Traveling wave solutions in a two-group SIR epidemic model with constant recruitment

Host heterogeneity can be modeled by using multi-group structures in the population. In this paper we investigate the existence and nonexistence of traveling waves of a two-group SIR epidemic model with time delay and constant recruitment and show that the existence of traveling waves is determined by the basic reproduction number R₀. More specifically, we prove that (i) when the basic reproduction number R₀> 1 , there exists a minimal wave speed c^∗> 0 , such that for each c≥ c^∗ the system admits a nontrivial traveling wave solution with wave speed c and for c< c^∗ there exists no nontrivial traveling wave satisfying the system; (ii) when R₀≤ 1 , the system admits no nontrivial traveling waves. Finally, we present some numerical simulations to show the existence of traveling waves of the system.