A model for the spatial spread of an epidemic

H. R. Thieme

doi:10.1007/BF00275082

A model for the spatial spread of an epidemic

H. R. Thieme

Research output: Contribution to journal › Article › peer-review

137 Scopus citations

Abstract

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).

Original language	English (US)
Pages (from-to)	337-351
Number of pages	15
Journal	Journal Of Mathematical Biology
Volume	4
Issue number	4
DOIs	https://doi.org/10.1007/BF00275082
State	Published - Dec 1977
Externally published	Yes

ASJC Scopus subject areas

Modeling and Simulation
Agricultural and Biological Sciences (miscellaneous)
Applied Mathematics

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10.1007/BF00275082

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abstract = "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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A model for the spatial spread of an epidemic

Abstract

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