Traveling waves for a two-group epidemic model with latent period in a patchy environment

Abstract

In this paper, we derive a two-group SIR epidemic model with latent period in a patchy environment by applying discrete Fourier transform. It is assumed that the infectious disease spreads between two groups and it has a fixed latent period. When the basic reproduction number R0>1, we prove that the system admits a nontrivial traveling wave solution for each admissible speed c (namely, c>c⁎, where c⁎ is the minimal wave speed). We also show that there is no positive traveling wave solution (ϕ1,ϕ2,φ1,φ2) satisfying φi(±∞)=0,ϕi(−∞)=Si0andϕi(+∞)=S⁎i when R0≤1 and c>0, or R0>1 and c∈(0,c⁎), where i=1,2.