Analysis of a two-patch SIS model with saturating contact rate and one- directing population dispersal

Ruixia Zhang; Shuping Li; Ruixia Zhang; Shuping Li

doi:10.3934/mbe.2022523

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 11217-11231. doi: 10.3934/mbe.2022523

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Analysis of a two-patch SIS model with saturating contact rate and one- directing population dispersal

Ruixia Zhang ^,,
Shuping Li

Department of Mathematics, North University of China, Taiyuan 030051, Shanxi, China

Academic Editor: Sen Pei

Received: 15 June 2022 Revised: 15 July 2022 Accepted: 20 July 2022 Published: 05 August 2022

In this paper, a two-patch SIS model with saturating contact rate and one-directing population dispersal is proposed. In the model, individuals can only migrate from patch 1 to patch 2. The basic reproduction number $ R_0^1 $ of patch 1 and the basic reproduction number $ R_0^2 $ of patch 2 is identified. The global dynamics are completely determined by the two reproduction numbers. It is shown that if $ R_0^1 < 1 $ and $ R_0^2 < 1 $, the disease-free equilibrium is globally asymptotically stable; if $ R_0^1 < 1 $ and $ R_0^2 > 1 $, there is a boundary equilibrium which is globally asymptotically stable; if $ R_0^1 > 1 $, there is a unique endemic equilibrium which is globally asymptotically stable. Finally, numerical simulations are performed to validate the theoretical results and reveal the influence of saturating contact rate and migration rate on basic reproduction number and the transmission scale.
- saturating contact rate,
- population dispersal,
- basic reproduction number,
- global asymptotic stability
Citation: Ruixia Zhang, Shuping Li. Analysis of a two-patch SIS model with saturating contact rate and one- directing population dispersal[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11217-11231. doi: 10.3934/mbe.2022523

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Abstract

In this paper, a two-patch SIS model with saturating contact rate and one-directing population dispersal is proposed. In the model, individuals can only migrate from patch 1 to patch 2. The basic reproduction number $ R_0^1 $ of patch 1 and the basic reproduction number $ R_0^2 $ of patch 2 is identified. The global dynamics are completely determined by the two reproduction numbers. It is shown that if $ R_0^1 < 1 $ and $ R_0^2 < 1 $, the disease-free equilibrium is globally asymptotically stable; if $ R_0^1 < 1 $ and $ R_0^2 > 1 $, there is a boundary equilibrium which is globally asymptotically stable; if $ R_0^1 > 1 $, there is a unique endemic equilibrium which is globally asymptotically stable. Finally, numerical simulations are performed to validate the theoretical results and reveal the influence of saturating contact rate and migration rate on basic reproduction number and the transmission scale.

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