A reaction–diffusion SIS epidemic model with saturated incidence rate and logistic source

Abstract

A reaction–diffusion SIS epidemic model with saturated incidence rate and logistic source for the susceptible individuals is considered. We establish the uniform bounds of parabolic system and investigate the extinction and persistence of infectious diseases in terms of the basic reproduction number. We further analyze the asymptotic profiles of the endemic equilibrium for small and large movement rates and large saturate rate. In particular, it is shown that large saturation may cause the elimination of disease and the logistic source can enhance persistence of infectious disease.

Keywords:

• SIS epidemic model with logistic source
• saturated incidence rate
• spatial heterogeneity
• endemic equilibrium
• asymptotic profile

2010 Mathematics Subject Classifications:

• 35K57
• 35J57
• 35B40
• 92D25

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Partially supported by Natural Science Foundation of Heilongjiang Province [grant number LH2020A012], Heilongjiang Provincial Postdoctoral Science Foundation [grant number LBH-Q17086] and the Fundamental Research Funds for Heilongjiang Provincial Universities [grant number 2018-KYYWF-0996].