A diffusive SIS epidemic model in a heterogeneous and periodically evolvingenvironment

Liqiong Pu; Zhigui Lin; Liqiong Pu; Zhigui Lin

doi:10.3934/mbe.2019153

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 3094-3110. doi: 10.3934/mbe.2019153

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A diffusive SIS epidemic model in a heterogeneous and periodically evolvingenvironment

Liqiong Pu ^1,2,
Zhigui Lin ^{1
,
,}

1.
School of Mathematical Science, Yangzhou University, Yangzhou 225002, China
2.
School of Mathematics and Statistics, Hexi University, Zhangye 734000, China

Received: 29 December 2018 Accepted: 18 March 2019 Published: 10 April 2019

To explore the impact of the periodic evolution in habitats on the prevention and control of the infectious disease, we consider a diffusive SIS epidemic model in a heterogeneous and periodically evolving domain. By assuming that the evolving domain is uniform and isotropic, the epidemic model in a evolving domain is converted to the reaction diffusion problem in a fixed domain. The basic reproduction number, which depends on the evolving rate of the domain and spatial heterogeneity, is defined. The driving mechanism of the model is obtained by using the principal eigenvalue and the upper and lower solutions method, and a biological explanation of the impact of regional evolution on disease is given. Our theoretical results and numerical simulations show that small evolving rate benefits the control of the infectious disease.
- diffusive SIS model,
- basic reproduction number,
- heterogeneous environment,
- evolving domain,
- stability
Citation: Liqiong Pu, Zhigui Lin. A diffusive SIS epidemic model in a heterogeneous and periodically evolvingenvironment[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 3094-3110. doi: 10.3934/mbe.2019153

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Abstract

To explore the impact of the periodic evolution in habitats on the prevention and control of the infectious disease, we consider a diffusive SIS epidemic model in a heterogeneous and periodically evolving domain. By assuming that the evolving domain is uniform and isotropic, the epidemic model in a evolving domain is converted to the reaction diffusion problem in a fixed domain. The basic reproduction number, which depends on the evolving rate of the domain and spatial heterogeneity, is defined. The driving mechanism of the model is obtained by using the principal eigenvalue and the upper and lower solutions method, and a biological explanation of the impact of regional evolution on disease is given. Our theoretical results and numerical simulations show that small evolving rate benefits the control of the infectious disease.

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