Open AccessDynamics and asymptotic profiles of steady states of an SIRS epidemic model in spatially heterogenous environment
Author(s) -
Baoxiang Zhang,
Yongli Cai,
Bingxian Wang,
Weiming Wang
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020047
Subject(s) - basic reproduction number , dynamics (music) , epidemic model , diffusion , statistical physics , reaction–diffusion system , mathematics , econometrics , mechanics , control theory (sociology) , environmental science , physics , computer science , demography , control (management) , mathematical analysis , thermodynamics , population , sociology , acoustics , artificial intelligence
This paper performs qualitative analysis on a reaction-diffusion SIRS epidemic system with ratio-dependent incidence rate in spatially heterogeneous environment. The threshold dynamics in the term of the basic reproduction number R 0 is established. And the asymptotic profile of endemic equilibrium is determined if the diffusion rate of the susceptible individuals is small. The results show that restricting the movement of susceptible individuals can effectively control the number of infectious individuals.