# Basic Reproduction Numbers for Reaction-Diffusion Epidemic Models

```@article{Wang2012BasicRN,
title={Basic Reproduction Numbers for Reaction-Diffusion Epidemic Models},
author={Wendi Wang and Xiao-Qiang Zhao},
journal={SIAM J. Appl. Dyn. Syst.},
year={2012},
volume={11},
pages={1652-1673}
}```
• Published 13 December 2012
• Mathematics
• SIAM J. Appl. Dyn. Syst.
The theory of the principal eigenvalue is developed for an elliptic eigenvalue problem associated with a linear parabolic cooperative system with some zero diffusion coefficients. Then the basic reproduction number and its computation formulae are established for reaction-diffusion epidemic models with compartmental structure. These theoretical results are applied to a spatial model of rabies to study the influence of spatial heterogeneity and population mobility on disease transmission.
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