### 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 language | English |
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Pages (from-to) | 289-302 |

Number of pages | 14 |

Journal | Mathematical Biosciences |

Volume | 63 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 1983 |

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### ASJC Scopus subject areas

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

### Cite this

*Mathematical Biosciences*,

*63*(2), 289-302. https://doi.org/10.1016/0025-5564(82)90044-X

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

Research output: Contribution to journal › Article

*Mathematical Biosciences*, vol. 63, no. 2, pp. 289-302. https://doi.org/10.1016/0025-5564(82)90044-X

}

TY - JOUR

T1 - Endemic disease in environments with spatially heterogeneous host populations

AU - Post, W. M.

AU - DeAngelis, D. L.

AU - Travis, C. C.

PY - 1983/4/1

Y1 - 1983/4/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0020735310&partnerID=8YFLogxK

U2 - 10.1016/0025-5564(82)90044-X

DO - 10.1016/0025-5564(82)90044-X

M3 - Article

AN - SCOPUS:0020735310

VL - 63

SP - 289

EP - 302

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 2

ER -