key: cord-1055864-r044iimd
authors: Goldsztejn, Uri; Schwartzman, David; Nehorai, Arye
title: Public policy and economic dynamics of COVID-19 spread: a mathematical modeling study
date: 2020-04-17
journal: nan
DOI: 10.1101/2020.04.13.20062802
sha: 45c20d510f70aff81b88e8c9d32f7f6997c27653
doc_id: 1055864
cord_uid: r044iimd

Summary Background: With the COVID-19 pandemic infecting millions of people, largescale quarantine policies have been enacted across the globe. Understanding how to maximize the effectiveness of these policies while mitigating economic damage is essential. We develop a mathematical model with different levels of population health and economic risk to assess the impact of quarantine measures on deaths, hospitalizations, and economic output. Methods: We combine an extended SEIR model that has multiple levels of health risk and economic vulnerability with disease parameters for the COVID19 pandemic to study the effects of quarantine policies. We examine the dynamics of infectious disease transmission and its economic impact for one year. We populate our model with a baseline of 95.6 % of high-risk people and 85.6 % of low-risk people in quarantine. We use our model to simulate leaving the current quarantine restrictions in place indefinitely. We then assess a policy where quarantine restrictions for lower-risk groups are gradually relaxed. Finally, we simulate relaxing quarantine restrictions more quickly. To compare outbreak outcomes under the same quarantine policies using different disease parameters, we also perform a sensitivity analysis on the contagiousness of infected people, the strictness of social isolation measures, and the amount that public policymakers value the economy in setting quarantine restrictions. Findings: We first consider a baseline scenario with constant quarantine level, finding that in a population of 330,000,000 million, there are 32,023 deaths among those under 60 and 174,682 deaths among those over 60, there is a peak of 189,136 hospitalizations, and the economy relative to the beginning of the quarantine state is 1.4 % smaller. In the scenario where higher-risk people are strictly quarantined, and for others the quarantine is slowly relaxed, there are 63,776 deaths among those under 60, 85,880 deaths among those over 60, a peak of 341,321 hospitalizations, and the economy relative to the beginning of the quarantine state is 6% larger. In the scenario where quarantine is more quickly lifted, there are 25,720 deaths among those under 60, 214,718 deaths among those over 60, a peak of 341,321 hospitalizations, and economic output relative to the beginning of the quarantine state is 4.5 % smaller. Interpretation: Strict restrictions on high-risk patients and a gradual lifting of quarantine for low-risk patients results in a limited number of deaths and lesser economic damage. We recommend this kind of strategy, combined with policies lowering the contagiousness of the disease and making quarantine more tolerable and economically viable for individuals.

Background With the COVID-19 pandemic infecting millions of people, largescale quarantine policies have been enacted across the globe. Understanding how to maximize the effectiveness of these policies while mitigating economic damage is essential. We develop a mathematical model to assess the impact of quarantine measures on deaths, hospitalizations, and economic output.

We expand the SEIR model to simulate the spread of COVID-19. We incorporate the effects of quarantine policies and segment the population based on health risk and economic vulnerability. Using our model, we simulate a baseline scenario that leaves the current quarantine restrictions in place. We then simulate a rapid relaxation of the quarantine restrictions for non-seniors shortly after the outbreak is contained. Finally, we gradually relax the quarantine restrictions for the young individuals, while maintaining extremely strict restrictions for seniors.

In the baseline scenario, we find that over 76 weeks in a population of 330 million, there are 32,131 deaths among those under 60 and 175,775 deaths among those over 60, there is a peak of 189,136 hospitalizations, and the economy shrinks by 0.56%. In the scenario where quarantine is quickly lifted a second outbreak takes place. Overall, there are 242,869 deaths among those under 60, 545,946 deaths among those over 60, a peak of 4,363,654 hospitalizations, and the economy expands by 5.2%. In the scenario where quarantine policies are progressively relaxed for the young individuals, there are 33,750 deaths among those under 60, 187,993 deaths among those over 60, a peak of 189,136 hospitalizations, and the economy expands by 4%.

Interpretation Strict restrictions on seniors combined with very gradual lifting of quarantine for the general population results in a limited number of deaths and lesser economic damage. We recommend this strategy and lowering contagiousness to control the pandemic while making quarantine economically viable.

Funding No funding to declare.

As of April 10th, 2020, the number of confirmed cases of coronavirus disease 2019 worldwide stands at over 1,690,000, and at least 102,500 individuals have died from this disease since the first reports of a pneumonia of unknown etiology in December, 2019. (1; 2; 3) As COVID-19 expands to new territories, after a latent phase with few new reported infections daily, the virus spreads rapidly and local outbreaks begin. The virus's containment is complicated by its high transmissibility, relatively low case fatality rate, and lengthy asymptomatic infectious period. (4) Currently, the most successful measure to prevent the rapid expansion of COVID-19 has been to restrain travels and physical interactions between individuals, a policy referred to as social distancing. (5; 6) Extreme social distancing has devastating consequences for the global economy. Quarantine policies may be an effective short-term measure, but indefinite quarantine until a vaccine becomes available would prevent billions of individuals worldwide from receiving an income, and could particularly devastate countries with weaker economies. This economic harm could increase mortality given the correlation between mortality and income, (7) especially for children. (8) Computational models that simulate the expansion of the disease can guide public policy makers in mitigating the detrimental outcomes of the outbreak (9) . Existing epidemiological models estimate the number of unknown infected individuals, forecast the number of patients requiring intensive care treatment, predict the death toll, and evaluate the outcomes of different policies. In compartmental modeling, different disease stages are modeled as compartments, and transitions between compartments are modeled by a system of differential equations. (10) Compartmental models provide useful insight into the mechanisms governing the spread of the disease and help evaluate public policies. (11; 12; 13) Some papers focus on how quarantine restrictions affect disease spread. (6; 13; 14; 15; 16) Time series approaches use available data to statistically forecast the evolution of the disease. (17; 18; 19) While times series models have precise results, they do not illuminate the dynamics of the disease spread.

To accurately predict the spread of disease and evaluate consequences beyond the infectious disease itself, models must take into account how mitigation measures might impact the economy. (20; 21; 22) Existing epidemiological models usually do not integrate the economic aspects of public policy aimed at controlling the spread of the disease. To the best of our knowledge, no models incorporating public policy responses take into account both the distinctions in risk types within the population and the differential economic impacts of quarantine policies.

We propose an ad hoc compartmental model for the spread of COVID-19 and 3 the economic effects of quarantine restrictions. Our model includes, among other compartments, a large group of asymptomatic infected individuals and compartments that represent quarantined individuals. We separate the population into four groups in our simulations, according to age and the economic impact of remaining in quarantine for an extended period of time. Upon infection, senior individuals present much larger co-morbidity and mortality rates than younger individuals. Also, generalized country-wide lockdowns completely suppress the productivity of some workers while having minimal implications for others. By modeling our population as having different risk groups, economic risks from quarantine, and productivity levels, we can make more specific predictions, and are able to provide more targeted policy recommendations than existing methods.

Evidence before this study

We searched PubMed, medRxiv, bioRxiv, arXiv, SSRN, Research Square, Virological, and Wellcome Open Research for peer-reviewed articles, preprints, and research reports on models of coronavirus disease 2019 (COVID-19), using the search terms "coronavirus", "2019-nCoV", "targeted quarantine", and similar terms up to April 5, 2020. Other studies, using a variety of data sources and statistical techniques, produce estimates of the hospitalized ratio, the case fatality rate, the length of the pre-symptomatic period, the proportion of hospitalized individuals, the length of hospitalization, and other important parameters. We use the available literature for our own estimates of these parameters.

Our primary contribution lies in modeling public policy as taking into account differential age-adjusted health risk and economic risk. Given that the state of the economy has important health effects and that public policy needs to incorporate economic effects and how citizens perceive lockdown restrictions, we model public policies that balance the number of deaths and damage to economic productivity. In addition, we model improvements in medical knowledge about a recently discovered disease as decreasing the case fatality rate over time.

The results of this study provide policymakers with three primary policy suggestions: 1) maintaining a non-strictly enforced quarantine policy and releasing the population after disease levels begin diminishing would lead to a second outbreak. 2) an extremely strict quarantine policy for the senior population, combined with a gradual removal of mandatory quarantine for younger citizens after the outbreak is largely controlled, can lessen economic damage without catastrophic increases in the number of hospitalized and dead individuals. However, if the quarantine policy for the senior population is not strictly enforced, there can be disastrous consequences. No quarantine restriction approach resolves the pandemic, and lockdown policies can only be used as a bridge to a global vaccination program. 3) Strict isolation policies and a strong reduction of contagiousness from the asymptomatic infected individuals can reduce the total number of hospitalizations and the number of deaths as compared to loosely enforced measures. Therefore, stark measures must be enforced to prevent a prolonged pandemic.

To model the spread of COVID-19, we design a compartmental model with ten interconnected compartments. Each compartment is subdivided into two parts, one containing the senior population and the other containing the rest of the population. A description of each compartment appears in Table 1 .

The connectivity of the compartments is illustrated in fig. 1 . Susceptible individuals get exposed to COVID-19 at a rate proportional to the number of asymptomatic and hospitalized infected individuals. Exposed individuals then become infected and asymptomatic. These individuals can either recover from their current state or develop serious symptoms and become hospitalized. The fraction of infected asymptomatic individuals that become hospitalized follows a Bernoulli distribution, with a low probability for the general population and a higher probability for the senior population.

The hospitalized individuals either die or recover at appropriate rates, which depend on whether the hospitalized population is above certain saturation points. The case fatality rate decreases over time to account for better knowledge by the healthcare system. Individuals who are not hospitalized enter or leave quarantine compartments according to public policy, expressed by κ and θ · v, where v is a vector containing the number of reported infections, deaths, and the current state of the economy, and θ is a weight vector that reflects the relative importance the public policy gives to the economy and the number of cases. The Greek letters represent the transition delays between the compartments and were derived from published data about the progression rate of COVID-19.

In our model, there are occupations more affected by lockdown and occupations less affected by lockdown. In our simulation, we have two types of workers: those whose productivity is highly damaged by a quarantine and those whose 5 . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint .

productivity is less damaged. The total economic output is the sum of the outputs of the individuals in each group minus the costs of treating the infected. For the long-term economic output beyond the pandemic period, deaths impose a penalty on future economic output, dependent on the discount rate r.

The productivity of each labor group is the sum of the productivity of all the individuals in that labor group. The cost of treating the infected is the number of individuals of each risk type times the cost of treating each risk type. Different workers of the same labor type might be under different lockdown restrictions based on their age or risk type. In our simulation, there are four levels of productivity for four types of workers: older workers whose jobs are highly damaged by a lockdown (y HRH ), older workers whose jobs are less damaged by a lockdown (y HRL ), younger workers whose jobs are highly damaged by a lockdown (y LRH ), and younger workers whose jobs are less damaged by a lockdown (y LRL ). The workers whose jobs are highly damaged by a lockdown lose a higher percentage of their productivity (represented by ψ) than workers who jobs are less damaged by a lockdown (represented by φ).

The dynamics of output in this model depend on the rate at which workers in different productivity and health groups move in and out of quarantine and the rates with which their health states change. The appendix contains a complete mathematical description of the model, the values used for transfer rates, and the initial conditions. Abbreviation Description S Susceptible population Q S Quarantined susceptible population E Exposed population Q E Quarantined exposed population I H Infected hospitalized population I A Infected asymptomatic population Q I A Quarantined infected asymptomatic population D dead population R Recovered population Q R Quarantined recovered population Table 1 . Abbreviations used in the compartmental model.

. CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04. 13.20062802 doi: medRxiv preprint Figure 1 : Compartmental model. Each box represents an individual compartment and the arrows represent transitions between the compartments. The individuals in every compartment are divided by age, as represented by the cyan bars, and by their productivity, as represented by the background color of the boxes. White boxes represent normal productivity, dead individuals (in red) have no productivity, quarantined individuals have a decreased productivity, and hospitalized individuals have no productivity and incur into treatment costs. As individuals recover, they receive a small boost in productivity due to their acquired immunity.

Using a population of 330 million, we simulate the evolution of public policy given the preferences of the policymakers over 76 weeks. In each scenario, to imitate current strict lockdown policies, we start with 85.6 % of non-seniors and 95.6 % of seniors in quarantine. Public policy and media information shifts the population in and out of quarantine. We keep the non-quarantined population above zero because some jobs that could potentially spread disease continue to operate because they are deemed essential in a pandemic economy. For this reason, there is not much room for further strengthening the quarantine for non-seniors.

Baseline scenario In the baseline scenario, we keep the current quarantine status (θ = 0, κ = 0). Leaving the quarantine in place results in 207,906 total deaths. The peak number of hospitalized is 189,136, which strains hospital capacity but does not saturate it, as shown in fig. 2a and fig. 2c . Deaths first accelerate as more non-quarantined people get infected, but then level off. There are 32,131 deaths among non-seniors and 175,775 among seniors, as shown in fig. 2b and fig. 2d , respectively. Since both young people and seniors have strict quarantine restrictions imposed on them, most of the deaths occur in the senior population, which is more vulnerable to the disease.

The economy in the baseline scenario, shown in fig. 3 , shrinks slightly from its initial restricted levels, as some people are hospitalized and die. This is costly for the economy, and there is no increase in productivity from others, as they are all still in quarantine. Given that the initial restrictions on economic output are high, the economic productivity in this scenario is quite low for a prolonged period of time.

. CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 

. CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04.13.20062802 doi: medRxiv preprint Sudden release of the population after control of outbreak, but before complete eradication

In this scenario, we maintain the level of social isolation detailed in the baseline simulation, and then release the non-senior isolated population at a rate of 10 % daily and the senior population at a rate of 0.1 % daily. As can be seen in fig.  4a , when the isolated population is released in week 40, a large second outbreak soon takes place after the release of the population. With a sudden release, the peak number of hospitalized is 4,363,654, which exceeds hospital capacity enough to increase the fatality rate. There are 788,815 total deaths, as shown in fig. 4b , with 242,869 deaths among non-seniors and 545,946 among seniors, necessitating a re-imposition of restrictions. Fig. 4a shows a decreasing number of infections before the second outbreak. During this period, the very low number of newly infected and deaths may suggest that COVID-19 has been successfully mitigated, and the pressure to resume normal activities may grow. The economy is strongly boosted shortly after strict restrictions are removed. However, due to the large initial fraction of asymptomatic infected individuals, a sudden relaxation of quarantine restrictions after the disease is largely controlled leads to a second outbreak, with increased deaths and infections. The economic dynamics of this scenario are shown in fig.  4c . After a short-term economic boost, the second outbreak damages economic productivity again, although the productivity boost for quarantined recovered individuals leads to a smaller jump.

. CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Progressive restart of the economy before the pandemic is over

In this scenario, we investigate a gradual relaxation of the quarantine restrictions. Various studies have shown that the case fatality rate for the senior population is larger than that of the younger population.(23; 24) The marked difference in mortality according to age suggests that enforcing an extremely strict isolation policy for the senior population while allowing the general population to slowly resume normal activities could potentially balance disease spread and economic damage. As in the sudden release scenario, policymakers loosen quarantine restrictions in week 40, releasing the non-senior isolated population at a rate of 0.1 % daily. This gradual relaxation does not lead to a second outbreak, as can be seen from the number of infected individuals in fig. 5a  and fig. 5c . In this state, the peak number of hospitalized is 189,136, which does not saturate the health care system. There are 33,750 non-senior deaths and 187,993 senior deaths, as shown in fig. 5b and fig. 5d , respectively. In this scenario, there are 13,837 more deaths than in the baseline scenario and a 4.0 % increase in economic productivity that is continuing to grow at 76 weeks.

We see in fig. 6 that relaxing restrictions on seniors as well does not improve economic productivity and results in substantially more deaths. Additionally, if 10 . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint .

the rate at which the general population abandons isolation measures increases rapidly, a second outbreak could take place. Strict enforcement of quarantine restrictions for seniors is vital, as without strict enforcement for senior individuals, the number of deaths is almost one million. Economic output is higher in the gradual quarantine relaxation scenario with strict enforcement of quarantine for seniors. However, since in this scenario COVID-19 becomes endemic and does not disappear, relaxing isolation policies for the senior population at any time leads to an extremely large number of hospitalized and dead individuals. Therefore, although this scenario can lead to an acceptable economic situation with a controlled number of hospitalizations and deaths, it is not a viable long-term solution. Any quarantine policy that does not eliminate the disease can serve only as bridge to a global vaccination campaign. 

. CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04.13.20062802 doi: medRxiv preprint Table 2 . Summary of predicted results from the different scenarios.

Maximum number of simultaneous hospitalizations during the pandemic, deaths from the low and high risk populations, and net change in productivity from current situation to a year and a half from the time of submission. In the baseline scenario, the restrictions do not change. In the sudden release scenario, after the disease is mostly brought under control, restrictions for non-seniors are suddenly relaxed. In the gradual release scenario, after the disease is mostly brought under control, restrictions for non-seniors are gradually relaxed.

First, from fig. 7a -c, we observe that the total number of hospitalizations and deaths decrease with the strictness of isolation of hospitalized patients ( ), while economic productivity grows slightly. We see a much larger decrease in hospitalizations and deaths, and a larger increase in economic productivity, as disease spread of asymptomatic patients (β) is reduced. This observation suggests the importance of enforcing quarantine measures, for example, by tracking diagnosed patients who are not hospitalized, and by strengthening specialized delivery systems.

Secondly, from Fig. 7d -f, we observe that as the strictness of isolation measures increase, the number of deaths and hospitalizations decrease, while economic output is first flat, and then at certain level of quarantine measures, begins to sharply decrease. Meanwhile, at higher levels of quarantine restrictions, the change in hospitalizations accelerates, but the change in deaths decelerates.

Finally, we see in fig. 7g -i that as policymakers put more emphasis on economic productivity, at lower levels of emphasis, there are increases in hospitalizations, deaths, and economic productivity, but as the policymaker prioritizes the economy more, hospitalizations and deaths continue to increase, while economic output shrinks. We see that if policymakers value short-term economic productivity highly relative to disease spread, there is a danger of quarantine policies leading to larger death tolls. 

. CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04. 13.20062802 doi: medRxiv preprint

We present a model of COVID-19 in a population with different risk groups and different levels of economic vulnerability to public policy aimed at preventing disease spread. We focus our model on a situation where disease is ongoing and quarantine measures are already in place. By modeling our population with different risk groups and economic groups, we are able to produce specific policy suggestions that allow for a finer targeting of the spread of COVID-19. The individuals most vulnerable to COVID-19 are primarily those who can be protected from the disease without crippling the economy. We suggest stringent lockdowns for higher-risk groups. Our simulations show that in order to protect the most vulnerable, any lockdown relaxation must be gradual, even for the less vulnerable.

Beyond the short-term, lockdown policy does not need to be as severe for lowerrisk groups. Quarantine restrictions can lessen over time for lower-risk people while still minimizing deaths. Lessening quarantine restrictions allows the economy to recover to −30 % of pre-restriction productivity, as opposed to −34 % when quarantine restrictions are left in place. It is important that policy relaxation be gradual, as this limits the spread of disease, and can allow for less restrictive measures in the future. In real-world terms, the gradual relaxation suggested by our model can correspond to the lifting of restrictions on in-person work operations several industries at a time, or to gradually increasing the number of low-risk people allowed to gather in one place.

These results also suggest that optimal policies may differ in various countries independent of the level of disease spread and healthcare capacity. For instance, in countries with more vulnerable economies that have a younger population, the consequences from disease may be less than in other countries, while consequences from lockdown policies may be higher than in other countries.

We also see that contagiousness of asymptomatic infected individuals (β) has an important effect on disease spread and mortality, and this suggests that strictly enforcing quarantines is especially important for policymakers to prioritize. If policymakers prioritize short-term economic productivity more, their quarantine policies may lead to many times more deaths and hospitalizations with minimal short-term economic gain.

Our results demonstrate that keeping a stringent quarantine on at least a substantial portion of the population is necessary to avert large numbers of deaths. More investigation is required as to how to keep such a quarantine sustainable over time, both through targeted relaxation, as we suggest, but also through safe provision of services to the quarantined and increased infrastructure for at-home economic productivity. (25) More workers may be required for maintaining a quarantined population over time. Additionally, continued compliance with quarantine may require a variety of measures, including enforcement, education from public health officials, and infrastructure for alternatives to traditional social and entertainment options.

Furthermore, policymakers should use other tools to supplement quarantine policy, including contact tracing and other containment measures. Successful quarantine policy can more quickly bring disease levels down to a level where more targeted tools can control future outbreaks. Our simulations suggest that quarantine policy alone cannot end a pandemic without a level of enforcement that may not be realistic, and one that necessitates extreme economic costs. Thus, policymakers should quickly incentivize vaccines and other medical treatments.

Our study has several limitations. Since there is no recent data on longterm health quarantines, it is unknown how individuals will react to lengthy restrictions related to infectious disease. Once more information on individuals' responses becomes available, their behavior should be incorporated into later models. We also do not model any individual-level differences in behavior or disease spread. This model could also be modified to incorporate the effects of testing and to have probability of infection depend on job type. Our model does not allow for any differences in disease spread between new and repeated contacts. (26; 27; 28) Additionally, due to the newness of COVID-19, the exact disease parameters and the effects of seasonality are not precisely known. (29; 30) Because of the uncertainty surrounding disease parameters, which change as the COVID-19 situation progresses, our numbers should not be taken as literal predictions, but rather as illustrating the consequences of different policy approaches.

During a fatal infectious disease outbreak of lengthy duration, making policy decisions with longer term consequences in mind is essential. Our model provides a framework for making such decisions that takes into account differences within the population and disease changes that may occur over time. We provide evidence about what quarantine policies may allow for minimal deaths while maximizing economic productivity. We find that once infection levels are somewhat controlled, very gradual relaxation of the restrictions on younger groups can minimize health consequences and economic damage. the manuscript. U.G. and D.S. contributed equally to this work.

We declare no competing interests.

. CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04.13.20062802 doi: medRxiv preprint . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04. 13.20062802 doi: medRxiv preprint 

An interactive web-based dashboard to track COVID-19 in real time. The Lancet infectious diseases

A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster

Clinical characteristics of coronavirus disease 2019 in China

Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study

The Effectiveness of Targeted Quarantine for Minimising Impact of COVID-19. medRxiv

Interventions to mitigate early spread of new engla-CoV-2 in Singapore: a modelling study. The Lancet Infectious Diseases

The association between income and life expectancy in the United States

Economic conditions and mortality: evidence from 200 years of data

With COVID-19, modeling takes on life and death importance

Containing papers of a mathematical and physical character

Early dynamics of transmission and control of COVID-19: a mathematical modelling study. The Lancet Infectious Diseases

Estimates of the severity of coronavirus disease 2019: a model-based analysis. The Lancet Infectious Diseases

Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions

The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study. The Lancet Public Health

Can we contain the COVID-19 outbreak with the same measures as for SARS? The Lancet Infectious Diseases

Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts. The Lancet Global Health

Artificial intelligence forecasting of covid-19 in china

A time series method to analyze incidence pattern and estimate reproduction number of covid-19

Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship

An seir infectious disease model with testing and conditional quarantine

What will be the economic impact of COVID-19 in the US? Rough estimates of disease scenarios. National Bureau of Economic Research

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

Clinical features of COVID-19 in elderly patients: A comparison with young and middle-aged patients

The psychological impact of quarantine and how to reduce it: rapid review of the evidence. The Lancet

Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees

Modelling disease outbreaks in realistic urban social networks

Estimating withinhousehold contact networks from egocentric data. The annals of applied statistics

Neher RA. 2019-novel Coronavirus (2019-nCoV): estimating the case fatality rate-a word of caution

Will COVID-19 go away on its own in warmer weather? Center for Communicable Disease Dynamics (CCDD) at the Harvard TH Chan School of Public Health