key: cord-0932892-swpv1mio authors: Balabdaoui, F.; Mohr, D. title: Age-stratified model of the COVID-19 epidemic to analyze the impact of relaxing lockdown measures: nowcasting and forecasting for Switzerland date: 2020-05-11 journal: nan DOI: 10.1101/2020.05.08.20095059 sha: 8ce30909dd1b3075df3ff733c1f5c0dcb89c5d53 doc_id: 932892 cord_uid: swpv1mio Compartmental models enable the analysis and prediction of an epidemic including the number of infected, hospitalized and deceased individuals in a population. They allow for computational case studies on non-pharmaceutical interventions thereby providing an important basis for policy makers. While research is ongoing on the transmission dynamics of the SARS-CoV-2 coronavirus, it is important to come up with epidemic models that can describe the main stages of the progression of the associated COVID-19 respiratory disease. We propose an age-stratified discrete compartment model as an alternative to differential equation based S-I-R type of models. The model captures the highly age-dependent progression of COVID-19 and is able to describe the day-by-day advancement of an infected individual in a modern health care system. The fully-identified model for Switzerland not only predicts the overall histories of the number of infected, hospitalized and deceased, but also the corresponding age-distributions. The model-based analysis of the outbreak reveals an average infection fatality ratio of 0.4% with a pronounced maximum of 9.5% for those aged [≥]80 years. The predictions for different scenarios of relaxing the soft lockdown indicate a low risk of overloading the hospitals through a second wave of infections. However, there is a hidden risk of a significant increase in the total fatalities (by up to 200%) in case schools reopen with insufficient containment measures in place. The coronavirus-induced COVID-19 epidemic 1 is constantly pushing governments to take rapid decisions on measures for protecting the public health while minimizing economic damage. The emergency to act after exceeding infection rates of 1 out of 10'000 individuals has been recognized by most governments. The coronavirus containment measures often started by recommending social distancing and improved hand hygiene and ended by the complete lockdown of countries in extreme cases. After putting a country into an extraordinary state in response to a first epidemic wave, the next challenge for governments is the timely release of drastic measures to reduce the psychological and economic damage while preventing a possible second epidemic wave. Timely decision making is crucial when implementing and relaxing measures. During those two phases, there is a competition between avoiding COVID-19 related fatalities and preventing harm (and secondary casualties) due to economic recession. Epidemic models 2 provide an important mathematical tool to support decision making. A prominent example are the simulations performed by Ferguson et al. 3 which (among others [4] [5] [6] provided convincing evidence in favor of implementing strong non-pharmaceutical interventions in response to the COVID-19 outbreak. The S-I-R compartmental models 7 divide a population into groups of susceptible (S), infected (I) and recovered (R) individuals. Adding more compartments allows for a refined description of specific epidemics. Such models range from SEIR 6, 8, 9 and SUQC 10 models of COVID-19 to models as complex as the SIDARTHE 11 model which considers susceptible, infected, diagnosed, ailing, recognized, threatened, healed and extinct compartments. An important feature of COVID-19 is its highly non-uniform attack of the different age strata of society. Statistical analysis of data collected during the COVID-19 epidemic in Hubei 12 reveals that the infection fatality ratio for individuals older than 80 is likely to be one order of magnitude higher than that for individuals of 50 years and younger. Agestratified epidemic models are therefore particularly relevant when estimating the hospital load and fatalities related to COVID-19. Moreover, the age-dependent patterns of social contacts may be incorporated into age-stratified models. As a result, the obtained mathematical models provide not only estimates of the overall dynamics of an epidemic, but they are also able to predict the effect of age-dependent relaxation measures such as reopening school. Here, we propose a novel approach to epidemic modeling to capture the age-dependent dynamics of COVID-19. Instead of using SIR-type of differential equations to describe the transfer between neighboring compartments, a discrete compartment model ( Fig. 1 ) is built which mimics the different "trajectories" of individuals from exposure to healing or death. Aside from the standard compartments for susceptible and exposed individuals, the model differentiates between symptomatic and asymptomatic infected individuals. The different compartments comprise susceptible (S), exposed (E), asymptomatic (A), symptomatic before (B) and in self-isolation (C), hospitalized in MCU (H) and ICU (Q), removed (R) and deceased (D) individuals. Individuals are classified into sub-compartments E1, E2, etc. according to the number of days they have spent in a given comportment. (b) age-dependent probability of hospitalization of symptomatic individuals, (c) probability of transfer from MCU to ICU, (d) fatality risk in ICU, (e) daily fatality ratio in ICU exemplarily shown for age-groups 80+, 70-74 and 60-64. The group of symptomatic is further split into a compartment of self-isolated individuals and those requiring hospitalization and admission to middle care (MCU) and intensive care units (ICU). Defining the first day of infection as Day 1, distinct sub-compartments are defined for all subsequent days until healing or death. The model is then updated on a daily basis by moving individuals to a specific sub-compartment for the subsequent day. Those moves are defined through shifting laws which account for the age-dependent probabilities of infection, admission to hospital, transfer to intensive care and death. As detailed in the Methods Section, the sizes of the compartments are set by the incubation time (5 days), the duration from the onset of symptoms to self-isolation (2 days), the average duration of viral shedding by asymptomatic individuals (8 days), the average duration spent in hospital (7 days) and in intensive care (8 days). In Fig. 1a , each encircled variable (E1, E2, etc) represents a vector whose components corresponds to the number of individuals in a certain age-group that are currently in a given sub-compartment (e.g. H2 for second day in hospital). In total, we symptomatic in self-isolation E1 E2 E3 E4 E5 A1 A2 A3 A4 A5 A6 A7 A8 symptom. infectious Supplementary Fig. 3 ). While up to 30% of the patients admitted to hospital will be transferred for age-groups 55 to 74 years, a significantly lower fraction of the individuals older than 70 years is transferred. The fatality risk in ICU (Fig. 1d) is estimated from the reported data after assuming that all deaths of individuals aged <75 years occur in ICU. Here, we observe a fatality risk of 40% in the age-group 70-74 years which appears to be low when compared to data reported for UK hospitals 16 . On the other hand, the canton Vaud reports that as many as 65% of all COVID-19 deaths occurs outside the hospital. We thus also allow for deaths of symptomatic patients in self-isolation with a probability of 2.3% and 7.3% for the age-groups 75-79 and ≥80 years, respectively. For the latter age-group, death is also assumed to occur in MCU with a probability of 18%. After setting the overall probability of deaths per compartment and age-group, a bump function is employed (Supplementary Information) to 5 determine the daily fatality risks (Fig. 1e ). Using the identified functions, the overall history of fatalities ( Fig. 2a ) and the age distribution of the deceased (Fig. 2b ) are predicted with reasonable accuracy. It is worth noting that about 70% of all COVID-19 related deaths in Switzerland are individuals aged 80 years or older, while the fraction of deceased is below 0.1% for those aged <50 years. The age-dependency of the probability of hospitalization for symptomatic individuals (Fig. 1b) is estimated based on the reported age-distribution in hospital. The resulting function HOSP  is then adjusted such that the model predicts the documented history ( Fig. 2c) and age-distributions of the individuals in hospital ( Fig. 2d) with good accuracy. The resulting probabilities of hospitalization per age-group fall into the 95% credible intervals for COVID-19 hospitalization estimated based on data for mainland China 17 . (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 preprint this version posted May 11, 2020. . Among the exposed, the groups 10-14 and 15-19 are the ones showing the highest infection ratios, while older age-groups appear to be protected by the contact patterns among age-groups in Switzerland. The age distribution of the exposed becomes more uniform after March 13 (Figs. 3b-d) mostly due to school closure and reduced presence at work. The age-stratified model predicts significant differences in the reproduction numbers among age-groups (Figs. 3e-g) with a max-to-min ratio of 3.6 to 0.6 on March 13 and of 0.9 to 0.3 two weeks later. It is worth noting that the reproduction number for those aged 65 years and over is always lower than 1. The non-uniformity of the attack of COVID-19 is even more pronounced when evaluating the infection fatality ratio (IFR). The trained model predicts an IFR of 9.5% for the individuals older than 80 years (Fig. 4) . It drops to 2.8% and 1.3% for the next two lower age-groups (75-79 and 70-74 years). Among the individuals in their sixties, there is still the risk of one death among 100 infected. An average IFR of about 0.38% is obtained when averaging over the whole age distribution of the infected. The estimated IFR for the 80+ age-group falls into the confidence interval for the IFR estimated based on data for mainland China 12 , while the IFRs for Switzerland are lower for all other age-groups. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission. (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 preprint this version posted May 11, 2020. . https://doi.org/10.1101/2020.05.08.20095059 doi: medRxiv preprint 8 To elucidate the importance of non-pharmaceutical intervention measures, we simulated the progression of the epidemic using the contact matrices and transmission probabilities that characterize the situation shortly before the lockdown (average reproduction number of 2.4). For this hypothetical scenario, herd immunity would have been reached within 2 to 3 months (Figs. 5a-c). By May 15, about 75% of the population would have been infected with an approximately uniform fraction of infected of about 85% in the 20 to 55 years age-groups (Fig. 5a ). Close to 97% of the 15-20 year old would have been infected, while less than 50% would have been exposed to the coronavirus among those older than 65 years. The associated peak ICU demand for COVID-19 patients would have been close to 60 beds per 100'000 capita (Fig. 5b ). The total of fatalities plateaus at about 22'000 with a loss of about 0.9% and 3% of the agegroups 75-79 and ≥80 years (Fig. 5c) . At the opposite extreme, we simulated the scenario where the extraordinary state is maintained without any relaxation of measures. Less than 10% of the population would have been infected by the end of 2020 (Fig. 5d) , while the peak in ICU need would have attained about 5 beds per 100'000 (Fig. 5e ). The total of fatalities remains below 2,300 with less than 0.4% of those aged 80 years and older losing their life because of COVID-19 (Fig. 5f ). (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 preprint this version posted May 11, 2020. . After putting the country into an extraordinary state that guarantees an overall reproduction number well below 1, the goal is to ease the measures in a way that a "new-normal" state is attained, which allows for a well-functioning economy (i.e. businesses reopen with most people back to work). The main constraint is that a second wave of infections needs to be avoided or at least be recognizable at an early stage to take corrective measures. Selected elements of the plan proposed by the Swiss government are summarized in Fig. 6 . (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 preprint this version posted May 11, 2020. . https://doi.org/10.1101/2020.05.08.20095059 doi: medRxiv preprint enforced (or at least masks are worn) at work and other locations, that 30% of the workforce is in home office and that venues such as restaurants and bars remain closed. The simulation results (Fig. 7a) suggest that the first release of measures will only have a minimal effect on the epidemic with a reproduction number staying well below 1 from April 27 to May 11. However, the second release (which involves the reopening of schools) is expected to cause a second peak of infections by mid-August, generating approximately the same daily hospital and ICU load as the first peak (Fig. 7c) . The second peak is less steep than the first. As a result, home work other school R3 All rights reserved. No reuse allowed without permission. (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 preprint this version posted May 11, 2020. . there is a two-month time window from early June to the end of July where the second peak could be detected through the monitoring of the increase of the hospitalizations. In other words, there would be less pressure on the government to take additional corrective measures quickly than at the beginning of the epidemic in March. However, this reasoning only applies when focusing on preventing the collapse of the healthcare system. The increased width of the second peak also implies a significantly higher death toll. While the first wave of infections generated about 2,000 fatalities, the second wave could generate almost 5,000 additional deaths (Fig. 7d) . It is thus extremely dangerous if the virus spreads with a reproduction number slightly higher than 1. The public perception may be positive as long as the healthcare system can handle the load of ICU patients, while many would silently die until reaching herd immunity. In the current scenario, herd immunity would be achieved by the end of 2020 after infecting about 30% of the total population. To gain insight into the robustness of the model predictions, a Monte-Carlo analysis is performed where we introduced six multipliers to perturb the probabilities of (i) developing symptoms, (ii) hospitalization, (iii) transfer to ICU, and (iv) death in self-isolation, To achieve a more positive outcome of the release of measures, we redid the above simulations with reduced probabilities of transmission at school (Fig. 8) . It turns out that the overall reproduction number after reopening schools will remain below 1 if the probability of transmission (per contact at school) is reduced by 50%. In that case, a second peak could be avoided. Moreover, and probably most importantly, the excess fatalities associated with school reopening would drop from 5,000 * ( 1.0) school   to less than 1,000 * ( 0.5) school   . Any failure of maintaining the rate of transmission at school reasonably low would result in a substantial increase in fatalities within a few months to a level that is significantly higher than the annual total of fatalities associated with influenza (about 1,000 for Switzerland). Repeating the above simulations with the assumption that 95% of the workforce is physically present at work (which also increases the probability of transmission at work from 0.3 to 0.5) resulted in similar results ( Supplementary Fig. 5 ). In the Supplementary Information, we also considered the immoral (and practically-infeasible) scenario of temporarily isolating individuals older than 70 years from the rest of the society while letting life resume for all other age-groups without any All rights reserved. No reuse allowed without permission. (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 preprint this version posted May 11, 2020. . restrictions (with an initial reproduction number of about 2.4). For that scenario, the total death toll would be 4,100 before reaching herd immunity (67% of total population infected) within two months (Supplementary Fig. 6) . However, the peak hospital and ICU demand of 29 beds (per 100'000) are likely to exceed the capacity which may cause additional fatalities for this scenario. (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 preprint this version posted May 11, 2020. We consider data sets collected by the private platform www.corona-virus.ch after sporadically cross-checking the data sets with those provided by official sources (Swiss Federal Office of Health (BAG) and the canton Vaud). Information on age-distributions is also obtained from the official sources. The age-distribution in Switzerland is obtained from data for 2016 reported on www.populationpyramid.net ( Supplementary Fig. 2) . . The main modeling assumptions are:  Symptomatic individuals are 50% more infectious than asymptomatic individuals 1 . Even though the viral loads in symptomatic and asymptomatic patients appear to be All rights reserved. No reuse allowed without permission. (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 preprint this version posted May 11, 2020. . https://doi.org/10.1101/2020.05.08.20095059 doi: medRxiv preprint similar 7 , the higher probability of infecting through coughing supports the assumption of a higher infectiousness for the symptomatic patients.  The new infections (i.e. individuals in sub-compartment (1) E ) are then given by (1) (2)  Symptomatic individuals are assumed to transfer to hospital on their 5 th day of selfisolation. This assumption is made to match reports from international media that it takes approximately two weeks from first exposure to hospitalization. All rights reserved. No reuse allowed without permission. (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 preprint this version posted May 11, 2020. . https://doi.org/10.1101/2020.05.08.20095059 doi: medRxiv preprint  The middle care unit (MCU) features seven sub-compartments to match the average duration of hospitalization (outside ICU) of 7 days reported by the Swiss canton Vaud.  The same canton also reported an average duration of a stay in ICU of 6 days. Due to the temporal distribution of the high number of deaths in ICU, the intensive care unit features eight sub-compartments in attempt to match the average duration in ICU of 6 days after accounting for deaths. Reproduction number. The reproduction number R is a vector whose components j R estimate the number of individuals (among all age-groups) that an infectious individual of agegroup j would infect during its period of communicability (8 days for asymptomatic, and 2 days for symptomatic individuals). Assuming that the effective contact matrix and number of susceptible individuals remains constant during the period of communicability, it can be given by the approximation The overall reproduction number R  is computed as weighted average using the current agedistribution of the exposed as weighting function. Clinical Characteristics of Coronavirus Disease 2019 in China The mathematics of infectious diseases Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand (preprint A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study. The Lancet 261-270 COVID-19: Forecasting short term hospital needs in France Estimating clinical severity of COVID-19 from the transmission dynamics in Wuhan, China A Computational Model for Estimating the Progression of COVID-19 Cases in the US West and East Coasts Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study Modeling the epidemic dynamics and control of COVID-19 outbreak in China Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy Adjusted age-specific case fatality ratio during the COVID-19 epidemic in Hubei, China Japanese National Institute of Infectious Diseases. Field Briefing: Diamond Princess COVID-19 Cases Suppression of COVID-19 outbreak in the municipality of Spread of SARS-CoV-2 in the Icelandic Population No reuse allowed without permission. (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 preprint this version posted doi: medRxiv preprint 16. Intensive Care National Audit & Research Centre (ICNARC), ICNARC report on COVID-19 in critical care Estimates of the severity of coronavirus disease 2019: a model-based analysis Reproductive number of the COVID-19 epidemic in Switzerland with a focus on the Cantons of Infection fatality rate of SARS-CoV-2 infection in a German community with a super-spreading event Projecting social contact matrices in 152 countries using contact surveys and demographic data. 1-21 Early Transmission Dynamics in Wuhan, China, of Novel Coronavisus-Infected Pneumonia Virological assessment of hospitalized cases of coronavirus disease Hence, we have the corresponding IFR for age-group i,As for the reproduction number, we make use of the age-distribution for the exposed to calculate the average IFR. The codes are available upon request to the corresponding author. Both authors contributed equally to the work. The authors declare no competing interests.All rights reserved. No reuse allowed without permission.(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.