Retarded Logistic Equation as a Universal Dynamic Model for the Spread of COVID-19

Abstract

ABSTRACTIn this work we propose the retarded logistic equation as a dynamic model for the spread of COVID-19 all over the world. This equation accounts for asymptomatic transmission, pre-symptomatic or latent transmission as well as contact tracing and isolation, and leads to a transparent definition of the instantaneous reproduction number R. For different parameter values, the model equation admits different classes of solutions. These solution classes correspond to, inter alia, containment of the outbreak via public health measures, exponential growth despite public health measures, containment despite reopening and second wave following reopening. We believe that the spread of COVID in every localized area such as a city, district or county can be accounted for by one of our solution classes. In regions where R > 1 initially despite aggressive epidemic management efforts, we find that if the mitigation measures are sustained, then it is still possible for R to dip below unity when far less than the region’s entire population is affected, and from that point onwards the outbreak can be driven to extinction in time. We call this phenomenon partial herd immunity. Our analysis indicates that COVID-19 is an extremely vicious and unpredictable disease which poses unique challenges for public health authorities, on account of which “case races” among various countries and states do not serve any purpose and present delusive appearances while ignoring significant determinants.