Effective containment explains sub-exponential growth in confirmed cases of recent COVID-19 outbreak in Mainland China

Benjamin F Maier; Dirk Brockmann

Initially, a small fraction of infecteds yields an exponential growth if the basic reproduction number is larger than unity. When the supply of susceptibles is depleted, the epidemic reaches a maximum and the infecteds decline. A simple reduction of contacts caused by isolation policies could be associated with a reduction in the effective reproduction number, which would, however, still yield an exponential growth in the fraction of infecteds as long as R 0 > 1, inconsistent with the observed scaling law t µ discussed above. To test the hypothesis that the observed growth behavior can be caused by isolation policies that apply to both, infected and susceptible individuals, by effective public shutdown policies, we extend the SIR model by two additional mechanisms one of which can be interpreted as a process of removing susceptibles from the transmission process. First, we assume that general public containment policies or individual behavioral changes in response to the epidemic effectively remove individuals from the interaction dynamics or significantly reduce their participation in the transmission dynamics. Secondly, we account for the removal of symptomatic infected individuals by quarantine procedures. The dynamics is governed by the system of ordinary differential equations: