key: cord-1041224-1tkbwk8u authors: Yu, X. title: Modeling Return of the Epidemic: Impact of Population Structure, Asymptomatic Infection, Case Importation and Personal Contacts date: 2020-05-01 journal: nan DOI: 10.1101/2020.04.26.20081109 sha: 520acb642762f4084bcf0a0ceae6ab4945172f44 doc_id: 1041224 cord_uid: 1tkbwk8u Background: Proactive interventions have halted the pandemic of coronavirus infected disease in some regions. However, without reaching herd immunity, the return of epidemic is possible. We investigate the impact of population structure, case importation, asymptomatic cases, and the number of contacts on a possible second wave of epidemic through mathematical modelling. Methods: we built a modified Susceptible-exposed-Infectious-Removed (SEIR) model with parameters mirroring those of the COVID-19 pandemic and reported simulated characteristics of epidemics for incidence, hospitalizations and deaths under different scenarios. Results: A larger percent of old people leads to higher number of hospitalizations, while a large percent of prior infection will effectively curb the epidemic. The number of imported cases and the speed of importation have small impact on the epidemic progression. However, a higher percent of asymptomatic cases slows the epidemic down and reduces the number of hospitalizations and deaths at the epidemic peak. Finally, reducing the number of contacts among young people alone has moderate effects on themselves, but little effects on the old population. However, reducing the number of contacts among old people alone can mitigate the epidemic significantly in both groups, even though young people remain active within themselves. Conclusion: Reducing the number of contacts among high risk populations alone can mitigate the burden of epidemic in the whole society. Interventions targeting high risk groups may be more effective in containing or mitigating the epidemic. The pandemic of coronavirus infected disease caused by the novel Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV2) [1, 2] has significantly impacted people's daily life and led to a global public health crisis [3] . As of April 14, 2020 Two important factors may contribute a second wave of epidemic. First, unlike the 2003 SARS epidemic in which mainly symptomatic cases are infectious [4] , asymptomatic infection of the SARS-CoV2 can transmit disease [5] [6] [7] [8] [9] . Studies have detected virus shedding in nasopharyngeal swap samples among asymptomatic cases [10] . A few case reports have shown some cluster of cases initiated by asymptomatic cases [5, 7, 9] . Researchers have postulated that asymptomatic and pre-symptomatic cases may play a significant role in sustaining the community transmission [6] . Second, government leaders have been pressed to allow people to return to normal work and life to avoid economic recession. After social activities are restored, both international and domestic travel ban will be lifted. Imported symptomatic and asymptomatic cases may kindle a second wave of epidemic in the community [6] . For example, despite Singapore has implemented possibly the most rigorous contact tracing, personal protection and social distancing measures, an unexpected surge of new cases has been observed, with daily newly confirmed cases doubled from 142 in April 7 to 287 in April 8, and still 334 in April 14 (https://www.gov.sg/article/covid-19-cases-in-singapore). As of this writing, the source of this sudden increase is still under investigation. From the health services perspective, the number of severe cases who require medical care is the most important indicator of the burden of epidemic. Heath care providers, hospital beds, and intensive care units (ICU) are limited resources. One main purpose of mitigating the epidemic is to alleviate the impact of epidemic on healthcare resources. Several reports have shown that about 20% of symptomatic COVID-19 cases require hospitalizations, and of them, about 30-50% may require ICU [11] [12] [13] (also https://gis.cdc.gov/grasp/COVIDNet/COVID19_3.html). More importantly, old people or people with existing chronic conditions have worse outcome than young people. For example, the mortality rate for age 50 or younger is below 1%, while the mortality rate increases to more than 10% among people aged 80 or above in the US [14] . Epidemic model simulation has been used extensively to estimate essential epidemic parameters, evaluate the epidemic progression and provide critical guidance to policy makers. Simulation studies based on early epidemic data from Wuhan, China and incorporating human travel and migration information have provided more accurate picture of epidemic [15] [16] [17] [18] [19] . In addition, based on simulating individual behaviors under realistic societal settings, several key simulation analyses have informed the policy makers about the effectiveness of various intervention strategies to halt the epidemic [20] [21] [22] [23] . Another simulation study updates daily about the impact All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 1, 2020. . https://doi.org/10.1101/2020.04. 26.20081109 doi: medRxiv preprint of COVID-19 epidemic on the use of health care resource and predicts the trend and peaks of health care use in the US [24] (https://covid19.healthdata.org/united-states-of-america). In this study, we will build a modified Susceptible-Exposed-Infectious-Removed (SEIR) model [25] to simulate the COVID-19 epidemic and investigate the impact of population structure, asymptomatic cases, case importation, and the number of contacts on the epidemic progression. We will explicitly evaluate the changes of hospitalizations and mortality under various scenarios for young and old people. Our analysis will provide theoretical evidence of possible strategies to prepare for a second wave of epidemic. The modified SEIR model is shown in Figure 1 (also see the modeling framework section in supplemental documents for details). Briefly, we divide the population into the susceptible population (S), self-quarantined susceptible people (Q), exposed but not infectious people (E), infectious compartment which includes those cases from quarantined susceptible (I Q ), symptomatic cases (I D ), asymptomatic cases (I U ) (also those with mild symptoms), and the removed compartment which includes those hospitalized (H), recovered (R), and dead (D). The self-quarantined persons are not based on individual contact tracing but rather refer to those who are alert to any possible infection in the community and may avoid contacting with any exposed persons. They are a special susceptible population who will not infect others if they are infected. Asymptomatic cases are often undiagnosed or unreported. All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 1, 2020. . https://doi.org/10.1101/2020.04. 26.20081109 doi: medRxiv preprint We also assume a dynamic population in which the numbers of imported susceptible persons and exposed persons (often have no symptom) are proportional (f 1 and f 2 ) to the size of total population (i.e., larger regions attract more visitors). We further assume the death rate due to other causes is a constant for all populations. For those who are symptomatic, diagnosed with the infection and hospitalized, their deaths are attributed to the infection or complications of the infection. In addition, at the beginning of the simulation, some proportion of the population have past infection (or immunized) (P). Therefore, the total population at the time t is N(t) = S(t) + Q(t) +E(t) + I D (t) + I U (t) + I Q (t) + H(t) + R(t) + P 0 . To account for population heterogeneity, we also apply the basic framework ( Figure 1 ) to both young (age < 65) and old (age >=65) populations. The two flowcharts are connected through cross-infection due to mutual contacts. The combined flowcharts can be translated into a set of ordinary differential equations (see supplemental document). The key equations relevant to the drive of epidemic and cross-infection between two age groups are for the change of exposed The model involves many parameters. Their definitions, default values, and ranges are listed in the supplemental document (supp. [18, 26, 27] . We adopt the R 0 =2.6 as a conservative estimate [28, 29] . The number of average contacts in the population ranges 2-30 [21, 30] . We assume a moderate 10 contacts for young, 7 contacts for old, and 3 contacts between young and old people in this study. Some seniors may have more contacts than the default value due to group living or regular community gathering. They are not considered in this population level modeling. The serial interval is the average duration between the infectious point (often symptom onset) of the index case and the symptom onset (or diagnosis) of secondary cases. Reported serial intervals vary significantly across different studies, with an average of 5 days [15, 17, 21, [31] [32] [33] . We adopt a conservative estimate of 6 days for young and 4 days for old people, ranging 3-10 days. Finally, we assume an overall hospitalization rate of 10%, as commonly reported in the United States (https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/). Hospital stay is 7-21 days, as most All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 1, 2020. . hospitalized people are elderly patients. The in-hospital mortality rate is 5% for young and 20% for old symptomatic patients, and an overall mortality of 1% and 10% for young and old patients, respectively [11, 13, [34] [35] [36] . The recovery duration for those who are not hospitalized is 5-20 days, typical for non-severe pneumonia. The default model is set on a region with 1 million residents, consisting of 20% elderly people and 20% of total population with past infection (or immunized). There is no existing symptomatic or asymptomatic case, and no person in self-quarantine in the region. We assume only one imported young exposed case every two days for 20 days (i.e., 10 imported cases). Analyses were performed based on the ranges of parameter estimates. We varied one parameter at a time, holding other factors at their default values. Key epidemic measures were presented in tables. Multi-parameter analyses with two or more factors varying together were also performed, important findings were discussed in the text. Additional outputs were included in the supplemental materials. The R package EpiModel was used for simulating the deterministic epidemic models [37] . The R codes for simulating the modified SEIR epidemic models are available (github address after review). This study is deemed exempt from ethics approval as the research involves no human subjects and we use publicly available data. All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 1, 2020. . Under the default model setting, all epidemic measures reflect the model parameters satisfactorily (Table 2 , also refer to supplemental Table 1 ). Starting with ten imported infectious persons and assuming 40% asymptomatic cases at the peak of epidemic, the epidemic reaches peak quickly within 73 days and lasts 172 days. It is ten days quicker among old people than among young people ( Table 2 ). The epidemic curves for incident cases (symptomatic and asymptomatic), hospitalizations and deaths by age groups are typical (Supplemental Figure 2 ). The modeling results in an overall hospitalization rate of 14.1%. The in-hospital mortality rate is 5.0% for young and 20.3% for old people, with an overall mortality rate of 1.9%, similar to those empirical measures in the COVID-19 epidemic in the US. Therefore, the default model represents the current COVID-19 epidemic sufficiently well. As summarized in Table 3 , the size of region and small percent change of self-quarantined susceptible do not change the epidemic progression except for the total number of cases. A smaller percent of elderly slows down the epidemic, while a much higher percent of elderly does not change the epidemic curve significantly. As expected, when over 60% people have prior infection, the epidemic takes very long to reach the peak and results in substantial fewer cases. The effects are similar in both young and old people (supplemental Table 2a & 2b) . Both the percent and infectivity of asymptomatic cases were investigated (Table 3 ). An increase of the percent of asymptomatic cases from 10% to 30% postpones the epidemic peak by 12 days All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 1, 2020. . due to less infectivity of asymptomatic cases, and results in significantly fewer hospitalizations and deaths. On the other hand, a higher infectivity of asymptomatic cases (e.g., 100% of symptomatic cases) results in a fast developing and narrow epidemic curve which reaches the peak within 60 days. There are more hospitalizations and deaths at the epidemic peak compared with the default model, both assumed 40% asymptomatic cases. In addition, a change of the percent of asymptomatic cases among old people leads to larger changes in hospitalizations and deaths than that of young people (Supplemental Table 2a & 2b) . For example, comparing 60% with 40% asymptomatic cases, the total hospitalizations are reduced only by half among old people, while it is a two third decrease among young people. Furthermore, when the effects of the percent and infectivity of asymptomatic cases are combined, for example, in a low risk epidemic with 60% asymptomatic cases but with a lower (30%) infectivity, the epidemic reaches its peak slower for both young and old people with peak hospitalizations almost half of the default model (40% asymptomatic cases and 50% infectivity) (supplemental Figure 3) . This epidemic model is initiated by imported infectious persons (may asymptomatic or presymptomatic cases). A daily arrival of two infectious people speeds up the epidemic by 8 days compared with one case every two days in the default model ( Table 3 ). The magnitudes of epidemic are similar between different importation scenarios. In addition, a longer importing duration shifts the epidemic only slightly. Finally, if we assume all the imported cases are asymptomatic cases, the epidemic curves are not significantly different from that of default model (supplemental Figure 4) . All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 1, 2020. . The number of contacts affect the epidemic curves in a complicate way (Figure 2 for young and old people, respectively, all significantly lower than those of default model ( Table 2 ). The times to the epidemic peak are also postponed in both curves. When both young and old people reduce contacts to 3 per day, such as under the stay-at-home rule, the epidemic curves on hospitalizations are significantly mitigated in both groups (Figure 2d ). Finally, we consider two extreme scenarios: 1) high risk scenario: assuming one imported case per day continuously throughout the epidemic, 30% asymptomatic cases at the epidemic peak, and the same infectivity between symptomatic and asymptomatic cases; 2) low risk scenario: assuming one imported case every two days for twenty days, 60% asymptomatic cases, and asymptomatic cases have only 30% infectivity of symptomatic cases. In both scenarios, limiting contacts among old people alone still has significant impact on hospitalizations in both age All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 1, 2020. . https://doi.org/10.1101/2020.04. 26.20081109 doi: medRxiv preprint groups, and a larger relative difference in the low risk scenario than high risk scenario ( Figure 3 and supplemental Figure 7 ). We created a modified SEIR model and parameterized it with estimates from the current COVID-19 epidemic. Our scenario analyses suggest that unless the population have reached herd immunity (e.g., over 60% people are immune to the disease, assuming a reproduction number of 2.6 [28, 29] ), a small number of imported cases within a short duration may rekindle the epidemic among the large susceptible pool. Despite young imported cases and only 3 contacts between young and old people, infection can quickly transmit into old people. Interestingly, our model demonstrates that reducing the number of contacts among old people alone can not only slowdown the epidemic but also reduce the magnitude of the epidemic among both young and old people. This spillover effect implies that interventions targeting high risk groups such as elderly population can have a larger impact on the whole society, without significantly disturbing the working life among young people. Our findings are consistent with that of prior simulation studies and real life experience in several Asian countries [1, 15, 16, 20, 22, 24] . Many countries have implemented more proactive interventions such as school closing and stay at home rules, which have mitigated the epidemic in many regions. One of the most effective strategies to curb an epidemic is to reduce personal interactions through social distancing and prohibiting large gatherings [21, 30, 38] . Our simulations have shown that reducing the number of contacts among young people alone does not affect the All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 1, 2020. . https://doi.org/10.1101/2020.04. 26.20081109 doi: medRxiv preprint burden of epidemic significantly. On the other hand, reducing the number of contacts among old people alone not only mitigates the impact of epidemic among themselves, but also changes the course of epidemic among young people, despite they still remain very active. Old people often have weaker immune system and multiple underlying chronic conditions. If infected with the virus, they are more likely to be symptomatic and more infectious because their bodies are not able to eliminate virus effectively. Therefore, during an epidemic such as COVID-19, old people are more likely to be hospitalized and die from the complications of infection. Thus, protecting old people not only decreases their risk of being infected but also reduces the burden of epidemic in the whole society. With growing availability of detection kits during the COVID-19 epidemic, more asymptomatic or mild symptomatic cases are identified. Ultimately, an optimal view is asymptomatic cases may account for 60% of infections. However, recent research and case reports have confirmed that asymptomatic or pre-symptomatic cases can shed enough quantify of virus to be infectious [5] [6] [7] [8] 10] . Furthermore, if the infectivity of asymptomatic cases is similar to that of symptomatic cases, a faster epidemic will occur. Despite more asymptomatic cases at the peak of epidemic, there are also significantly more hospitalizations and deaths, while may overwhelm the health care system. With a lower infectivity (30% infectivity), the epidemic reaches its peak later and results in half of hospitalizations at the peak compared with the default model (Supplemental Figure 3 ). In addition, a closely related issue is case importation [23] . Imported cases are often pre-symptomatic, asymptomatic or with mild symptoms. They seed of a second outbreak, even with just a few cases. Therefore, proactively identifying asymptomatic cases and isolating them thereafter will prevent the occurrence of an epidemic [20] . All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 1, 2020. . Our study has some strengths. We devised a modified SEIR model to incorporate both symptomatic and asymptomatic cases. We emphasized population heterogeneity such as age structure in the model. We included a self-quarantined group who will not infect other people if they are infected with the virus. Naturally, these settings can be extended to represent other high risk or special groups with revised parameters. In addition, we separated hospitalization from other removed compartments to explicitly estimate the impact of an epidemic on hospitalizations. Furthermore, we explored a few key determinants of epidemic explicitly, leading to many insights on epidemic prevention strategies. There are a few limitations in our study. As inherent in all modeling studies, simulation interpretations are heavily dependent on model assumptions and parameter estimations. Our epidemic model is a population model. Although we take account of population heterogeneity such as age in the current model, our age group is overly broad. A more detained age grouping scheme, including children, young adults, middle age group, and elderly, may reflect the agespecific epidemic more realistically. In addition, we assume random mixing within and between the groups. As a population model, we cannot assess the impact of individual behaviors such as the way of reducing contacts, social distancing and travelling. Furthermore, it ignores clustering within the population such as senior group living, community gatherings (e.g., churches, community centers), worksites and schools. These clusters are hotbeds for superspreading events which may lead to a sudden increase of new cases and overwhelm the healthcare system unexpectedly. Furthermore, the quarantine compartment in the model is not contact tracing based. Modeling contact tracing based quarantine is more relevant to public health interventions [39] . Therefore, the goal of our future research is to exploring the effect of these factors with stochastic simulations of individual behavior [22, 40] and network analysis [41] . Additionally, our All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 1, 2020. . https://doi.org/10.1101/2020.04. 26.20081109 doi: medRxiv preprint model is set on a mid-size region with 1 million residents. We did not intend to model pandemic, as all prevention strategies are ultimately local. Finally, out study only examines a small subset of scenarios during the epidemic. Multi-interventions are more effective in mitigating an epidemic but less sustainable in the long run. After the initial epidemic ends, society will return to normal, and only one or two interventions such as social distancing may be practiced, often partially. Thus, one parameter analysis under various scenarios is important for evaluating the probability of a second epidemic. In summary, with a modified SEIR model, we have demonstrated that simple intervention strategies such as reducing the number of contacts through social distancing, even among high risk population alone, can not only reduce the risk of infection and alleviate disease burden among themselves, but also mitigate the impact of a second epidemic in the whole society. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 1, 2020. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 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The peak self-quarantined is 2% of the susceptible population but changes with the prevalence of disease. The hospitalization rate is 5% for young, and 30% for old symptomatic cases, respectively. The mortality rate is 5% for hospitalized young people and 20% for hospitalized elderly. There are no prior symptomatic or asymptomatic cases or quarantined people in the total population