Dynamics of a time-periodic two-strain SIS epidemic model with diffusion and latent period. (February 2020) - Zhao, Lin; Wang, Zhi-Cheng; Ruan, Shigui
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 R 0 i and introduce the invasion number R ˆ 0 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 R 0 i ⩽ 1 ( i = 1, 2 ), then the disease-free periodic solution is globally attractive; if R 0 i > 1 ⩾ R 0 j ( i ≠ j, i, j = 1, 2 ), then competitive exclusion, where the j th strain dies out and the i th strain persists, is a possible outcome; and if R ˆ 0 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.