Open AccessSpatial dynamics of a diffusive SIRI model with distinct dispersal rates and heterogeneous environment
Author(s) -
Lian Duan,
Lihong Huang,
Chuangxia Huang
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021120
Subject(s) - biological dispersal , limiting , basic reproduction number , dynamics (music) , statistical physics , spatial heterogeneity , zero (linguistics) , mathematics , biology , demography , ecology , physics , population , mechanical engineering , sociology , acoustics , engineering , linguistics , philosophy
In this paper, we are concerned with the dynamics of a diffusive SIRI epidemic model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected individuals. We first establish the basic properties of solutions to the model, and then identify the basic reproduction number \begin{document}$ \mathscr{R}_{0} $\end{document} which serves as a threshold parameter that predicts whether epidemics will persist or become globally extinct. Moreover, we study the asymptotic profiles of the positive steady state as the dispersal rate of the susceptible or infected individuals approaches zero. Our analytical results reveal that the epidemics can be extinct by limiting the movement of the susceptible individuals, and the infected individuals concentrate on certain points in some circumstances when limiting their mobility.