Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate

Renhao Cui

doi:10.3934/dcdsb.2020217

Article Contents

2021, Volume 26, Issue 6: 2997-3022. Doi: 10.3934/dcdsb.2020217

This issue Previous Article Lyapunov exponents of discrete quasi-periodic gevrey Schrödinger equations Next Article The Keller-Segel system with logistic growth and signal-dependent motility

Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate

Renhao Cui^,

Y.Y.Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, China

^* Corresponding author: Renhao Cui
^* Corresponding author: Renhao Cui

Received: December 2019

Revised: May 2020

Early access: July 2020

Published: June 2021

Renhao Cui is partially supported by National Natural Science Foundation of China (No.11571364), Natural Science Foundation of Heilongjiang Province (JJ2016ZR0019) and the Fundamental Research Funds for Heilongjiang Provincial Universities (2018-KYYWF-0996)

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Abstract

In this paper, we consider a reaction-diffusion SIS epidemic model with saturated incidence rate in advective heterogeneous environments. The existence of the endemic equilibrium (EE) is established when the basic reproduction number is greater than one. We further investigate the effects of diffusion, advection and saturation on asymptotic profiles of the endemic equilibrium. The individuals concentrate at the downstream end when the advection rate tends to infinity. As the the diffusion rate of the susceptible individuals tends to zero, a certain portion of the susceptible population concentrates at the downstream end, and the remaining portion of the susceptible population distributes in the habitat in a non-homogeneous way; on the other hand, the density of infected population is positive on the entire habitat. The density of the infected vanishes on the habitat for small diffusion rate of infected individuals or the large saturation. The results may provide some implications on disease control and prediction.

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Mathematics Subject Classification: Primary: 35K57, 35J57, 35B40, 92D25.

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