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Asymptotic profile of endemic equilibrium to a diffusive epidemic model with saturated incidence rate

1 Key Laboratory of Modern Teaching Technology, Ministry of Education, Xi’an, Shaanxi, 710062, China
2 School of Computer Science, Shaanxi Normal University, Xi’an, Shaanxi, 710119, China
3 School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi, 710119, China
4 School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, 221116, China

Special Issues: Spatial dynamics for epidemic models with dispersal of organisms and heterogenity of environment

We study the existence and asymptotic profile of endemic equilibrium (EE) of a diffusive SIS epidemic model with saturated incidence rate. By introducing the basic reproduction number R0, the existence of EE is established when $\mathcal {R}_0$ > 1. The effects of diffusion rates and the saturated coefficient on asymptotic profile of EE are investigated. Our results indicate that when the diffusion rate of susceptible individuals is small and the total population N is below a certain level, or the saturated coefficient is large, the infected population dies out, while the two populations persist if at least one of the diffusion rates of the susceptible and infected individuals is large. Finally, we illustrate the influences of the population diffusion and the saturation coefficient on this model numerically.
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Keywords SIS epidemic model; diffusion; saturated incidence rate; endemic equilibrium; asymptotic profile; extinction/persistence

Citation: Yan’e Wang , Zhiguo Wang, Chengxia Lei. Asymptotic profile of endemic equilibrium to a diffusive epidemic model with saturated incidence rate. Mathematical Biosciences and Engineering, 2019, 16(5): 3885-3913. doi: 10.3934/mbe.2019192

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