdown measures date and the pink curve shows the weekly effective reproduction numbers from the mobility affected by average contact\nrate in that region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11\n6 Reduction in mobility influenced by contact rate throughout 2020. The week that reduction happened is highlighted by ”month/day” in each\nbar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12\n7 A comparison of the effective reproduction number as obtained from the incidence data (yellow curves), to our theoretical estimate from\nSection 3.1 (solid pink curves) using mobility data. Beyond the date of mask mandate enactment in each region, we show the theoretically-\nestimated incidence both with (solid pink) and without (dashed pink) the added effect of mask-wearing. The red and black dashed lines in\neach panel show the lockdown and mask-wearing mandate dates, respectively, in each region as publicly available. . . . . . . . . . . . . . 14\n8 Effect of other NPI measures (e.g. 6 feet (2m) social distancing, hand washing, etc.). Mandatory masks were introduced at dates represented\nby the vertical dashed line in each panel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15\n9 Effect of other NPI measures in Sweden and Indonesia. Mandatory masks were never introduced in Sweden until November 2020, but they\nare present earlier in Indonesia. Nationwide lockdown was never used in these countries in 2020. . . . . . . . . . . . . . . . . . . . . . . 16\n10 Effect of other NPI measures in Ontario and Argentina. Mandatory masks were introduced at dates represented by the vertical dashed line\nin each panel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17\n11 Maximum-likelihood estimate of maskef f for each region so that the fit of Ref f−mobile toRef f−data is optimized. Curves in dark pink\ncolor are the new Ref f−mobilemask estimates, where for each country we use the deduced value of maskef f listed. . . . . . . . . . . . 19\nTables\n1 Countries under consideration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3\n2 Parameter values for our model 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5\n3 Nonpharmaceutical Interventions (NPIs) measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6\n4 The basic reproduction number, R0, at the beginning of the COVID-19 pandemic and contact average rate, contactav, before the COVID-\n19 outbreak for each geographical location under study. The table also contains total population numbers and an estimated level of mask\ncompliance in each population - data sources highlighted in Section 2.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9\n5 Average Ref f−data at each location after the initial drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10\n6 Maximum likelihood best fit values for maskef f per country . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 23 of 24\n5 Appendix\n5.1 Next generation matrix and reduced Jacobian\nThe Jacobian matrix near the disease-free equilibrium (DFE, which consists of S(0) =N andI(0) = 0) for the\nsystem of equations (2) is:\nJ =\n\n\n0 0 −β 0 0\n0 −σ β 0 0\n0 σ −(γ−ϵ(γ−k)(1−perasy)) 0 0\n0 0 ϵk(1−perasy) −γ 0\n0 0 γ−ϵ(1−perasy) γ 0\n\n\nUsing the next generation matrix method around the DFE ([34]) we compute R0 as the largest eigenvalue of\nthe matrix FV−1 and we obtain its closed form expression:\nR0 = β\n(ϵγperasy−ϵκperasy−ϵγ +ϵκ +γ). (9)\nFurther, using [55], we can compute the eigenvalues of the reduced Jacobian above and find that there is one\npositive eigenvalue (responsible for the growth near the DFE) which can be derived in closed form:\nρ =−ϵγperasy +ϵκperasy +ϵγ−ϵκ−γ−σ\n2 +\n√\nϵ2γ2perasy2− 2ϵ2γκperasy 2 +ϵ2κ2perasy2− 2ϵ2γ2perasy + 4ϵ2γκperasy− 2ϵ2κ2perasy +ϵ2γ2− 2ϵ2γκ +ϵ2κ2\n4\n+\n√\n2ϵγ2perasy− 2ϵγκperasy− 2ϵγperasyσ + 2ϵκperasyσ− 2ϵγ2 + 2ϵγκ + 2ϵγσ− 2ϵκσ + 4βσ +γ2− 2γσ +σ2\n4 ,\nwhich in turn can be solved for an expression of β as a function of the growth factor ρ near the DFE:\nβ =β(ρ) := ϵγperasyρ +ϵγperasyσ−ϵκperasyρ−ϵκperasyσ−ϵγρ−ϵγσ +ϵκρ +ϵκσ +γρ +γσ +ρ2 +ρσ\nσ .\nFinally we can estimate R0 as a function of the growth factor near the DFE in each region using 9 as:\nR0(ρ) = ϵγperasyρ +ϵγperasyσ−ϵκperasyρ−ϵκperasyσ−ϵγρ−ϵγσ +ϵκρ +ϵκσ +γρ +γσ +ρ2 +ρσ\nσ((ϵγperasy−ϵκperasy−ϵγ +ϵκ +γ)) .\n(10)\n5.2 Mask Efficacy\nFirst several months of the pandemic, there was considerable debate on the effect of face masks on limiting\nthe spread of the COVID-19 pandemic and whether to recommend the general public to use a face mask.\nLater, articles, scientific reports, and data proved the impact of face masks in altering the outcomes of peak\nhospitalization [5]. Notably, face masks are found to be useful in both preventing asymptomatic transmission\nand illness in healthy persons. We adapt our previously developed SEIRL model [56] for transmission of COVID-\n19 with the impact of public use of face masks. Moreover, varying efficacy and compliance of masks have an\nimpact on the transmission dynamics and control of the COVID-19 pandemic [4].\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint \n\nMohammadi et al. Page 24 of 24\nA review [57] of observational studies estimates that surgical and comparable cloth masks are 67% effective in\nprotecting the wearer. Some reports show that even a cotton T-shirt can block half of the inhaled aerosols and\nalmost 80% of exhaled aerosols measuring 2µm across e.g. unpublished work by Linsey Marr, an environmental\nengineer at Virginia Tech in Blacksburg. We consider 50% efficacy in our model.\n5.3 Compliance with Mask\nThe proportion of a population wearing face masks differs across countries/regions based on social norms,\npolitical reasons, the consequences of non-compliance e.g., fines. The results from a study surveying are different\nfor example:\n• The Institute for Health Metrics and Evaluation (IHME), a global health research center at the Univer-\nsity of Washington [51] is reported the percentage of mask use in Italy was between 63% to 93% from\nSeptember 1st till December 31, 2020, Sweden 1-7% , Saudi Arabia 73-76%, Ontario 75-85%, Florida\n66-70%, Romania 63-86%, Ghana 50-36%, South Africa 80-81%, Indonesia 74-76%, Nepal 64-63%, Brazil\n68-59%, Argentina 89-83%.\n• According to data from the Institute for Health Metrics and Evaluation at the University of Washington\nin Seattle, mask use has held steady around 50% since late July in the United States. It was predicted\nto increase to 95% as of 23 September. (see [51]) Whereas, a survey from Gallup [58] shows 72% of U.S.\nadults say they either always wear a face mask or wear one often when going to public places.\n• Percentage of people who worn a face mask outside their home always is reported 93.9% in Italy and\n12.1% in Sweden 12.1% by YouGov; Imperial College London [52].\nWe adapt our SEIRL model with the compliance of mask-wearing value denoted as compl in table 1 for each\nregion.\n5.4 Deriving average contact rates\nIn contact transmissible diseases e.g. COVID-19, contact rate has an important role in epidemic models. Prem\net al. [21] provide data-driven contact matrices in the home, work, school, and other locations for 152 countries\nof the world. We amalgamated the average contact rate in home, work, and other locations, then we computed\nthe weighted average of a given projected contact matrix in a region with the corresponding proportions of\n5-year age population groups in 2020 to determine one single average contact rate.\nAll rights reserved. No reuse allowed without permission. \n(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. \nThe copyright holder for this preprintthis version posted May 1, 2022. ; https://doi.org/10.1101/2022.04.29.22274485doi: medRxiv preprint","source_license":"Public-Domain","license_restricted":false}