Open AccessGlobal behavior of solutions to an SI epidemic model with nonlinear diffusion in heterogeneous environment
Author(s) -
Shisen Xu,
AUTHOR_ID,
Xiaojuan Li,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022377
Subject(s) - homogeneous , nonlinear system , diffusion , mathematics , reaction–diffusion system , statistical physics , mathematical analysis , thermodynamics , physics , combinatorics , quantum mechanics
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.