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 R 0 is derived and a threshold-type result on its global dynamics in terms of R 0 is established. More precisely, we show that the disease-free equilibrium is globally asymptotically stable if R 0 ≤ 1 ; while there exists a positive stationary solution and the disease is uniformly persistent if R 0 > 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.