| Abstract: |
| A reaction-diffusion SIR model describing the overall population dynamics of the fox rabies is considered. The model was presented by R.M. Anderson et al to explain the epidemiological patterns observed in Europe, including 3 to 5 year cycle in fox populations infected with rabies. We study the dynamics of both the original system and its shadow system, a limiting system of the original SIR model in which the diffusion rate of the rabid foxes tends to infinity. In addition, we show the convergence property between solutions of the original system and its shadow system. Moreover, the basic reproduction number of the shadow system is defined and shown to give a sharp threshold that determines whether or not the disease dies out. |
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