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

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 R₀ ⁱ and introduce the invasion number Rˆ₀ ⁱ 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 R₀ ⁱ⩽1(i=1,2), then the disease-free periodic solution is globally attractive; if R₀ ⁱ>1⩾R₀ ^j(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 Rˆ₀ ⁱ>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.