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. 
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