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

Authors

Chayu Yang, University of Nebraska-LincolnFollow
Jin Wang, University of Tennessee at Chattanooga

Date of this Version

7-19-2023

Citation

MBE, 20(8): 15201–15218. DOI: 10.3934/mbe.2023680

Comments

Open access.

Abstract

We consider a class of k-dimensional reaction-diusion epidemic models (k = 1; 2; • • • ) 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.