Basic reproduction numbers for reaction-diffusion epidemic models. (English) Zbl 1259.35120
Summary: 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.
MSC:
35K57 | Reaction-diffusion equations |
92D30 | Epidemiology |
35P99 | Spectral theory and eigenvalue problems for partial differential equations |
35K51 | Initial-boundary value problems for second-order parabolic systems |