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Dynamics of a diffusion epidemic SIRI system in heterogeneous environment
Wenjie Li1, Ying Zhang1, Jinchen Ji2
1Department of Systems and Applied Mathematics, Kunming University of Science and Technology, Kunming, 650500 Yunnan People's Republic of China.
Abstract:
This paper studies the dynamical behaviors of a diffusion epidemic SIRI system with distinct dispersal rates. The overall solution of the system is derived by using theory and the Young's inequality. The uniformly boundedness of the solution is obtained for the system. The asymptotic smoothness of the semi-flow and the existence of the global attractor are discussed. Moreover, the basic reproduction number is defined in a spatially uniform environment and the threshold dynamical behaviors are obtained for extinction or continuous persistence of disease. When the spread rate of the susceptible individuals or the infected individuals is close to zero, the asymptotic profiles of the system are studied. This can help us to better understand the dynamic characteristics of the model in a bounded space domain with zero flux boundary conditions.
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