A periodic reaction-diffusion-advection SIS epidemic model with a saturated incidence function

Xiaodan Chen; Renhao Cui; Xiao-Qiang Zhao

doi:10.3934/dcds.2025156

Article Contents

2026, Volume 49: 39-74. Doi: 10.3934/dcds.2025156

This volume Previous Article Poincaré-Treshchëv mechanism in integrable Hamiltonian systems under almost-periodic perturbations Next Article Solutions for a critical elliptic system with periodic boundary condition

A periodic reaction-diffusion-advection SIS epidemic model with a saturated incidence function

1.
Y.Y.Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, China
2.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada

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

Received: May 2025

Revised: September 2025

Early access: October 10, 2025

Published online: October 10, 2025

The first author is supported by National Natural Science Foundation of China (No. 12171125) and China Scholarship Council (No. 202308230305). R. Cui was supported by National Natural Science Foundation of China (No. 12171125), and X.-Q. Zhao was supported by the NSERC of Canada (RGPIN-2019-05648 and RGPIN-2025-04963).

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Abstract

This paper is concerned with a reaction-diffusion-advection SIS (susceptible-infected-susceptible) epidemic model with a saturated incidence function in a spatio-temporally heterogeneous environment. We introduce the basic reproduction number $ \mathcal{R}_0 $ and establish the threshold dynamics for the disease transmission in terms of $ \mathcal{R}_0 $. The global attractivity of both the disease-free and endemic periodic solution are shown in the special case of equal diffusion rates. More precisely, we explore the asymptotic properties of $ \mathcal{R}_0 $ with respect to the dispersal rates, the advection rate and the total population number. We further study the monotonicity and limiting profiles of $ \mathcal{R}_0 $ with respect to the period parameter. Moreover, we determine the spatial distribution of the disease when the diffusion rate of the infected population is sufficiently small. Our findings suggest that lowering the movement rate of infected individuals is an effective strategy to eliminate the infectious disease.

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Mathematics Subject Classification: Primary: 35K57, 35B10; Secondary: 35B40, 92D25.

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