Summary
We set up a deterministic model for the spatial spread of an epidemic. Essentially, the model consists of a nonlinear integral equation which has an unique solution. We show that this solution has a temporally asymptotic limit which describes the final state of the epidemic and is the minimal solution of another nonlinear integral equation. We outline the asymptotic behaviour of this minimal solution at a great distance from the epidemic's origin and generalize D. G. Kendall's pandemic threshold theorem (1957).
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Thieme, H.R. A model for the spatial spread of an epidemic. J. Math. Biol. 4, 337–351 (1977). https://doi.org/10.1007/BF00275082
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DOI: https://doi.org/10.1007/BF00275082