TRAVELING WAVES FOR A TWO-GROUP EPIDEMIC MODEL WITH LATENT PERIOD AND BILINEAR INCIDENCE IN A PATCHY ENVIRONMENT

In this paper, we consider a two-group SIR epidemic model with bilinear incidence in a patchy environment. It is assumed that the infectious disease has a fixed latent period and spreads between two groups. Firstly, when the basic reproduction number R-0 > 1 and speed c > c*, we prove that the system admits a nontrivial traveling wave solution, where c* is the minimal wave speed. Next, when R-0 <= 1 and c > 0, or R0 > 1 and c is an element of (0, c*), we also show that there is no positive traveling wave solution, where k = 1, 2. Finally, we discuss and simulate the dependence of the minimum speed c* on the parameters.

Automated summary

This paper examines the transmission patterns of a two-group SIR epidemic model with bilinear incidence in a patchy environment, discussing the dependence of minimum speed c* on parameters.