Influence of Human Behavior on COVID-19 Dynamics Based on a Reaction-Diffusion Model.

To investigate the influence of human behavior on the spread of COVID-19, we propose a reaction-diffusion model that incorporates contact rate functions related to human behavior. The basic reproduction number R0 is derived and a threshold-type result on its global dynamics in terms of R0 is established. More precisely, we show that the disease-free equilibrium is globally asymptotically stable if R0 ≤ 1; while there exists a positive stationary solution and the disease is uniformly persistent if R0 > 1. By the numerical simulations of the analytic results, we find that human behavior changes may lower infection levels and reduce the number of exposed and infected humans.