Open AccessAnalysis on a diffusive SIS epidemic system with linear source and frequency-dependent incidence function in a heterogeneous environment
Author(s) -
Jin Zhe Suo,
Bo Li
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.2020023
Subject(s) - persistence (discontinuity) , basic reproduction number , diffusion , incidence (geometry) , function (biology) , population , mathematics , constant (computer programming) , epidemic model , reaction–diffusion system , statistical physics , mathematical analysis , physics , demography , computer science , biology , thermodynamics , evolutionary biology , geotechnical engineering , geometry , sociology , engineering , programming language
In this paper, we consider a diffusive SIS epidemic reaction-diffusion model with linear source in a heterogeneous environment in which the frequency-dependent incidence function is SI /( c + S + I ) with c a positive constant. We first derive the uniform bounds of solutions, and the uniform persistence property if the basic reproduction number $\mathcal{R}_{0}>1$. Then, in some cases we prove that the global attractivity of the disease-free equilibrium and the endemic equilibrium. Lastly, we investigate the asymptotic profile of the endemic equilibrium (when it exists) as the diffusion rate of the susceptible or infected population is small. Compared to the previous results [1, 2] in the case of c =0, some new dynamical behaviors appear in the model studied here; in particular, $\mathcal{R}_{0}$ is a decreasing function in c ∈[0, ∞) and the disease dies out once c is properly large. In addition, our results indicate that the linear source term can enhance the disease persistence.