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. 2021 Mar 16;37(1):5–31. doi: 10.1002/sdr.1673

Behavioral dynamics of COVID‐19: estimating underreporting, multiple waves, and adherence fatigue across 92 nations

Hazhir Rahmandad 1,✉, Tse Yang Lim 1, John Sterman 1
PMCID: PMC8250772  PMID: 34230767

Abstract

Effective responses to the COVID‐19 pandemic require integrating behavioral factors such as risk‐driven contact reduction, improved treatment, and adherence fatigue with asymptomatic transmission, disease acuity, and hospital capacity. We build one such model and estimate it for all 92 nations with reliable testing data. Cumulative cases and deaths through 22 December 2020 are estimated to be 7.03 and 1.44 times official reports, yielding an infection fatality rate (IFR) of 0.51 percent, which has been declining over time. Absent adherence fatigue, cumulative cases would have been 47 percent lower. Scenarios through June 2021 show that modest improvement in responsiveness could reduce cases and deaths by about 14 percent, more than the impact of vaccinating half of the population by that date. Variations in responsiveness to risk explain two orders of magnitude difference in per‐capita deaths despite reproduction numbers fluctuating around one across nations. A public online simulator facilitates scenario analysis over the coming months. © 2021 System Dynamics Society.

Introduction

Effective responses to the COVID‐19 pandemic require an understanding of its global magnitude and the drivers of variations in outbreaks across nations. Yet nearly a year after WHO declared a global pandemic, the true number of cases and the infection fatality rate remain uncertain, and the experience of different nations varies widely. As of late December 2020, countries have reported cumulative cases ranging between 7.03 and 7200 per 100,000, and case fatality rates between 0.05 percent and 9.0 percent. Asymptomatic infection (Gudbjartsson et al., 2020), variation in testing rates across countries (Roser et al., 2020), and false negatives (Fang et al., 2020; Li et al., 2020b; Wang et al., 2020) complicate assessment of the true magnitude of the pandemic from official data. The inference problem also requires disentangling other explanatory mechanisms: (i) differences in population density and social networks create variations in the effective reproduction number, RE; (ii) risk perceptions, behavior change, adherence fatigue, and policy responses alter transmission rates endogenously; (iii) testing is prioritized based on symptoms and risk factors, so detection depends on both testing rates and current prevalence (Onder et al., 2020); (iv) limited hospital capacity is allocated based on case severity, affecting fatality rates; (v) age, socioeconomic status, comorbidities, differential adherence to nonpharmaceutical interventions (NPIs) such as social distancing and masking and improvements in treatment affect transmission risk and case severity (Guan et al., 2020; O'Driscoll et al., 2021; Wu and McGoogan, 2020;); (vi) weather may play a role in transmission (Xu et al., 2020); and (vii) all these vary across nations.

Prior studies have shed light on important parts of the puzzle by estimating basic epidemiological parameters and IFR in well‐controlled settings (Russell et al., 2020), assessing the asymptomatic fraction and prevalence in specific populations (Hao et al., 2020; Li et al., 2020a; Mizumoto et al., 2020; Salje et al., 2020; Sutton et al., 2020), estimating the role of undocumented infections (Ghaffarzadegan and Rahmandad, 2020; Li et al., 2020a; Moghadas et al., 2020a), illuminating the effects of various NPIs on expected future cases (Chinazzi et al., 2020; Flaxman et al., 2020; Hsiang et al., 2020; Kissler et al., 2020; Ruktanonchai et al., 2020; Walker et al., 2020; Wu et al., 2020), and contrasting risks and healthcare demands across countries and populations (Britton et al., 2020; Gatto et al., 2020; Moghadas et al., 2020b; Struben, 2020; Walker et al., 2020).

Endogenous changes in behaviors and policies in response to outbreaks could also drive large variations in outcomes across nations. However, classical epidemic models, such as the Susceptible‐Exposed‐Infectious‐Recovered (SEIR) model, do not include endogenous behavior and policy responses. The classical models project exponential outbreaks that are ultimately limited by depletion of the susceptible pool or by the exogenous introduction of interventions that lower the effective reproduction rate (RE). Prior work in system dynamics shows that endogenous behavioral responses to infectious diseases significantly alter the dynamics. Sterman (2001, Chapter 9.4) describes a wide range of behavioral feedbacks in the context of the HIV/AIDS epidemic and shows that endogenous responses to risk can shift the dynamics from a single outbreak to an endemic condition with periods of reduced incidence followed by large outbreaks. Further, Rahmandad and Sterman (2008) showed that the impact of endogenous behavior change in the SEIR model is large compared to variations caused by different values of epidemic parameters determining the basic reproduction rate, R0, and by different structures for the contact network among individuals.

The history of the COVID‐19 pandemic to date strongly suggests a role for behavioral feedbacks. Many nations have experienced multiple waves of COVID‐19 as outbreaks induced behavior change and government policies that reduced transmission, only to see second or even third waves as the resulting reductions in incidence and deaths eroded NPI adherence by individuals and relaxation of government policies. To fit the data, many COVID‐19 models capture changes in transmission rates (i) as a function of time; (ii) using data on policy adoption timing in specific nations; or (iii) by incorporating policy switches that turn on in response to risks (Flaxman et al., 2020; Kissler et al., 2020; Li et al., 2020a; Walker et al., 2020). These approaches improve the fit of models to past data but perform poorly in counterfactual experiments and long‐term projections where historical data are uninformative and extrapolation of time‐based functions unreliable. A smaller group of studies have taken a more endogenous view of responses where ongoing (Ghaffarzadegan and Rahmandad, 2020; Struben, 2020) or expected risks (Acemoglu et al., 2020; Farboodi et al., 2020) condition contact rates and transmission. Prior work, however, has not used these risk‐driven response functions to explain the large cross‐national variations in outcomes (Struben (2020) provides an exception).

As the crisis unfolds, policymakers and the public seek a global view of the pandemic that is simultaneously consistent with the more focused findings, explains the orders‐of‐magnitude variation in official per‐capita case and death rates across countries, offers reliable projections consistent with multiple waves of mortality and incidence (Lopez and Rodo, 2020), and accounts for the impact of vaccination. Doing so requires modeling relevant biological and behavioral mechanisms and an empirical estimation strategy to reliably identify the critical feedback processes they create. Here we tackle this challenge.

Model

We use a multicountry modified SEIR model to simultaneously estimate SARS‐CoV‐2 transmission across 92 countries—all nations that report data sufficient to enable estimation. For each country, the model tracks the population from susceptible through presymptomatic, infected, and recovered or deceased states, with explicit stocks for those whose cases are detected or undetected and hospitalized or not (Figure 1a). Infection moves people from the Susceptible population (S) into the Presymptomatic Infected stock. After an Incubation Period, these presymptomatic individuals flow into the Infected Predetection stock. After a further Onset to Detection Delay, this group splits among multiple pathways. First, those testing positive for COVID‐19 flow into either Detected COVID+ Not Hospitalized or Detected COVID+ Hospitalized. Infected individuals who do not receive a positive test result, whether for lack of testing or a false negative test result, transition into either Undetected COVID+ or Undetected COVID+ Hospitalized. We assume demand for testing and hospitalization are driven by symptoms, so all asymptomatic individuals will be in the Undetected COVID+ stock.

Fig. 1.

Fig. 1

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Model overview. (a) Expanded SEIR model for each country highlighting key stocks and flows. (b) Major feedbacks captured in the model [Color figure can be viewed at wileyonlinelibrary.com]

In addition to its multicountry scope, the model includes three novel features (Figure 1b). First, tests are allocated to individuals based on symptom severity relative to available testing capacity. Individuals with more severe symptoms, including those with COVID‐19 and those without but presenting with similar symptoms (e.g. influenza) or risk factors (e.g. frontline healthcare workers), get priority for testing. We model symptom severity with a zero‐inflated Poisson distribution, where zero severity indicates asymptomatic infection. In this framework, originally developed in the context of testing in project models (Rahmandad and Hu, 2010), each increment of symptom severity increases the chance of receiving a COVID test, become hospitalized, or die. The formulation provides a consistent method to capture the significant heterogeneity in symptom severity, from asymptomatic to life‐threatening cases, and its impact on testing and hospitalization, without the need to disaggregate the population by different severity levels. Such disaggregation would make parameter estimation prohibitively time consuming (S1 and Figure S3 in the online supporting information provide details). Besides its computational benefits, the formulation keeps the number of free (estimated) parameters to a minimum, specifically two: the fraction of asymptomatic cases and the mean severity of symptomatic COVID+ individuals. Severity‐prioritized test allocation determines the ascertainment rate of COVID‐positive cases as a function of prevalence and the current testing rate. It also results in different average COVID severity in the tested vs. untested populations. We also account for false negatives from tests (Fang et al., 2020; Wang et al., 2020).

Second, hospital capacity is allocated between COVID‐positive cases and demand from non‐COVID patients. The COVID infection fatality rate therefore depends endogenously on the adequacy of hospital capacity relative to the burden of severe cases, along with the age distribution of the population (Guan et al., 2020; O'Driscoll et al., 2021; Wu and McGoogan, 2020). Furthermore, we account for reductions in IFR that may result from improved treatments, deaths of high‐risk populations such as the elderly and those with comorbidities in the first wave of the pandemic, heterogeneous adherence to NPIs as higher‐risk subpopulations perceive greater risk than those lacking risk factors, shifting incidence toward younger, lower‐risk people, and other factors.

Third, the hazard rate of transmission responds to the perceived risk of COVID. Perceived risk reduces transmission through adoption of NPIs, from social distancing and masking to lockdowns. Perceived risk is based on subjective perceptions of the hazard of death, which respond with a lag to both official data (reported in the media) and actual deaths (gleaned from personal experience and word of mouth). Rising mortality eventually increases perceived risk, driving the hazard rate of transmission down, while declining cases and deaths can lead to the erosion of perceived risk, potentially leading to rebound outbreaks. We also account for adherence fatigue, modeled as a reduction in the impact of perceived risk on behaviors that reduce contacts. We use the recent (last 100 day) reduction in contacts compared to prepandemic levels as the driver of adherence fatigue and estimate a country‐level parameter quantifying resulting reductions in the population's responsiveness to increases in perceived risk.

Estimation

Model parameters are specified based on prior literature and formal estimation. Parameters specified from the literature include the incubation period (mean μ = 5 days (Guan et al., 2020, Linton et al., 2020)), onset‐to‐detection delay (μ = 5 days (Linton et al., 2020)), postonset illness duration (μ = 15 days (Guan et al., 2020)), and the sensitivity of RT‐PCR‐based testing (70 percent (Fang et al., 2020, Wang et al., 2020)). Sensitivity analysis is presented in S7 in the online supporting information.

We estimate the remaining parameters using a panel of data covering all nations with at least 1000 confirmed COVID‐19 cases by 22 December 2020 and sufficient testing data to enable parameter estimation, a total of 92 nations spanning 4.92 billion people. These include all disease hotspots to date, with two notable exceptions, China and Brazil, for which reliable testing data are not available. The panel includes reported daily testing rates, reported COVID cases and deaths, and all‐cause mortality (where available), along with population, population density, age distribution, hospital capacity, and daily meteorological data.

The model is nonlinear and complex, and any estimation framework is unlikely to have clean analytical solutions or provable bounds on errors and biases. Therefore, in designing our estimation procedure we apply three criteria: (i) being conservative by incorporating uncertainties; (ii) avoiding overfitting; and (iii) enhancing the generalizability and robustness of estimates and projections. To do so we use a negative binomial likelihood function, which accommodates overdispersion and autocorrelation; we keep the number of estimated parameters to the minimum feasible, typically one or two for each mechanism; we utilize a hierarchical Bayesian framework (Gelman and Hill, 2006) to couple parameter estimates across different countries, reducing the risk of overfitting; and we use existing knowledge characterizing parameters and their expected similarity across countries to inform the priors for the magnitude of that coupling across countries. For example, the asymptomatic fraction of cases and other parameters representing biological processes should have low cross‐national variance, whereas parameters specifying risk perceptions and responses are expected to vary more widely (see S7 in the online supporting information for sensitivity analysis on priors). Compared to more common choices in similar estimation settings (e.g. Gaussian likelihood functions), these choices tend to widen the credible regions for our estimates and reduce the quality of the fit between model and data by having fewer parameters and imposing coupling among them. In return, the results may better capture uncertainties, are more informative about the underlying processes, and provide more reliable projections. For example, better fits to individual nations could be obtained by estimating every parameter separately for each nation, or including more free parameters, but doing so would increase the number of parameters to be estimated, would falsely assume that the experience of every nation is completely independent of all others, and could yield estimates that differ significantly across countries even for parameters, such as the asymptomatic fraction of cases, that should vary little across nations on an age‐adjusted basis.

The estimation method identifies both the most likely value and the credible regions for the unknown parameters, given the data on reported cases and deaths (and excess total mortality where available). To avoid overfitting, we do not use any time‐varying parameters in the estimation. The maximum likelihood method described above and in the online supporting information yields the estimated parameters. To quantify the uncertainties in parameters and projections, we use a Markov Chain Monte Carlo method designed for high‐dimensional parameter spaces (Vrugt et al., 2009); see S2 in the online supporting information for details.

Building confidence in the model

Estimating parameters for a complex model and assessing its ability to capture important real‐world processes are both critical and challenging. Before discussing results, we present four sets of analyses addressing these challenges and later report extensive sensitivity analyses to quantify various uncertainties. First, we compare model outputs to data. Figure 2a compares actual and simulated reported daily new cases and deaths for 18 larger countries using data through 22 December 2020. S5 and S6 in the online supporting information report the full sample. Over the full set of nations and full sample, Mean Absolute Errors Normalized by the mean of the actual data (MAEN) are 5.6 percent and 5.0 percent for cumulative infections and deaths, respectively, and less than 20 percent for 69 (75.0 percent) and 64 (69.6 percent) of the 92 nations, despite wide variation in the size and dynamics of national outbreaks, from those nearly quenched (New Zealand, Thailand), to those still growing (e.g. Latvia, Hungary), to those exhibiting multiple waves (e.g. Iran, Israel, United States). R2 exceeds 0.9 for 54 percent of 368 country‐specific time series and exceeds 0.5 for 86 percent. Aggregation of within‐nation heterogeneities reduces the quality of fit in a few countries. For example, we do not explicitly model outbreaks concentrated among subpopulations such as migrant workers (important in, e.g. Qatar, Singapore) or nursing homes (important in, e.g. Belgium, France). The coupling of parameters across countries also limits the fit for outliers. Moreover, the model does not include any time‐varying parameters such as Thanksgiving gatherings in the United States, school and university schedules, and other calendrical events that condition contacts. Nevertheless, 80 percent and 85 percent of official infection and death rates fall within the 95 percent uncertainty intervals from the beginning of the pandemic through the end of 2020.

Fig. 2.

Fig. 2

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Model projections vs. data. (a) Simulated (thick lines, Solid and Dashed for cases and deaths) vs. data (thin, dotted lines) for reported cases (top lines; right axis, thousands/day) and deaths (bottom lines; left axis; deaths/day) in countries with more than 45 million population and 300,000 confirmed cases by 22 December 2020 and testing data until at least September 2020. (b) Out‐of‐sample death predictions for the same countries comparing data (dashed line) against estimates (thick solid line; 95% CIs are thin solid lines) using data until 30 September 2020 (denoted by vertical line). Numbers on each graph show the fraction of actual data during the prediction period inside the 95% confidence interval. High frequency noise (e.g. reported cases in Mexico) is due to weekly cycles in testing data [Color figure can be viewed at wileyonlinelibrary.com]

Second, we assess out‐of‐sample accuracy. Figure 2b shows out‐of‐sample prediction performance for reported deaths after fitting the model to data through 30 September 2020, then projecting outcomes through 22 December 2020. Across all predictions, 70 percent and 72 percent of observations for infections and deaths, respectively, fall within the 95 percent prediction intervals over the last 82‐day period. Out‐of‐sample projections are limited by the fact that by 30 September 2020, the majority of countries had not experienced second waves or significant adherence fatigue, limiting the ability to estimate the magnitude of these behavioral feedbacks with the truncated sample. Despite these challenges, the model correctly predicts the existence of second waves in the majority of countries and in many cases correctly predicts the timing and magnitude as well (see S6 in the online supporting information for details and full results).

Third, we validated the estimation framework using synthetic data generated by simulating the model with known parameters and adding autocorrelated noise in infection rates and IFR. Our estimation procedure accurately identifies the vast majority of parameters in the synthetic dataset. The absolute error between the estimated and true values was significantly smaller than the estimated uncertainty (median error 21 percent of the 95 percent credible interval (CI), with 77 percent of the absolute errors less than half the 95 percent CI (see S3 in the online supporting information for details).

Finally, we compare model estimates of actual cumulative cases against available national‐level estimates from serological surveys. Few national seroprevalence studies include reliably representative samples. Nevertheless, using the SeroTracker project (Arora et al., 2020) we identified nine country‐level meta‐estimates for actual prevalence. Figure 3 compares those meta‐analytic estimates against official data from testing and model estimates. Seroprevalence and official counts vary by an order of magnitude or more. Model estimates are close for seven of the nine seroprevalence estimates and higher than surveys for Spain and Luxembourg. Note that seroprevalence data were not used in model specification or parameter estimation.

Fig. 3.

Fig. 3

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Comparison of cumulative percentage of cases based on official data (black diamond, left), seroprevalence estimates (blue circles with 95% CIs, middle), and model estimates (red squares with 95% CIs, right) for 9 countries at various dates [Color figure can be viewed at wileyonlinelibrary.com]

Results

Quantifying underreporting

We find COVID‐19 prevalence and deaths are widely underreported. Across the 92 nations, the estimated ratio of actual to reported cumulative cases through 22 December 2020 is 7.03, corresponding to 465 million undetected cases (95 percent CI 478–513 million). Underreporting varies substantially across nations (10th–90th percentile range 3.2–18; Figure 4a).

Fig. 4.

Fig. 4

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Underestimation of cases and deaths. (a) Ratio of (estimated) actual to reported cases (blue circles) and deaths (red squares) by country; log scale as of 22 December 2020. (b) Ratio of (estimated) actual to reported cases (solid line; left logarithmic axis) and total tests per day (dotted line; right axis) over time for the full sample (all 92 nations) [Color figure can be viewed at wileyonlinelibrary.com]

Underreporting is due in part to the large fraction of asymptomatic infections, estimated at 50 percent, consistent with other estimates (Oran and Topol, 2020). The mean interquartile range, MIQR, of the credible intervals in the national estimates is 1.3 percent. However, the estimated asymptomatic fraction varies little across nations (standard deviation, σ = 0.9 percent) and therefore cannot explain the large cross‐national variation in the ratio of estimated to reported cases (Figure 4a).

The extent of underestimation depends primarily on testing capacity and how it is utilized. If every person could be tested regularly, the estimated ratio of actual to reported cases would be approximately 1.43, given assumed test sensitivity of ≈70 percent (Fang et al., 2020; Wang et al., 2020). Testing capacity is limited, however. When testing capacity is small relative to the need, individuals presenting with COVID and COVID‐like symptoms are prioritized, along with at‐risk groups such as health‐care providers. Consequently, a larger proportion of those tested will be positive, but many infected individuals will go undetected, increasing the degree of underestimation, as seen in, for example, Mexico. Conversely, when testing capacity is high relative to the population, more of those infected will be identified, as seen in, for example, New Zealand. Over the full sample, increased testing has been continuously reducing the undercount ratio, though with diminishing returns (Figure 4b).

COVID‐19 deaths are also underreported (Figure 4a). We estimate 2.07 (2.04–2.32) million deaths by 22 December 2020 across the 92 countries, 1.44 times larger than reported. Results are consistent with some country‐specific estimates (Weinberger et al., 2020; Woolf et al., 2020). Underreporting is significantly less for deaths than cases because deaths are concentrated among severe cases who are more likely to have been tested, and post‐mortem testing corrects some of the undercount.

Trends and fluctuations in cases and mortality

National IFR estimates are reported in Figure 5a. IFR across the 92 nations through 22 December 2020 is 0.51 percent (CI: 0.47 percent–0.53 percent), with wide cross‐national variation, from 0.04 percent (CI: 0.03 percent–0.04 percent; Qatar) to 1.99 percent (CI: 1.44 percent–2.21 percent; France), a range similar to estimates across counties in the United States (Basu, 2020). These variations arise in the model from differences in age distribution (O'Driscoll et al., 2021; Wu and McGoogan, 2020) and the adequacy of health care. Consistent with prior estimates (Walker et al., 2020), we find hospitalization can reduce the age‐ and severity‐adjusted risk of death to 46 percent of the rate without treatment, with large cross‐national variation likely due to variations in treatment quality across nations (σ = 22 percent; MIQR: 7 percent). Simulated IFR varies endogenously over time, exhibiting fluctuations around an overall declining trend (Figure 5b). The fluctuations are due to variations in the adequacy of treatment capacity, with IFR rising when surging caseloads overtake hospital capacity. The peak in global IFR in spring 2020 arose as cases overwhelmed hospital capacity in several nations, including many European countries with older populations. Since then, many—but not all—countries show notable reductions in IFR, due to factors including (i) improvements in treatments and greater availability of ventilators and PPE; (ii) heterogeneity in cases as some in the highest‐risk populations were lost in the early waves; and (iii) heterogeneity in risk perceptions and responses as older, high‐risk individuals adhere more strongly to NPIs compared those who perceive less personal risk, resulting in a decline in the average age of new confirmed cases in many nations. Available data do not enable us to identify the contribution of these different processes, but their combined effect is estimated to reduce IFR by 32.5 percent (σ = 23.7 percent; MIQR = 10.3 percent) for every doubling in cumulative cases. Despite the overall decline in IFR, hospital capacity shortages caused by renewed waves of infection increase IFR above the trend (e.g. India in June and July).

Fig. 5.

Fig. 5

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Fatality rates. (a) Average estimated infection fatality rates (%) across countries as of 22 December 2020. (b) IFR trajectories over time for the full sample and selected nations [Color figure can be viewed at wileyonlinelibrary.com]

We also find significant heterogeneity across countries in the initial effective reproduction number, RE (median 2.73, IQR 2.16–3.66), reflecting differences in population density, social networks, and cultural practices (Figure S9 in the online supporting information provides details). We find a composite index of weather conditions by nation (Xu et al., 2020) strongly affects transmission, generally increasing the hazard rate of transmission with the onset of winter.

Importantly, the effective reproduction rate, RE, changes over time as people and policymakers respond to perceived risk (Pan et al., 2020). We find behavioral and policy responses to the perceived risk of death reduce transmission and RE with a mean lag of 38 days, though with substantial cross‐national variation (σ = 53.4; MIQR: 13.3). These responses are relaxed as perceived risk falls, though more slowly (mean lag 245 days; σ = 188; MIQR: 64).

The model endogenously captures the multiple waves observed across many countries through 22 December 2020 despite their different magnitudes and timing (Figure 2a). These rebounds are due to lags in the perception of and responses to the risk of COVID‐19. Initial reductions in transmission eventually lower deaths, leading to lower adherence to NPIs as perceived risk gradually falls, setting the stage for renewed outbreaks. Rebounds could also be triggered by changes in weather conditions, particularly the onset of colder weather. Rebound waves are larger where reductions in IFR are larger, because the decline in mortality erodes perceived risk and thus adherence to NPIs.

Testing and adherence fatigue shape pandemic trajectories

Testing, treatment, risk perceptions, individual behavior, and government policy all change through several important feedbacks. We find that those receiving a positive test notably reduce their infectious contacts (Mean: 17.3 percent of original contact rate; σ = 12.4 percent; MIQR: 9.9 percent). These reductions are especially important because symptomatic individuals, who are more likely to get tested, are estimated to be more infectious than asymptomatic ones (Mean asymptomatic infectiousness vs. symptomatic: 29.3 percent; σ = 0.26 percent; MIQR: 1.3 percent; consistent with (Li et al., 2020a).

Testing also regulates the reported rate of deaths, which drives perceived risk. More reported deaths increase perceived risk, triggering behavioral and policy responses that reduce transmission. Plentiful early testing results in high detection rates, greater perceived risk, and stronger responses, slowing transmission. Conversely, insufficient early testing increases underestimation, limiting perceived risk and allowing transmission to further outpace testing. Testing thus reduces future cases, allowing a larger fraction of severe cases to be hospitalized, saving lives and reducing IFR. The exponential nature of contagion means even small early differences can lead to notable differences in epidemic size (Pei et al., 2020), IFR, and total deaths.

Figure 6 (dashed line) shows the impact of enhanced early testing by comparing the estimated results to a counterfactual in which all countries test 0.1 percent of their population per day, a rate currently exceeded over the full sample (See Figure 3b). We assume enhanced testing begins when WHO declared COVID‐19 a pandemic (11 March 2020). We find enhanced testing would have reduced total cases from 496 million to 427 (CI: 404–445) million, with a reduction in deaths from 2.16 to 2.00 million (CI: 1.85–2.14).

Fig. 6.

Fig. 6

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Counterfactual Experiments. Most likely estimate (solid lines; 95% CIs in thin lines) of cumulative cases (a) and deaths (b) compared with counterfactuals for Scenario I, in which testing rises to 0.1% of population per day starting 11 March 2020 (dashed line), and Scenario II with no adherence fatigue (dotted line) [Color figure can be viewed at wileyonlinelibrary.com]

Importantly, we also find that extended periods of contact reduction, and the personal and economic hardship it causes, lead to adherence fatigue—a reduction in the impact of perceived risk on behaviors that reduce contacts, with an estimated average elasticity of 1.24 (σ = 1.07; MIQR: 0.19). A counter‐factual simulation (Figure 6, dotted line) shows that, absent adherence fatigue, total cases and deaths through 22 December 2020 would have been 47 percent and 45 percent lower, respectively, corresponding to 265 (252–278) million cases and 1.18 (1.14–1.22) million deaths.

Projections with endogenous responses to risk and vaccination

We explore four scenarios projecting the pandemic through 30 June 2021 (Figure 7): (I) Baseline: assumes country‐specific testing rates continue as of 22 December 2020 with country‐specific estimated parameters. (II) Responsive: countries become 20 percent more responsive to risk (details in supplement S5 in the online supporting information). Scenario II represents a modest increase in responsiveness given levels of perceived risk: on average, contact rates fall by 7 percent (σ = 17 percent) January–June 2021, comparable to the impact of enhanced mask use (Chu et al., 2020). (III) Vaccination: Assumes every country will be fully vaccinated by the end of 2021 using a constant vaccination rate. This timeline is optimistic for developing countries; furthermore, the vaccine is assumed to be perfectly protective, to face no resistance, and to be administered with priority to high‐risk individuals. (IV) Enhanced responsiveness and vaccination, combining Scenarios II and III.

Fig. 7.

Fig. 7

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Projections across four scenarios. Estimated true cumulative cases (a) and deaths (b) across 92 countries until 30 June 2021 under Scenarios I (No vaccine, same responsiveness; solid line), II (20% more responsive; dashed), III (vaccinating population over 2021; dotted), and IV (responsiveness and vaccination, II + III; dash‐dot). (c) Median (95% CI) estimated true cumulative cases (blue circles; bottom axis) and deaths (red squares; top axis) as % of population, projected by the end of June 2021 under Scenario I (Logarithmic Scale). D) Median (95% CI) reductions in cumulative cases in Scenario II (20% more responsive) compared with Scenario I (in % of population) for top 20 countries (blue circles; bottom scale); red squares (top scale) represent average change in contacts compared to Scenario I for January–June 2021 period [Color figure can be viewed at wileyonlinelibrary.com]

Figure 7 contrasts the results. Scenario I yields 900 million cumulative cases by 30 June 2021. Most cases are concentrated in a few countries, with the United States (115 million median cumulative cases; 95 percent CI 108–122 million), Mexico (96 million; 82–105), India (60 million; 57–65), and Iran (40 million; 35–44) suffering the largest burdens. Figure 7a and 7b show estimated cumulative actual cases and deaths by 30 June 2021 (Supplement S5 in the online supporting information provides Scenario I projections over time). The responsive scenario (II) reduces cases (Figure 7a) and deaths (Figure 7b) by 14 percent (CI: 12 percent–16 percent) and 12 percent (CI: 7 percent–17 percent). The largest reductions arise in countries with large populations and that are estimated to have a large potential for new waves (Figure 7d), including India (12.3 million fewer cases), the United States (9.51 million), Mexico (7.48 million), and Italy (6.3 million) among others. The vaccination scenario brings down cases and deaths by 2.7 percent and 9.1 percent, to 875 million (CI: 851–898) and 3.68 million (CI: 3.45–3.90) respectively, less than the impact of greater responsiveness to risk. Combining the two provides additional benefit but with decreasing returns for cases (16 percent; CI: 13 percent–18 percent). The relatively small impact of vaccination through mid‐2021 is due to two factors. First, by mid‐2021 we assume approximately half the population is immunized (but with a vaccine assumed to be 100 percent protective). Second, behavioral feedbacks undermine the impact of immunization: to the extent immunization reduces deaths and perceived risk, adherence to NPIs erodes, leading to more new cases.

These scenarios should not be interpreted as predictions: changes in testing, vaccination, individual behavior, and government responses to risk not accounted for in the model are possible, perhaps likely, in the coming months. The general finding is the significant sensitivity of outcomes to behavioral and policy responses to risk. Stronger responses to perceived risk would significantly reduce future cases. Lax responses and greater adherence fatigue would lead to larger rebound outbreaks. Moreover, responsiveness comes at a low cost in terms of cumulative reductions in contacts, a proxy for the reductions in travel, dining, shopping, and other activities that lead to unemployment and harm businesses. We next explore this important finding in more depth.

A global dilemma: Similar behaviors, different outcomes

Across scenarios, a few nations are projected to experience significant growth in incidence before vaccines become widely available, but most are able to stabilize their epidemics through NPIs, albeit with occasional new outbreak waves. Endogenous risk perceptions create an important balancing (negative) feedback that leads most countries to converge to an effective reproduction number RE ≈ 1: RE > 1 leads to rapid growth in cases and deaths, increasing perceived risk and renewed use of NPIs that bring RE down; RE < 1 lowers cases and deaths, leading to the erosion of perceived risk and reduced adherence to NPIs that then lead to more cases, raising RE back toward 1.

Critically, however, RE fluctuates around 1 at very different quasi‐steady‐state infection and fatality rates across nations. Recall that RE ≈ 1 means that, on average, infected individuals infect one new case before they are removed from the infectious pool by recovery or death. That balance can be achieved at a high or low level of prevalence. Those nations with high responsiveness to risk settle at RE ≈ 1 with low prevalence and death rates, while those with lower responsiveness to perceived risk achieve that balance only when cases and deaths rise high enough to drive RE down toward 1. The large cross‐national variation in the estimated behavioral responses to risk lead to death rates more than two orders of magnitude higher in nations with weak responsiveness and greater adherence fatigue compared to those with sustained strong responses (Figure 8). Over the 6 months preceding 22 December 2020, average estimated RE values have approximately converged to ≈1 (mean = 1.19, σ = 0.21), indicating comparable levels of contact reduction across nations. In contrast, deaths per million over the same period show a 10‐90th percentile range of 0.033 to 3.7.

Fig. 8.

Fig. 8

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Effective reproduction number RE vs. estimated true daily deaths per million in each nation, averaged over the 6 months ending 22 December 2020, with a few countries highlighted. Inset: Oscillation in death rate vs. RE in the United States caused by lags in the perception of and behavioral responses to the risk of death and lags between behavioral responses that reduce transmission and subsequent deaths. Data are weekly averages over the 6‐month period ending 22 December 2020 (darker circles are the more recent weeks) [Color figure can be viewed at wileyonlinelibrary.com]

Summary of main results

We find prevalence and mortality are substantially underreported by official data: across the 92 nations for which data are available, estimated cumulative COVID cases are approximately 7 times greater than official reports, with underreporting across nations spanning three orders of magnitude. The magnitude of underreporting has declined over time as testing has increased. Nevertheless, and despite the large magnitude of underreporting, estimated cumulative cases through the end of 2020 constitute small fractions of the populations, so herd immunity remains distant in nearly all nations (see S5 in the online supporting information).

We find deaths are 1.44 times larger than official reports. The overall infection fatality rate to date is ≈0.51 percent, consistent with growing evidence (Russell et al., 2020; Verity et al., 2020). We also find substantial cross‐national variation in IFR. The variation arises from differences in population age structure, and in the burden of severe cases relative to hospital capacity, highlighting the importance of limiting case growth. We also find that IFR has, on average, declined substantially since the onset of the pandemic. Despite the overall declining trend in IFR, mortality surges when renewed outbreaks overwhelm treatment capacity.

We estimate that approximately half of infections are asymptomatic, consistent with estimates from smaller samples (Gudbjartsson et al., 2020; Lavezzo et al., 2020; Mizumoto et al., 2020), with asymptomatic individuals estimated to be about one‐third as infective as symptomatic patients.

The wide variation across nations arises endogenously and without major differences in biological parameters. First, inadequate early testing in some countries has led to greater underestimation of prevalence, and thus later and weaker responses, causing faster epidemic growth, further outstripping testing and treatment capacity in a self‐reinforcing (positive) feedback. Second, the growth rate, timing, and size of outbreak waves depend strongly on the magnitude of behavioral and policy responses to perceived risk, and the lags in forming and eroding those perceptions, which we find vary notably across countries and determine the gain and phase lag in the negative feedbacks that lead to outbreak waves. These feedbacks amplify minor differences in testing and responsiveness to perceived risk, generating significant heterogeneity in cases and deaths despite convergence of RE to ≈1 across nations. Projections through 30 June 2021 show that modest reductions in transmission through NPIs can lead to large reductions in cumulative cases and deaths in many countries, even absent effective vaccines. In contrast, the early impact of vaccines is modest, because risk‐driven response leads to relaxation of NPIs and keeps cases and deaths high until a large fraction of the population is vaccinated.

Due to the rapidly evolving nature of the pandemic, behavior and policies, and vaccine availability and uptake, we have developed and will regularly recalibrate and update an online simulator enabling users to explore alternative vaccination and responsiveness scenarios over the coming months. The simulator is freely available at https://exchange.iseesystems.com/public/mitsdl/covidglobal/.

Robustness and boundary conditions

We conducted several analyses to assess the robustness of the results. (i) We ensured MCMC chains had converged (100 percent of Gelman‐Rubin convergence statistics were below 1.2 percent and 97 percent under 1.1). (ii) We varied the priors for cross‐country parameter variances to 4 and 0.25 times the base values, resulting in <3 percent change across historical measures, though scenario results for a few countries are more sensitive (S7 in the online supporting information provides details). (iii) To see if any country disproportionately affects the results, we repeated the analysis using three different samples, excluding the top 5 countries by (a) estimated cases, (b) reported cases, and (c) population. Only India and the United States appear in all three sets. Average outcomes across the remaining countries changed less than 1 percent (see S7). (iv) We assessed the sensitivity of results to the parameters estimated from prior research by calculating the elasticities of key outcomes to parametric assumptions. Across metrics most elasticities are less than approximately 0.5. The largest is for the impact of test sensitivity; greater sensitivity reduces underestimation.

These robustness tests do not address a few limitations that temper the interpretation of the results. Some arise from limits on data availability across nations. For example, we are unable to include China and Brazil because they do not report adequate testing data. Other useful data, such as excess all‐cause mortality, are not available for some nations. Some limitations arise from the computational burden of estimation: although we limit the number of parameters to be estimated to avoid overfitting, the analyses we report, including estimation of credible intervals via MCMC and sensitivity runs, take 2 weeks of continuous parallelized computation on a 48‐core server.

Other limitations are due to inherent uncertainties. First, we do not represent within‐nation heterogeneity that may affect the course of the epidemic. These variations likely matter especially in large, diverse nations (e.g. United States), including differences in transmission risk between rural and urban areas, differences in adherence to NPIs based on political views, and especially differences in the ability of individuals and households to limit transmission risk or receive treatment based on socioeconomic status, race and ethnicity, and other factors affecting social justice (Britton et al., 2020; Laxminarayan et al., 2020; Painter and Qiu, 2020). Second, we model IFR as depending on age distribution and hospitalization, but we do not explicitly model how well different nations are able to protect vulnerable subpopulations (the effect is aggregated into the overall impact of cumulative cases on IFR). Third, the model aggregates behavioral and government policy responses and does not represent the effectiveness of specific NPIs. Fourth, due to the computational burden it would impose, we did not use filtering (e.g. Kalman or particle) or state‐resetting methods to account for time‐varying determinants of transmission (e.g. the impact of holidays). Fifth, we do not account for emergence of new variants of the virus that may alter transmissibility or IFR. Finally, without explicit travel networks our results may underestimate the risk of reintroduction of the disease where it has been contained.

Discussion

The study yields conceptual, methodological, and policy implications. Conceptually, the model we develop integrates the biological and social factors conditioning transmission captured in typical SEIR models with a range of behavioral factors, some of which are novel in epidemiological modeling. We include endogenous test allocation and hospitalization based on symptom severity relative to capacity; endogenous risk perceptions and responses, including adherence fatigue; and learning and other factors that cause the infection fatality rate to decline on average over time. While these mechanisms are intuitively plausible, empirical estimation of each feedback loop is indispensable for: selecting which mechanisms to include in the model and which to leave out; inferring the actual toll of COVID‐19; explaining the multiple waves of infection; offering reliable long‐term projections; and assessing the likely impact of policies. Quantification also enables us to explain the orders of magnitude variations in outcomes across nations without resorting to exogenous time‐varying parameters or ad hoc nation‐specific fixed effects and with parameters characterizing COVID‐19 that are consistent with prior research. Endogenous inclusion of behavioral feedbacks could significantly enhance many existing epidemiological models.

Two methodological contributions may inform future work. Our modeling framework captures heterogeneity in disease severity, which conditions test and treatment‐capacity allocation, without the need for explicit disaggregation into subpopulations or to the individual level. Our approach makes estimation computationally feasible and provides a consistent method to model the allocation of testing, hospital capacity, and the impact of acuity on mortality. The method can be applied to other settings where the perfect mixing assumption of traditional compartment models is inappropriate due to within‐compartment heterogeneity, especially if that heterogeneity influences transition rates. Second, our hierarchical Bayesian estimation framework enables us to use the data from all nations to inform the estimated parameters for each. As expected, parameters capturing biological attributes of SARS‐CoV‐2 and COVID‐19, such as the asymptomatic fraction of cases, have far less cross‐national variation than parameters characterizing risk perceptions and behavioral responses to the threat. The estimation method developed here can be applied to other levels of analysis for COVID‐19, such as states in the United States, and more broadly to any issue where the parameters of dynamic models must be estimated in the presence of heterogeneity in feedback strengths across multiple units such as countries, states, firms, or individuals. Such applications enable researchers to move from models of single cases to generalized testing of dynamic models across larger, diverse samples.

A counterintuitive finding provides important policy implications. After controlling the initial peak, most countries have settled into a quasi‐steady state with the effective reproduction number RE fluctuating around one, but with caseloads and death rates varying by two orders of magnitude. This result arises directly from the endogenous inclusion of behavioral feedbacks: lower mortality erodes adherence to NPIs, raising RE and leading to rebound outbreaks, which then leads to renewed contact reductions that bring RE back down. However, the estimated responsiveness to risk varies widely across nations. Those with strong responses bring RE to 1 with few cases and deaths, while those with weak responses require much larger death rates to drive RE toward 1. Consequently, different nations pay widely different prices in lost lives. Although we do not carry out a detailed analysis of the economic costs of different NPIs, the behavioral and policy changes that reduce contacts enough to bring RE to 1 are a rough measure of the self‐isolation, distancing, and other actions that reduce economic activity and employment by cutting travel, dining, shopping, and other activities sustaining commerce and industry. Critically, vaccine introduction does not change this result: vaccines save lives, triggering the relaxation of NPIs. The initial reduction in death rates will therefore be slower than expected based purely on the protection offered by vaccines. Thus, by increasing responsiveness to risks, communities and nations can bring down death rates at little additional economic cost, a finding consistent with analysis of the 1918 influenza pandemic (Correia et al., 2020). Although contrary to the intuitions of many policymakers, the results suggest no strong trade‐off between saving lives and saving the economy. Stronger responsiveness to risk and adherence to NPIs offer an opportunity to save lives at low costs even as vaccines are approved and deployed.

Author contributions

HR designed the study; HR and TYL collected the data; HR and TYL conducted the analysis; HR, JS, TYL revised the model and prepared the manuscript.

Competing interests

Authors declare no competing interests.

Data and materials availability

Supplementary materials provide model documentation and full estimates. All data, code, and simulation models are available at: https://github.com/tseyanglim/CovidGlobal

Supporting information

Appendix S1 Supporting Information.

Click here for additional data file. (4.7MB, pdf)

Acknowledgements

We thank Tom Fiddaman and Ventana Systems for access to the Vensim parallel simulation engine; Stephen Eubank, Navid Ghaffarzadegan, and Madhav Marathe for thoughtful comments on an earlier draft; X.H. Chan and K. Jani for sharing clinical insights; and Nezam Jazayeri for assistance with graphs.

Biographies

Hazhir Rahmandad is an Associate Professor of System Dynamics at the MIT Sloan School of Management. Hazhir's research applies dynamic modeling to complex organizational and public health problems, from strategy to pandemics. His methodological work contributes to parameter estimation methods for dynamic models and aggregation of prior statistical findings.

Tse Yang Lim is a PhD candidate at the MIT Sloan School of Management. John Sterman is the Jay W. Forrester Professor of Management at the MIT Sloan School of Management and Director of the MIT System Dynamics Group.

Accepted by Yaman Barlas

REFERENCES

  1. Acemoglu D, Chernozhukov V, Werning I, Whinston MD (2020) Optimal targeted lockdowns in a multi‐group SIR model. NBER Working Paper 27102.
  2. Arora RK, Joseph A, Van Wyk J, Rocco S, Atmaja A, May E, Yan T et al. 2020. SeroTracker: A global SARS‐CoV‐2 seroprevalence dashboard. Lancet Infect Dis. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Basu A. 2020. Estimating the infection fatality rate among symptomatic COVID‐19 cases in the United States. Health Aff (Millwood), 39(7): 1229–1236. [DOI] [PubMed] [Google Scholar]
  4. Britton T, Ball F, Trapman P. 2020. A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS‐CoV‐2. Science 369(6505): 846–849. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Chinazzi M, Davis JT, Ajelli M, Gioannini C, Litvinova M, Merler S, Pastore y Piontti A, et al. (2020) The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID‐19) outbreak. Science, 368(6489): 395–400. 10.1126/science.aba9757. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Chu DK, Akl EA, Duda S, Solo K, Yaacoub S, Schunemann HJ, authors C‐SURGEs . 2020. Physical distancing, face masks, and eye protection to prevent person‐to‐person transmission of SARS‐CoV‐2 and COVID‐19: A systematic review and meta‐analysis. Lancet 395(10242): 1973–1987. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Correia S, Luck S, Verner E (2020) Pandemics depress the economy, public health interventions do not: Evidence from the 1918 flu. SSRN.
  8. Fang Y, Zhang H, Xie J, Lin M, Ying L, Pang P, Ji W. 2020. Sensitivity of chest CT for COVID‐19: Comparison to RT‐PCR. Radiology 296(2): E115–E117. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Farboodi M, Jarosch G, Shimer R (2020) Internal and external effects of social distancing in a pandemic. Report
  10. Flaxman S, Mishra S, Gandy A, Unwin HJT, Mellan TA, Coupland H, Whittaker C et al. 2020. Estimating the effects of non‐pharmaceutical interventions on COVID‐19 in Europe. Nature 584(7820): 257–261. [DOI] [PubMed] [Google Scholar]
  11. Gatto M, Bertuzzo E, Mari L, Miccoli S, Carraro L, Casagrandi R, Rinaldo A. 2020. Spread and dynamics of the COVID‐19 epidemic in Italy: Effects of emergency containment measures. Proceedings of the National Academy of Sciences of the United States of America 117(19): 10484–10491. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Gelman A, Hill J. 2006. Data analysis using regression and multilevel/hierarchical models. Cambridge University Press: Cambridge, England. [Google Scholar]
  13. Ghaffarzadegan N, Rahmandad H. 2020. Simulation‐based estimation of the early spread of COVID‐19 in Iran: Actual versus confirmed cases. System Dynamics Review 36(1): 101–129. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Guan WJ, Ni ZY, Hu Y, Liang WH, Ou CQ, He JX, Liu L et al. 2020. Clinical characteristics of coronavirus disease 2019 in China. The New England Journal of Medicine 382(18): 1708–1720. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Gudbjartsson DF, Helgason A, Jonsson H, Magnusson OT, Melsted P, Norddahl GL, Saemundsdottir J, Sigurdsson A, Sulem P, Agustsdottir AB. 2020. Spread of SARS‐CoV‐2 in the Icelandic population. New England Journal of Medicine 382(24): 2302–2315. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Hao X, Cheng S, Wu D, Wu T, Lin X, Wang C. 2020. Reconstruction of the full transmission dynamics of COVID‐19 in Wuhan. Nature 584(7821): 420–424. [DOI] [PubMed] [Google Scholar]
  17. Hsiang S, Allen D, Annan‐Phan S, Bell K, Bolliger I, Chong T, Druckenmiller H et al. 2020. The effect of large‐scale anti‐contagion policies on the COVID‐19 pandemic. Nature 584(7820): 262–267. [DOI] [PubMed] [Google Scholar]
  18. Kissler SM, Tedijanto C, Goldstein E, Grad YH, Lipsitch M. 2020. Projecting the transmission dynamics of SARS‐CoV‐2 through the postpandemic period. Science 368(6493): 860–868. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Lavezzo E, Franchin E, Ciavarella C, Cuomo‐Dannenburg G, Barzon L, Del Vecchio C, Rossi L, Manganelli R, Loregian A, Navarin N. 2020. Suppression of a SARS‐CoV‐2 outbreak in the Italian municipality of Vo. Nature 584(7821): 425–429. [DOI] [PubMed] [Google Scholar]
  20. Laxminarayan R, Wahl B, Dudala SR, Gopal K, Mohan BC, Neelima S, Jawahar Reddy KS, Radhakrishnan J, Lewnard JA. 2020. Epidemiology and transmission dynamics of COVID‐19 in two Indian states. Science 370(6517): 691–697. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Li R, Pei S, Chen B, Song Y, Zhang T, Yang W, Shaman J. 2020a. Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS‐CoV2). Science 368(6490): 489–493. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Li Y, Yao L, Li J, Chen L, Song Y, Cai Z, Yang C. 2020b. Stability issues of RT‐PCR testing of SARS‐CoV‐2 for hospitalized patients clinically diagnosed with COVID‐19. Journal of Medical Virology 92(7): 903–908. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Linton NM, Kobayashi T, Yang Y, Hayashi K, Akhmetzhanov AR, Jung SM, Yuan B, Kinoshita R, Nishiura H. 2020. Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: A statistical analysis of publicly available case data. Journal of Clinical Medicine 9(2): 538–546. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Lopez L, Rodo X. 2020. The end of social confinement and COVID‐19 re‐emergence risk. Nature Human Behaviour 4(7): 746–755. [DOI] [PubMed] [Google Scholar]
  25. Mizumoto K, Kagaya K, Zarebski A, Chowell G. 2020. Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID‐19) cases on board the Diamond Princess cruise ship, Yokohama, Japan, 2020. Eurosurveillance, 25(10). 10.2807/1560-7917.es.2020.25.10.2000180. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Moghadas SM, Fitzpatrick MC, Sah P, Pandey A, Shoukat A, Singer BH, Galvani AP. 2020a. The implications of silent transmission for the control of COVID‐19 outbreaks. Proceedings of the National Academy of Sciences of the United States of America 117(30): 17513–17515. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Moghadas SM, Shoukat A, Fitzpatrick MC, Wells CR, Sah P, Pandey A, Sachs JD et al. 2020b. Projecting hospital utilization during the COVID‐19 outbreaks in the United States. Proceedings of the National Academy of Sciences of the United States of America 117(16): 9122–9126. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. O'Driscoll M, Dos Santos GR, Wang L, Cummings DAT, Azman AS, Paireau J, Fontanet A, Cauchemez S, Salje H. 2021. Age‐specific mortality and immunity patterns of SARS‐CoV‐2. Nature 590(7844): 140–145. [DOI] [PubMed] [Google Scholar]
  29. Onder G, Rezza G, Brusaferro S. 2020. Case‐fatality rate and characteristics of patients dying in relation to COVID‐19 in Italy. JAMA 323(18): 1775–1776. [DOI] [PubMed] [Google Scholar]
  30. Oran DP, Topol EJ. 2020. Prevalence of asymptomatic SARS‐CoV‐2 infection: A narrative review. Annals of Internal Medicine 173(5): 362–267. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Painter M, Qiu T (2020) Political beliefs affect compliance with covid‐19 social distancing orders. SSRN 3569098.
  32. Pan A, Liu L, Wang C, Guo H, Hao X, Wang Q, Huang J et al. 2020. Association of Public Health Interventions with the epidemiology of the COVID‐19 outbreak in Wuhan, China. JAMA 323(19): 1915–1923. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Pei S, Kandula S, Shaman J. 2020. Differential effects of intervention timing on COVID‐19 spread in the United States. Science Advances 6(49): eabd6370. [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. Rahmandad H, Hu K. 2010. Modeling the rework cycle: Capturing multiple defects per task. System Dynamics Review 26(4): 291–315. [Google Scholar]
  35. Rahmandad H, Sterman J. 2008. Heterogeneity and network structure in the dynamics of diffusion: Comparing agent‐based and differential equation models. Management Science 54(5): 998–1014. [Google Scholar]
  36. Roser M, Ritchie H, Ortiz‐Ospina E, Hasell J. 2020. Coronavirus Pandemic (COVID‐19). Our World in Data. https://ourworldindata.org/coronavirus-testing.
  37. Ruktanonchai NW, Floyd JR, Lai S, Ruktanonchai CW, Sadilek A, Rente‐Lourenco P, Ben X et al. 2020. Assessing the impact of coordinated COVID‐19 exit strategies across Europe. Science 369(6510): 1465–1470. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Russell TW, Hellewell J, Jarvis CI, van Zandvoort K, Abbott S, Ratnayake R, Flasche S, Eggo RM, Edmunds WJ, Kucharski AJ. 2020. Estimating the infection and case fatality ratio for coronavirus disease (COVID‐19) using age‐adjusted data from the outbreak on the Diamond Princess cruise ship, February 2020. Eurosurveillance, 25(12). 10.2807/1560-7917.es.2020.25.12.2000256. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. Salje H, Tran Kiem C, Lefrancq N, Courtejoie N, Bosetti P, Paireau J, Andronico A et al. 2020. Estimating the burden of SARS‐CoV‐2 in France. Science 369(6500): 208–211. [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. Sterman J. 2001. Instructor's manual for business dynamics: systems thinking and modeling for a complex world. Irwin/McGraw‐Hill: New York, NY. [Google Scholar]
  41. Struben J. 2020. The coronavirus disease (COVID‐19) pandemic: Simulation‐based assessment of outbreak responses and postpeak strategies. System Dynamics Review, 36(3): 247–293. [DOI] [PMC free article] [PubMed] [Google Scholar]
  42. Sutton D, Fuchs K, D'Alton M, Goffman D. 2020. Universal screening for SARS‐CoV‐2 in women admitted for delivery. The New England Journal of Medicine 382(22): 2163–2164. [DOI] [PMC free article] [PubMed] [Google Scholar]
  43. Verity R, Okell LC, Dorigatti I, Winskill P, Whittaker C, Imai N, Cuomo‐Dannenburg G, Thompson H, Walker PG, Fu H. 2020. Estimates of the severity of coronavirus disease 2019: A model‐based analysis. The Lancet Infectious Diseases 20(6): 669–677. [DOI] [PMC free article] [PubMed] [Google Scholar]
  44. Vrugt JA, Ter Braak C, Diks C, Robinson BA, Hyman JM, Higdon D. 2009. Accelerating Markov chain Monte Carlo simulation by differential evolution with self‐adaptive randomized subspace sampling. International Journal of Nonlinear Sciences and Numerical Simulation 10(3): 273–290. [Google Scholar]
  45. Walker PGT, Whittaker C, Watson OJ, Baguelin M, Winskill P, Hamlet A, Djafaara BA et al. 2020. The impact of COVID‐19 and strategies for mitigation and suppression in low‐ and middle‐income countries. Science 369(6502): 413–422. [DOI] [PMC free article] [PubMed] [Google Scholar]
  46. Wang W, Xu Y, Gao R, Lu R, Han K, Wu G, Tan W. 2020. Detection of SARS‐CoV‐2 in different types of clinical specimens. JAMA 323(18): 1843–1844. [DOI] [PMC free article] [PubMed] [Google Scholar]
  47. Weinberger DM, Chen J, Cohen T, Crawford FW, Mostashari F, Olson D, Pitzer VE et al. 2020. Estimation of excess deaths associated with the COVID‐19 pandemic in the United States, march to May 2020. JAMA Internal Medicine 180(10): 1336–1344. [DOI] [PMC free article] [PubMed] [Google Scholar]
  48. Woolf SH, Chapman DA, Sabo RT, Weinberger DM, Hill L. 2020. Excess deaths from COVID‐19 and other causes, march‐April 2020. JAMA 324(5): 510–513. [DOI] [PMC free article] [PubMed] [Google Scholar]
  49. Wu JT, Leung K, Leung GM. 2020. Nowcasting and forecasting the potential domestic and international spread of the 2019‐nCoV outbreak originating in Wuhan, China: A modelling study. Lancet 395(10225): 689–697. [DOI] [PMC free article] [PubMed] [Google Scholar]
  50. Wu Z, McGoogan JM. 2020. Characteristics of and important lessons from the coronavirus disease 2019 (COVID‐19) outbreak in China: Summary of a report of 72 314 cases from the Chinese Center for Disease Control and Prevention. JAMA 323(13): 1239–1242. [DOI] [PubMed] [Google Scholar]
  51. Xu R, Rahmandad H, Gupta M, DiGennaro C, Ghaffarzadegan N, Amini H, Jalali MS (2020) Weather Conditions and COVID‐19 Transmission: Estimates and Projections. medRxiv.

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Supplementary Materials

Appendix S1 Supporting Information.

Click here for additional data file. (4.7MB, pdf)

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