key: cord-0987129-c2lei4lk
authors: Ayoub, H. H.; Chemaitelly, H.; Seedat, S.; Makhoul, M.; Al Kanaani, Z.; Al Khal, A.; Al Kuwari, E.; Butt, A. A.; Coyle, P.; Jeremijenko, A.; Kaleeckal, A. H.; Latif, A. N.; Shaik, R. M.; Yassine, H. M.; Al Kuwari, M. G.; Al Romaihi, H. E.; Al-Thani, M. H.; Bertollini, R.; Abu-Raddad, L. J.
title: Mathematical modeling of the SARS-CoV-2 epidemic in Qatar and its impact on the national response to COVID-19
date: 2020-11-10
journal: nan
DOI: 10.1101/2020.11.08.20184663
sha: a8e952836f1180620d6f10bd4bc8571f246fb37a
doc_id: 987129
cord_uid: c2lei4lk

Background: Mathematical modeling constitutes an important tool for planning robust responses to epidemics. This study was conducted to guide the Qatari national response to the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) epidemic. The study investigated the time course of the epidemic, forecasted healthcare needs, predicted the impact of social and physical distancing restrictions, and rationalized and justified easing of restrictions. Methods: An age-structured deterministic model was constructed to describe SARS-CoV-2 transmission dynamics and disease progression throughout the population. Results: The enforced social and physical distancing interventions flattened the epidemic curve, reducing the peaks for incidence, prevalence, acute-care hospitalization, and intensive care unit (ICU) hospitalizations by 87%, 86%, 76%, and 78%, respectively. The daily number of new infections was predicted to peak at 12,750 on May 23, and active-infection prevalence was predicted to peak at 3.2% on May 25. Daily acute-care and ICU-care hospital admissions and occupancy were forecast accurately and precisely. By October 15, 2020, the basic reproduction number R0 had varied between 1.07-2.78, and 50.8% of the population were estimated to have been infected (1.43 million infections). The proportion of actual infections diagnosed was estimated at 11.6%. Applying the concept of Rt tuning, gradual easing of restrictions was rationalized and justified to start on June 15, 2020, when Rt declined to 0.7, to buffer the increased interpersonal contact with easing of restrictions and to minimize the risk of a second wave. No second wave has materialized as of October 15, 2020, five months after the epidemic peak. Conclusions: Use of modeling and forecasting to guide the national response proved to be a successful strategy, reducing the toll of the epidemic to a manageable level for the healthcare system.

Mathematical modeling has become a fundamental tool to guide surveillance of infectious diseases and emergency responses to epidemics [1] [2] [3] . Powered by surveillance and outbreak data, infection transmission models help monitor and predict epidemiological trends using realtime estimation of key indicators, such as incidence of infection, severe and critical disease cases, disease mortality, and basic reproduction number ( 0 R ; the number of secondary infections each infection would generate in a fully susceptible population [4] ) [3] .

Qatar is a peninsula located in the Arabian Gulf, with a diverse population of 2.8 million people [5] . Like other countries, Qatar has been affected by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic [6] [7] [8] [9] . Yet, the nation mounted an evidence-informed national response, in which in addition to early case identification, isolation, and quarantine through contact tracing, diverse standardized and centralized sources of data were generated, including population-based surveys. This wealth of data provided a special opportunity to understand infection transmission dynamics, predict healthcare needs associated with the resulting disease, coronavirus disease 2019 (COVID-19) [10] , and to inform the global epidemiology of this infection.

Qatar has a unique socio-demography that affected the transmission patterns of SARS-CoV-2 [8, 11] , a respiratory infection that propagates through social networks. Nearly 90% of the population are expatriates [5, 12, 13] with craft and manual workers (CMWs) constituting 60% of the population [14] . Of the national subpopulations, Indians (28%) constitute the largest population segment, followed by Bangladeshis (13%), Nepalese (13%), Qataris (11%), Egyptians (9%), and Filipinos (7%) [13] . The CMW population is predominantly male, single, 5 and young, with the top three countries of origin being India, Bangladesh, and Nepal [14] . Most

CMWs live in shared housing accommodations akin to dormitories [15] .

This study was conducted to describe SARS-CoV-2 transmission dynamics in Qatar and to craft a national response using mathematical modeling of the epidemic time-course, predicting the impact of social and physical distancing restrictions and the impact of easing those restrictions, and forecasting healthcare needs, in terms of hospitalizations requiring acute-care and intensive care unit (ICU) beds. The study was initiated before the identification of the first laboratoryconfirmed case of community transmission on March 6, 2020, and has continued to provide realtime projections and forecasts since then.

The overarching aim of the present article was to provide the technical tools and a "case study"

to demonstrate how individual countries can use mathematical modeling to effectively craft national public-health responses and to formulate evidence-based policy decisions that minimize the epidemic's toll on morbidity, mortality, societies, and economies.

Building on our previously developed models [8, [16] [17] [18] [19] , an age-structured, meta-population, deterministic mathematical model was constructed to describe SARS-CoV-2 transmission dynamics and disease progression ( Figure S1 of Supplementary Material (SM)). The model stratified the Qatari population into groups ("compartments") according to the major nationality groups (Indians, Bangladeshis, Nepalese, Qataris, Egyptians, Filipinos, and all other nationalities), age group by decile, infection status (infected, uninfected), severity of illness 6 (asymptomatic/mild, severe, critical), and disease/hospitalization stage (severe, critical), using sets of coupled, nonlinear, differential equations. A detailed description of the model is available in the SM. The model was parameterized using the best available data for SARS-CoV-2 natural history and epidemiology. A detailed description of model parameters, definitions, values, and justifications is found in Tables S1-S2 in the SM. The size and demographic structure of the population of Qatar were based on a population census conducted by Qatar's Planning and Statistics Authority [5] . Life expectancy was obtained from the United Nations World Population Prospects database [21] .

The model was fitted to the standardized and centralized databases of SARS-CoV-2 testing, infections, hospitalizations, and mortality [8] , as well as to findings of ongoing epidemiologic 7 studies [8, 11, 22, 23] . 

The model was also used to predict the impact of different scenarios for easing of social and physical distancing restrictions.

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The copyright holder for this this version posted November 10, 2020. ; https://doi.org/10.1101/2020.11.08.20184663 doi: medRxiv preprint 8 Five hundred simulation runs were conducted to determine the range of uncertainty attending model predictions. At each run, Latin Hypercube sampling was applied in selecting input parameter values [27,28] from pre-specified ranges that assume ±30% uncertainty around parameter point estimates. The model was then refitted to input data. The resulting distribution for each model prediction, based on the 500 runs, was used to derive the mean and 95% uncertainty interval (UI).

Mathematical modeling analyses were conducted in MATLAB R2019a (Boston/MA/USA) [29] whereas statistical analyses were performed in STATA/SE 16.1 (College Station, TX) [30]. Figures S2-S3) . Figure 1 shows model predictions for evolution of SARS-CoV-2 incidence, cumulative incidence, active-infection prevalence, and attack rate in the total population. Peak incidence was estimated at 12,750 new infections on May 23, 2020 while peak prevalence was estimated at 3.2% on May 25, 2020. By Based on the model-predicted evolution of t R at that time ( Figure 3A) , it was advised that no easing of restrictions should occur before the epidemic peak, then predicted to occur on May 20, as the epidemic was still in its exponential growth phase ( 1 t R  ). Model simulations confirmed that premature easing of restrictions would result in epidemic amplification ( Figure 3B ). To minimize the likelihood of a second wave and to buffer against a potential increased contact rate in the population, it was advised that easing of restrictions should not start before t R reached 0.70, and that easing of restrictions should be implemented gradually over at least two months.

Model simulations confirmed this rationale, and indicated that gradual easing of restrictions after t R reached 0.70 would minimize the risk of a second wave ( Figure 3C ). Accordingly, policymakers planned and subsequently implemented a gradual easing of restrictions starting June 15, 2020, the day on which t R was predicted to decline to 0.7. This line of analysis and rationale proved successful, as no second wave had materialized as of October 15, 2020, five months after the epidemic peak ( Figure 3D ).

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Our study demonstrates that mathematical modeling was influential in informing the national public-health response and in formulating evidence-based policy decisions to minimize the pandemic's toll on health, society, and the economy. The model, which was implemented in realtime, starting from March 2020, and was continuously updated and refined as more data became available, predicted with reasonable accuracy and precision the key epidemiologic indicators, All rights reserved. No reuse allowed without permission. preprint (which 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 this version posted November 10, 2020. ; https://doi.org/10.1101/2020.11.08.20184663 doi: medRxiv preprint 11 such as the epidemic peak and the impact of easing of restrictions, as well as healthcare needs, at a time of uncertainty in which knowledge of the epidemiology of this infection was growing but still limited.

One of the highlights of this modeling approach is the application of the concept of rational t R tuning for managing the easing of restrictions ( Figure 4 ). Grounded on a theoretical foundation [4] , rational t R tuning proved to be a successful and effective strategy in safely easing the restrictions so as to ensure social and economic stability and functionality, while minimizing the risk of a second wave ( Figure 3 ). Another highlight is the estimation of healthcare needs that guided resource-allocation planning well before the time when these resources were needed.

Throughout the epidemic, including the epidemic peak, healthcare needs in Qatar remained well within the health system capacity, avoiding any serious strain. Importantly, this forecasting of healthcare needs also prevented resource waste by avoiding overestimation of healthcare needs.

Despite the large number of infections in Qatar, results show that the epidemic would have been far worse if no social and physical distancing interventions had been enforced. In absence of interventions, the epidemic would have progressed very rapidly to a peak nearly 10-fold higher than what was actually observed ( Figure 4 ). Disease burden would have been much larger and the healthcare system would have been strained to the point of collapse. This demonstrates that for a respiratory infection with such large 0 R and serious disease sequalae, inaction would have had dire consequences, and that the national strategy focused on flattening the epidemic curve was appropriate to manage the epidemic.

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An important finding of this study is that PCR-confirmed infections constitute only a small fraction of the actual number of infections. Only 11.6% of infections were estimated to have ever been diagnosed, probably because most infections were asymptomatic or mild. Indeed, a nationwide population-based survey in Qatar showed that 58.5% of those who were PCR positive in this survey reported no symptoms during the last two weeks preceding the survey [8] . The growing number of serological testing studies in Qatar have also shown that the vast majority of those who are antibody-positive were never diagnosed with this infection [8, 11, 22, 23] . For instance, out of all those antibody-positive in a nation-wide seroprevalence survey of the CMW population, only 9.3% had a documented, PCR-confirmed infection prior to antibody testing, affirming that as estimated by the model, nine of every 10 infections were never diagnosed.

These findings are also consistent with a growing body of serological evidence from other

We found that >97% of infections estimated to have occurred did not require hospitalization. The low infection severity appears to be a consequence of the young age profile of the population, with only 2% being >60 years of age [5, 8, 17, 36] , in addition to a well-funded healthcare system that emphasizes a proactive, high-quality standard of care [8] , and possibly high levels of T cell cross-reactivity against SARS-CoV-2, reflecting T cell memory of circulating 'common cold' coronaviruses [37] [38] [39] [40] [41] .

This study has limitations. Model estimates are contingent on the validity and generalizability of input data. Our estimates were based on current SARS-CoV-2 natural history and disease progression parameters, but our understanding of this infection is still evolving. Available input data were most complete at the national level. We did not have sufficient data about social All rights reserved. No reuse allowed without permission. preprint (which 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 this version posted November 10, 2020. ; https://doi.org/10.1101/2020.11.08.20184663 doi: medRxiv preprint 13 networks of different national subpopulations and patterns of mixing between those subpopulations to factor them into the model. Despite these limitations, our model, tailored to the complexity of the epidemic in Qatar, was able to reproduce observed epidemic trends, and to provide useful and consequential predictions and insights about infection transmission and healthcare needs. Importantly, the modeling estimates successfully influenced the national response.

In conclusion, Qatar experienced a large SARS-CoV-2 epidemic, but avoided a burdensome epidemic, such as that unfolding in other counties. Mathematical modeling played an influential role in guiding the national public-health response by characterizing and understanding the epidemic, forecasting healthcare needs, predicting the impact of social and physical distancing restrictions, and rationalizing and justifying the easing of restrictions. While this article illustrates a successful case study, the modeling tools employed here can be adapted and applied in other countries to guide SARS-CoV-2 epidemic control, preparedness for the current or future waves of infection, or enforcement and easing of restrictions or other interventions, such as vaccination [19] .

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The copyright holder for this this version posted November 10, 2020. ; https://doi.org/10.1101/2020.11.08.20184663 doi: medRxiv preprint analytical insights, and for his instrumental role in enacting data information systems that made these studies possible. We further extend our appreciation to the SWICC Committee and the Scientific 

HHA co-designed the study, constructed and parameterized the mathematical model and conducted the mathematical modeling analyses. HC conducted the statistical analyses, contributed to the parameterization of the mathematical model, and wrote the first draft of the manuscript. LJA conceived and co-designed the study and led the construct and parameterization of the mathematical model, conduct All rights reserved. No reuse allowed without permission. preprint (which 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 this version posted November 10, 2020. ; 15 of analyses, and drafting of the article. All authors contributed to conceptualization of the analyses, discussion and interpretation of the results, and writing of the manuscript. All authors have read and approved the final manuscript.

We declare no competing interests.

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The copyright holder for this this version posted November 10, 2020. ; https://doi.org/10.1101/2020.11.08.20184663 doi: medRxiv preprint Figure 3 . A) Effective reproduction number R t and easing of social and physical distancing restrictions. B) Prediction of the number of daily new infections with early easing of restrictions, three weeks before the epidemic peak. C) Prediction of the number of daily new infections with delayed easing of restrictions, three weeks after the epidemic peak. This figure demonstrates the rationale and criteria used for the start of easing of restrictions. The figure shows the model fit and results at the time when the policy decision was actually made. An updated prediction for R t is in Figure S4 of SM. The figure also shows in D) the number of daily new diagnosed and laboratory-confirmed infections.

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The copyright holder for this this version posted November 10, 2020. Epidemic dynamics were described using a system of coupled nonlinear differential equations for each age group and subpopulation (nationality) group. Each age group, a , denoted a ten-year age band apart from the last category which grouped together all individuals ≥80 years of age.

The population was divided into seven resident subpopulation groups i ( ) 1, 2,3, 4,5, 6, 7 i = representing the subpopulations of Indians, Bangladeshis, Nepalese, Qataris, Egyptians, Filipinos, and all other nationalities, respectively-these are the largest nationality subpopulation groups in Qatar. Qatar's population composition and subpopulations size and demographic structure were based on findings of "The Simplified Census of Population, Housing, and Establishments" conducted by Qatar's Planning and Statistics Authority [6] . Life expectancy was obtained from the United Nations World Population Prospects database [7] . All rights reserved. No reuse allowed without permission. preprint (which 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 this version posted November 10, 2020. ; https://doi.org/10.1101/2020.11.08.20184663 doi: medRxiv preprint Figure S1 . Schematic diagram describing the basic structure of the SARS-CoV-2 mathematical model.

The model was expressed in terms of the following system of coupled nonlinear differential equations for each subpopulation group and age group: Table S1 . preprint (which 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 this version posted November 10, 2020. Proportion of infections that will progress to be infections that require hospitalization in acute-care beds To account for temporal variation in the basic reproduction number ( 0 R ), we incorporated temporal changes in the rate of infectious contacts. We parameterized the temporal variation (time dependence of  ) through the following combined function of the Woods-Saxon and logistic functions.

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The copyright holder for this this version posted November 10, 2020. ; sum of all entries adds up to 1. q parametrizes the connectivity to other subpopulations relative to the connectivity within the same subpopulation.

The survey assessing active-infection using PCR, 10) age-distribution of antibody positivity [4, 8, 9] , and 11) nationality subpopulation distribution of antibody positivity [4, 8, 9] .

Model input parameters were based on best available empirical data for SARS-CoV-2 natural history and epidemiology. Model parameter values are listed in Table 2 . The following parameters were derived by fitting the model to data: 

Based on existing estimate [10] and based on observed time to recovery among persons with mild infection [10, 14] and observed viral load in infected persons [12, 13, 15] . All rights reserved. No reuse allowed without permission. preprint (which 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 this version posted November 10, 2020. ; https://doi.org/10.1101/2020.11.08.20184663 doi: medRxiv preprint Figure S3 . Model fits to A) daily hospital admissions in acute-care beds, B) daily hospital admissions in ICU-care beds, C) hospital occupancy of COVID-19 patients (number of beds occupied at any given time) in acute-care beds, and D) hospital occupancy of COVID-19 patients in ICU-care beds. v All rights reserved. No reuse allowed without permission. preprint (which 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 this version posted November 10, 2020. ; https://doi.org/10.1101/2020.11.08.20184663 doi: medRxiv preprint Figure S4 . Evolution of the basic reproduction number R0 (A) and effective reproduction number Rt (B) in Qatar.

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The copyright holder for this this version posted November 10, 2020. ; https://doi.org/10.1101/2020.11.08.20184663 doi: medRxiv preprint Figure S5 . Impact of the social and physical distancing interventions on A) cumulative number of infections, B) cumulative number of deaths, C) cumulative number of hospital admissions in acute-care beds, and D) cumulative number of hospital admissions in ICU-care beds.

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The copyright holder for this this version posted November 10, 2020. ; https://doi.org/10.1101/2020.11.08.20184663 doi: medRxiv preprint Figure S6 . Uncertainty analysis. Mean and 95% uncertainty interval (UI) for the evolution of SARS-CoV-2 A) incidence (number of daily new infections), B) cumulative number of infections, C) active-infection prevalence (those latently infected or infectious), and D) attack rate (proportion ever infected), in the total population of Qatar.

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The copyright holder for this this version posted November 10, 2020. ; https://doi.org/10.1101/2020.11.08.20184663 doi: medRxiv preprint Figure S7 . Uncertainty analysis. Mean and 95% uncertainty interval (UI) for the evolution of COVID-19 A) daily hospital admissions in acute-care beds, B) daily hospital admissions in ICUcare beds, C) cumulative number of hospitalizations in acute-care beds, D) cumulative number of hospitalizations in ICU-care beds, E) hospital occupancy of COVID-19 patients (number of beds occupied at any given time) in acute-care beds, and F) hospital occupancy of COVID-19 patients in ICU-care beds.

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We thank Her Excellency Dr. Hanan Al Kuwari, Minister of Public Health, for her vision, guidance, leadership, and support. We also thank Dr. Saad Al Kaabi, Chair of the System Wide Incident Command and Control (SWICC) Committee for the COVID-19 national healthcare response, for his leadership,

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