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Basic Reproduction Numbers for a Class of Reaction-Diffusion Epidemic Models

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Abstract

We study the basic reproduction numbers for a class of reaction-diffusion epidemic models that are developed from autonomous ODE systems. We present a general numerical framework to compute such basic reproduction numbers; meanwhile, the numerical formulation provides useful insight into their characterizations. Using matrix analysis, we show that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important cases that include, among others, a single infected compartment, constant diffusion rates, uniform diffusion patterns among the infected compartments, and partial diffusion in the system.

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Acknowledgements

This work was partially supported by the National Institutes of Health under Grant Number 1R15GM131315. The authors are grateful to the two anonymous referees for their helpful comments that have significantly improved the original manuscript.

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  1. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA

    Chayu Yang & Jin Wang

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  1. Chayu Yang
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  2. Jin Wang
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Correspondence to Jin Wang.

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Yang, C., Wang, J. Basic Reproduction Numbers for a Class of Reaction-Diffusion Epidemic Models. Bull Math Biol 82, 111 (2020). https://doi.org/10.1007/s11538-020-00788-x

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