Traveling waves of the SIR epidemic model with discrete diffusion and treatment

Abstract

In a recent paper (Deng and Zhang, 2021), Deng and Zhang studied a discrete diffusive SIR epidemic model with treatment, and obtained some existence result for R0>1 and c≥c∗ and nonexistence results for R0>1 and 0<c<c∗ or R0<1 on the traveling waves with speed c, where R0 denotes the basic reproduction number and c∗>0 is a critical number. However, the convergence of susceptible component as the wave variable goes to infinity remains open. In this paper, we aim to solve this open problem and estimate the L1−norm of infectious components. Moreover, we establish the nonexistence of traveling waves with any non-positive speed c≤0 for R0>1.