Abstract
<p style='text-indent:20px;'>In this paper, we study the influence of spatial-dependent variables on the basic reproduction ratio (<inline-formula><tex-math id="M1">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula>) for a scalar reaction-diffusion equation model. We first investigate the principal eigenvalue of a weighted eigenvalue problem and show the influence of spatial variables. We then apply these results to study the effect of spatial heterogeneity and dimension on the basic reproduction ratio for a spatial model of rabies. Numerical simulations also reveal the complicated effects of the spatial variables on <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> in two dimensions.</p>
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