Extended Bass model on the power-law epidemics growth and its implications on spatially heterogeneous systems

Abstract

This work explores the sub-exponential power-law growth that is observed in human and animal epidemics, using percolation analysis. Through numerical simulations, it identifies a large class of diffusion cases on networks that can be classified under an extended version of the discrete Bass model, with solutions that i) follow the Weibull probability distribution, ii) are consistent with the large power-law growth exponents $\beta >2$ reported for epidemics such as covid-19, and iii) have a clear physical meaning in agent-based models with specific behavioral dynamics. In particular, the Weibull power exponent is related to the restricted mobility of agents regarding social confinement. The mathematical formalism then depicts the time dependent diffusion in human (covid-19) and animal (foot-and-mouth) epidemics. In addition, it is used to describe the spatiotemporal heterogeneous diffusion over modular networks that model interconnected geographical regions and is applied in the case of covid-19 diffusion across USA Counties.