# 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} }

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.

## 280 Citations

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