Endemic disease in environments with spatially heterogeneous host populations

W. M. Post, D. L. DeAngelis, C. C. Travis

Research output: Contribution to journalArticle

46 Citations (Scopus)

Abstract

The main interest in epidemic models stems from their use in uncovering certain qualitative features of epidemic processes. A deterministic model of a general epidemic in a population with an arbitrary number of separate population centers is presented. The mixing within each center is assumed to be homogeneous, and the usual threshold theorem holds for each population. The mixing between centers is nonhomogeneous. This model is used to identify the necessary and sufficient conditions under which a disease will become endemic in the general population when each population center is below the threshold required for establishment of the disease and does not mix with other centers. These conditions depend critically on the concavity of the infection rate function with respect to the length of host-vector time. The application of these results to hoste-vector models is discussed.

Original languageEnglish
Pages (from-to)289-302
Number of pages14
JournalMathematical Biosciences
Volume63
Issue number2
DOIs
StatePublished - Apr 1 1983

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Endemic Diseases
Population
Rate Function
Concavity
Epidemic Model
Deterministic Model
Infection
endemic diseases
Necessary Conditions
stems
Sufficient Conditions
Arbitrary
Theorem
Model
infection

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Endemic disease in environments with spatially heterogeneous host populations. / Post, W. M.; DeAngelis, D. L.; Travis, C. C.

In: Mathematical Biosciences, Vol. 63, No. 2, 01.04.1983, p. 289-302.

Research output: Contribution to journalArticle

Post, W. M. ; DeAngelis, D. L. ; Travis, C. C. / Endemic disease in environments with spatially heterogeneous host populations. In: Mathematical Biosciences. 1983 ; Vol. 63, No. 2. pp. 289-302.
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