SARS-CoV-2 infection dynamics in Denmark, February through October 2020: Nature of the past epidemic and how it may develop in the future

Rasmussen, S.; Petersen, M. S.; Hoiby, N.

Background: There has long been uncertainty about the relative size of the "dark" numbers, the infected population sizes and the actual fatality rate in the COVID-19 pandemic and thus how the pandemic impacts 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 robust method for reliable estimation of the epidemic and the healthcare system load in Denmark, both retrospectively and prospectively. To do this a new pandemic simulation had to be developed that accounts for the size and the infection impact of the infectious incubating and asymptomatic infected individuals (dark numbers). Methods: Our epidemic simulation is based on a SEIRS (Susceptible - Exposed - Infected - Recovered - Susceptible) model, coupled to a simple healthcare model that also includes deaths outside hospital settings. The SEIRS model has separate assessments of asymptomatic and symptomatic cases with different immunological memories. The main data used for parameter estimation in the models are hospital and ICU occupations, death data, serological data of antibody prevalence from the onset through August 2020 together with hospital data and clinical data about the viral infection. 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 the infected population sizes are obtained by using a quasi steady state method. Results: The age adjusted 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 found, the actual mortality rate to date is 0.4%. However, with no behavioral and policy restrictions the COVID-19 death toll would have more than doubled the national average yearly deaths within a year. The transmission rate Ro 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 estimated infected population size July 15 to August 15 was 2,100 and 12,200 for October 1 - 20, 2020. The efficiency of the applied daily testing strategy for both periods are estimated to be 40% of the PCR observable infected. Of more theoretical interest we demonstrate how the critical infection parameters for COVID-19 are tightly related in a so-called iso-symptomatic infection diagram. Conclusions: Our simulation may be useful if a major infection wave occurs in the 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. Our simulation may also be useful to assess a future controlled epidemic, e.g. as a basis for evaluating different testing strategies based on estimated infected population sizes. Finally, we believe our simulation can be adjusted and scaled to other regions and countries, which we illustrate with Spain and the US.