Concentration phenomenon of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with spontaneous infection

Chengxia Lei; Xinhui Zhou

doi:10.3934/dcdsb.2021174

Article Contents

2022, Volume 27, Issue 6: 3077-3100. Doi: 10.3934/dcdsb.2021174

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Concentration phenomenon of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with spontaneous infection

Chengxia Lei^, and
Xinhui Zhou

School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu Province, China

^* Corresponding author: Chengxia Lei
^* Corresponding author: Chengxia Lei

Received: February 2021

Revised: May 2021

Published: June 2022

The research was partially supported by NSF of China (No. 11971454, 11801232, 11671175), the Priority Academic Program Development of Jiangsu Higher Education Institutions, the Natural Science Foundation of the Jiangsu Province(No. BK20180999), the Foundation of Jiangsu Normal University (No. 17XLR008)

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Abstract

In this paper, we investigate the effect of spontaneous infection and advection for a susceptible-infected-susceptible epidemic reaction-diffusion-advection model in a heterogeneous environment. The existence of the endemic equilibrium is proved, and the asymptotic behaviors of the endemic equilibrium in three cases (large advection; small diffusion of the susceptible population; small diffusion of the infected population) are established. Our results suggest that the advection can cause the concentration of the susceptible and infected populations at the downstream, and the spontaneous infection can enhance the persistence of infectious disease in the entire habitat.

Keywords:

Reaction-diffusion-advection SIS epidemic model,
spontaneous infection,
endemic equilibrium,
concentration.

Mathematics Subject Classification: Primary: 35K57, 35B32; Secondary: 92D25.

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