A reaction-diffusion-advection SIS epidemic model with linear external source and open advective environments

Xu Rao; Guohong Zhang; Xiaoli Wang

doi:10.3934/dcdsb.2022014

Article Contents

2022, Volume 27, Issue 11: 6655-6677. Doi: 10.3934/dcdsb.2022014

This issue Previous Article Studies on reversal permanent charges and reversal potentials via classical Poisson-Nernst-Planck systems with boundary layers Next Article On dynamics and stationary pattern formations of a diffusive predator-prey system with hunting cooperation

A reaction-diffusion-advection SIS epidemic model with linear external source and open advective environments

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

^* Corresponding author: Guohong Zhang
^* Corresponding author: Guohong Zhang

Received: August 31, 2021

Revised: November 30, 2021

Early access: January 2022

Published: October 2022

G.-H. Zhang is partially supported by grants from National Science Foundation of China(11871403); X.-L. Wang is partially supported by grants from Fundamental Research Funds for the Central Universities (XDJK2020B050)

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Abstract

In this paper, we propose a reaction-diffusion-advection SIS epidemic model with linear external source to study the effects of open advective environments on the persistence and extinction of infectious diseases. Threshold-type results on the global dynamics in terms of the basic reproduction number $ \mathcal{R}_{0} $ are established. It is found that the introduction of open advective environments leads to different monotonicity and asymptotic properties of the basic reproduction number $ \mathcal{R}_0 $ with respect to the diffusion rate $ d_I $ and advection speed $ q $. Our analytical results suggest that increasing the advection speed or decreasing the diffusion rate of infected individuals helps to eradicate the diseases in open advective environments.

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Mathematics Subject Classification: Primary: 35K57, 35J57, 92D30; Secondary: 35B40, 92D25.

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Figure 1. Illustration of the parameter regions of $ (d_{I}, q) $ in Theorem 1.4 and Theorem 1.5 on condition that $ \int_{0}^{L}\beta(x)\;dx>\int_{0}^{L}\gamma(x)\;dx $ and $ \int_{0}^{L}\beta(x)\;dx<\int_{0}^{L}\gamma(x)\;dx $, respectively. The curve is determined by $ \mathcal{R}_0(d_I, q_1(d_I)) = 1, d_I \in (0, \infty) $ and $ \mathcal{R}_0(d_I, q_2(d_I)) = 1, d_I \in (0, d_I^*) $

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