Dynamics of a time-periodic two-strain SIS epidemic model with diffusion and latent period

Abstract

Coinfection of hosts with multiple strains or serotypes of the same agent, such as different influenza virus strains, different human papilloma virus strains, and different dengue virus serotypes, is not only a very serious public health issue but also a very challenging mathematical modeling problem. In this paper, we study a time-periodic two-strain SIS epidemic model with diffusion and latent period. We first define the basic reproduction number R0i and introduce the invasion number Rˆ0i for each strain i(i=1,2), which can determine the ability of each strain to invade the other single-strain. The main question that we investigate is the threshold dynamics of the model. It is shown that if R0i⩽1(i=1,2), then the disease-free periodic solution is globally attractive; if R0i>1⩾R0j(i≠j,i,j=1,2), then competitive exclusion, where the jth strain dies out and the ith strain persists, is a possible outcome; and if Rˆ0i>1(i=1,2), then the disease persists uniformly. Finally we present the basic framework of threshold dynamics of the system by using numerical simulations, some of which are different from that of the corresponding multi-strain SIS ODE models.