Mitigation and herd immunity strategy for COVID-19 is likely to fail

Wolfgang Bock; Barbara Adamik; Marek Bawiec; Viktor Bezborodov; Marcin Bodych; Jan Pablo Burgard; Thomas Goetz; Tyll Krueger; Agata Migalska; Barbara Pabjan; Tomasz Ozanski; Ewaryst Rafajlowicz; Wojciech Rafajlowicz,; Ewa Skubalska-Rafajlowicz; Sara Ryfczynska; Ewa Szczurek; Piotr Szymanski

We use an individual based SIR model to describe the spread of COVID-19. Compared to classical ODE models of epidemic spread, microsimulations have the advantage of a better representation of epidemiologically relevant heterogeneity in the population. In addition, the description of the individual disease progression can be used to study the impact of complex countermeasures such as extensive backtracking, testing and quarantine. The model is a non-Markov stochastic process in continuous time based on the infection probability of susceptibles in contact with infected individuals. The contact structure outside of households is represented as an inhomogeneous directed random graph where each node corresponds to an infected individual and the degree of that node corresponds to the number of secondary infections created by that individual. The degree itself depends on how long the individual stays infectious (infectivity time). Population structure: Our sample population is based on the census data on the census data (2011) as well as more recent official statistics (2019) from Poland 17-19 and a synthetic reproduction of the microcensus in Germany (2014) 9 (see Appendix A) and involves age and household composition. For the relative frequencies of the household sizes see Supplement A. Sample populations were used to represent two major cities with typical urban household structures: Wroc law and Berlin. Since we focus on a conceptual question, more detailed structures like spatial assignment, gender, profession or comorbidity relevant health status are omitted. Disease progression within patients: The Covid-19 progression within patients is modelled according to the present medical knowledge. The incubation time is assumed to follow a lognormal distribution with median 3.92 and variance 5.516 [lognormal parameters: shape=0.497, loc=0.0, scale=3.923]. The age dependence of the probability to be hospitalised or to have severe progression or to have critical progression with requirement for ICU treatment is given in Table 1 . Table 1 : Age dependence of the probability to develop a certain level of symptoms. The probability for death was assumed to be 49% within the critical patients.