Global behavior of solutions to an SI epidemic model with nonlinear diffusion in heterogeneous environment

In this paper, a nonlinear diffusion SI epidemic model with a general incidence rate in heterogeneous environment is studied. Global behavior of classical solutions under certain restrictions on the coefficients is considered. We first establish the global existence of classical solutions of the sys...

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 4; pp. 6779 - 6791
Main Authors Xu, Shenghu, Li, Xiaojuan
Format Journal Article
LanguageEnglish
Published AIMS Press 2022
Subjects
cross-diffusion
general incidence rate
global solution
si epidemic model
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Summary:In this paper, a nonlinear diffusion SI epidemic model with a general incidence rate in heterogeneous environment is studied. Global behavior of classical solutions under certain restrictions on the coefficients is considered. We first establish the global existence of classical solutions of the system under heterogeneous environment by energy estimate and maximum principles. Based on such estimates, we then study the large-time behavior of the solution of system under homogeneous environment. The model and mathematical results in [M. Kirane, S. Kouachi, Global solutions to a system of strongly coupled reaction-diffusion equations, Nonlinear Anal. , 26 (1996), 1387-1396.] are generalized.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022377