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Boundedness and asymptotic behavior of solutions for a diffusive epidemic model
Author(s) -
Touil Asma,
Youkana Amar
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4029
Subject(s) - mathematics , bounded function , infinity , class (philosophy) , reaction–diffusion system , epidemic model , diffusion , uniform boundedness , mathematical analysis , mathematical economics , computer science , physics , sociology , thermodynamics , population , demography , artificial intelligence
The aim of this paper is to study the existence and the asymptotic behavior of solutions for some reaction–diffusion equations arising in epidemic biology phenomena. We will show that for a rather broad class of nonlinearities, the solutions are global and uniformly bounded, and under suitable assumptions on the parameters of the system, these solutions converge as time goes to infinity to a disease‐free equilibrium point. Copyright © 2016 John Wiley & Sons, Ltd.