Rasmussen, Steen; Michael Skytte Petersen and Niels Hobby

Background Initially, the relative sizes of the asymptomatic and the symptomatic infected populations were not known for the COVID-19 pandemic and neither was the actual fatality rate. There- fore it was not clear either how the pandemic would impact the healthcare system. As a result it was initially predicted that the COVID-19 epidemic in Denmark would overwhelm the healthcare system and thus both the diagnosis and treatment of other hospital patients were compromised for an extended period. Aim To develop a mathematical model, which includes both asymptomatic and symptomatic infected persons, for early estimation of the epidemic’s course, its Infection Fatality Rate and the healthcare system load in Denmark, both retrospectively and prospectively. Methods The SEIRS (Susceptible—Exposed—Infected—Recovered—Susceptible) model including deaths outside hospitals and separate assessments of symptomatic and asymptomatic cases (based on seroprevalence) with different immunological memories. Optimal model parameters are in part identified by Monte Carlo based Least Square Error methods while micro-outbreaks are modeled by noise and explored in Monte Carlo simulations. Estimates for infected population sizes are obtained by using a quasi steady state method. Results The calculations and simulations made by the model were shown to fit with the observed development of the COVID-19 epidemic in Denmark. The antibody prevalence in the general population in May 2020 was 1.37%, which yields a relative frequency of symptomatic and asymptomatic cases of 1 to 5.2. Due to the large asymptomatic population, the Infection Mortality Rate was only 0.4%. However, with no non-pharmacological restrictions the COVID-19 death toll was calculated to have more than doubled the national average yearly deaths within a year. The transmission rate <0 was 5.4 in the initial free epidemic period, 0.4 in the lock-down period and 0.8–1.0 in the successive re-opening periods through August 2020. The large asymptomatic population made the termination of the epidemic difficult and micro-outbreaks occurred when the country re-opened. The estimated infected population size July 15 to August 15 was 2,100 and 12,200 for October 1–20, 2020. Conclusions The results of the model show, that COVID-19 has a low Infection Fatality Rate because the majority of infected persons are either asymptomatic or with few symptoms. A minority of the infected persons, therefore, requires hospitalization. That means that for a given infection pressure of both symptomatic and asymptomatic infected there will be a lower pressure on the capacity of the health care system than previously predicted. Further the epidemic will be difficult to terminate since about 84% of the infected individuals are asymptomatic but still contagious. The model may be useful if a major infection wave occurs in the autumn-winter season as it could make robust estimates both for the scale of an ongoing expanding epidemic and for the expected load on the healthcare system. The simulation may also be useful to evaluate different testing strategies based on estimated infected population sizes. The model can be adjusted and scaled to other regions and countries, which is illustrated with Spain and USA.