TY - JOUR
T1 - Stability Analysis of an SIS Epidemic Model in Heterogeneous Environment
AU - Bai , Xueli
AU - Du , Wenping
AU - Li , Fang
AU - Zhou , Maolin
JO - CSIAM Transactions  on Life Sciences
VL - 2
SP - 280
EP - 298
PY - 2025
DA - 2025/06
SN - 1
DO - http://doi.org/10.4208/csiam-ls.SO-2024-0007
UR - https://global-sci.org/intro/article_detail/csiam-ls/24163.html
KW - SIS epidemic model, endemic equilibrium, local stability, spatial heterogeneity.
AB - <p style="text-align: justify;">This paper studies an susceptible-infected-susceptible reaction-diffusion
model in spatially heterogeneous environment proposed in [Allen et al., Discrete Contin. Dyn. Syst., 21, 2008], where the existence and uniqueness of the endemic equilibrium are established and its stability is proposed as an open problem. However, till
now, there is no progress in the stability analysis except for special cases with either
equal diffusion coefficients or constant endemic equilibrium. In this paper, we demonstrate the first criterion in determining the stability of the non-constant endemic equilibrium with different diffusion coefficients. Thanks to this criterion, when one of the
diffusion rates is small or large, the impact of spatial heterogeneity on the stability can
be characterized based on the asymptotic behavior of the endemic equilibrium.</p>