Spreading speed of a reaction–diffusion two-strain SIR epidemic model

In this paper, we study a non-monotonic reaction–diffusion two-strain SIR epidemic model, describing coinfection of hosts with multiple strains or serotypes of the same agent. The main question is that we investigate the spreading speed of the model, which exhibits a more complex propagating pattern. We first define the basic reproduction number [Formula: see text] and invasion number [Formula: see text] of each strain [Formula: see text], which can determine the ability of one strain to invade the other single-strain. In addition, the spreading speed and the invasion speed of each strain are denoted by [Formula: see text] and [Formula: see text], respectively. Then it is shown that if [Formula: see text], then the disease-free equilibrium is globally attractive; if [Formula: see text], then for each [Formula: see text], it happens the competitive exclusion, where the infection of the ith strain dies out and the jth strain persists; however, the infections of the two strains die out for each [Formula: see text]; if [Formula: see text] and [Formula: see text], then the infectious disease of strain [Formula: see text] invades successfully. In particular, if [Formula: see text] and [Formula: see text], then the both infectious diseases persist uniformly; if [Formula: see text] and [Formula: see text], then some infectious diseases persist uniformly. Finally, we present some numerical simulations to show the spreading behavior of this epidemic model.