Computation of the basic reproduction numbers for reaction-diffusion epidemic models

Chayu Yang; Jin Wang; Chayu Yang; Jin Wang

doi:10.3934/mbe.2023680

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 15201-15218. doi: 10.3934/mbe.2023680

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Computation of the basic reproduction numbers for reaction-diffusion epidemic models

Chayu Yang ¹,
Jin Wang ^{2
,
,}

1.
Department of Mathematics, University of Nebraska-Lincoln, 1400 R Street, Lincoln, NE 68588, USA
2.
Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403, USA

Academic Editor: Xiang-Sheng Wang

Received: 28 April 2023 Revised: 19 June 2023 Accepted: 14 July 2023 Published: 19 July 2023

We consider a class of $ k $-dimensional reaction-diffusion epidemic models ($ k = 1, 2, \cdots $) that are developed from autonomous ODE systems. We present a computational approach for the calculation and analysis of their basic reproduction numbers. Particularly, we apply matrix theory to study the relationship between the basic reproduction numbers of the PDE models and those of their underlying ODE models. We show that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important scenarios. We additionally provide two numerical examples to verify our analytical results.
- reaction-diffusion systems,
- numerical calculation,
- matrix analysis
Citation: Chayu Yang, Jin Wang. Computation of the basic reproduction numbers for reaction-diffusion epidemic models[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 15201-15218. doi: 10.3934/mbe.2023680

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Abstract

We consider a class of $ k $-dimensional reaction-diffusion epidemic models ($ k = 1, 2, \cdots $) that are developed from autonomous ODE systems. We present a computational approach for the calculation and analysis of their basic reproduction numbers. Particularly, we apply matrix theory to study the relationship between the basic reproduction numbers of the PDE models and those of their underlying ODE models. We show that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important scenarios. We additionally provide two numerical examples to verify our analytical results.

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