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| Dynamics of a Diffusive SIR Epidemic Model with Time Delay |
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| KeyWord:Diffusion SIR epidemic model time delay basic reproduction number stability Lyapunov functional |
| Author Name | Affiliation | | Bounsanong Sounvoravong | College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China (Permanent address: Department of Mathematics, Faculty of Science, National University of Laos, Vientiane Capital, DongDok Campus, P.O. Box 7322, Laos) | | Shangjiang Guo | College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China |
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| Abstract: |
| This paper is devoted to a reaction-diffusion system for a SIR epidemic model with time delay and incidence rate. Firstly, the nonnegativity and boundedness of solutions determined by nonnegative initial values are obtained. Secondly, the existence and local stability of the disease-free equilibrium as well as the endemic equilibrium are investigated by analyzing the characteristic equations. Finally, the global asymptotical stability are obtained via Lyapunov functionals. |
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