Asymptotic profiles of the endemic equilibrium of a diffusive SIS epidemic system with saturated incidence rate and spontaneous infection

A susceptible‐infected‐susceptible (SIS) epidemic reaction‐diffusion model with saturated incidence rate and spontaneous infection is considered. We establish the existence of endemic equilibrium by using a fixed‐point theorem. The global asymptotic stability of the constant endemic equilibrium is d...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 44; no. 1; pp. 517 - 532
Main Authors Zhang, Jialiang, Cui, Renhao
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 15.01.2021
Subjects
asymptotic profile
Asymptotic properties
Diffusion effects
Diffusion rate
Disease control
endemic equilibrium
Epidemics
Existence theorems
Infections
Infectious diseases
saturated incidence rate
SIS epidemic model
small/large diffusion
spontaneous infection
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Summary:A susceptible‐infected‐susceptible (SIS) epidemic reaction‐diffusion model with saturated incidence rate and spontaneous infection is considered. We establish the existence of endemic equilibrium by using a fixed‐point theorem. The global asymptotic stability of the constant endemic equilibrium is discussed in the case of homogeneous environment. We mainly investigate the effects of diffusion and saturation on asymptotic profiles of the endemic equilibrium. When the saturated incidence rate tends to infinity, the susceptible and infective distributes in the habitat in a nonhomogeneous way; this result is in strong contrast with the case of no spontaneous infection, where the endemic equilibrium tends to the disease free equilibrium. Our analysis shows that the spontaneous infection can enhance the persistence of an infectious disease and may provide some useful implications on disease control.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6754