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

In this article, we study the likelihood of success of such strategies, based on a semi-realistic microsimulation model for the spread of COVID-19. Simulations with census based household compositions and age distribution were carried out for Germany and Poland and for two representative major cities, Berlin and Wroc law. Microsimulations are considered an appropriate tool to describe complex structures of infection paths and disease progression and have been performed in the past for influenza 7 and recently also for Covid-19 8 . Our model summarises the net effect of all secondary infections caused by an infected individual outside its own household into an out-reproduction number R* which is the only free parameter in our model. We assume that the interactions within the household are hardly affected by social distancing strategies. Thus, the R* parameter best reflects the strength of nonpharmaceutical interventions. The stronger the interventions, the lower the R*. The mitigation strategy, however, needs to allow R* to be high enough to enable the population to reach herd immunity. We show that that the margin of R* for which successful mitigation into an overcritical but not ICU capacity-threatening epidemic can be achieved is extremely narrow, implying that this strategy is likely to fail. Moreover, we quantify the average extent to which social contacts have to be reduced in the population to achieve reasonable times for disease extinction. We present estimates in the case of subcritical epidemics for time till extinction as a function of R* and the initial number of infected individuals. The time till extinction has direct economic implications and depends strongly on R*, showing the critical importance of introducing strong social distancing measures. For Germany, at least an 80% reduction of social contacts outside households is required for the epidemic to become subcritical, and with this reduction, the time to disease extinction amounts to more than a year. An extinction time shorter than a year is only possible with a reduction of social contacts by more than 95 %. For the city of Wroc law we additionally discuss the combined effect of testing coverage and social contact reduction. High testing rates -defined here as the rate of uncovering mild cases -and household quarantine of positive cases allow for less stringent contact reduction but are on their own not sufficient to guarantee a subcritical progression of the epidemic. Finally, we estimate R* for the present situation in both countries under the assumption that no further spread-preventing actions are taken. Comparing the ratio of the present R* value with the value at which the epidemic becomes subcritical is a good indicator for the strengths of non-pharmaceutical interventions for a suc-cessful extinction strategy. For end-prevalence in the overcritical parameter domain we were able to derive theoretical predictions which match very well with the simulation results. The theoretical results show the strong impact which differences in the household size distribution have on the prevalence and demonstrate complementary to the numerical results how sensitive the prevalence depends on R* (see Appendix C).