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**An epidemic model in a patchy environment.**
*(English)*
Zbl 1048.92030

Summary: An epidemic model is proposed to describe the dynamics of disease spread among patches due to population dispersal. We establish a threshold above which the disease is uniformly persistent and below which disease-free equilibrium is locally attractive, and globally attractive when both susceptible and infective individuals in each patch have the same dispersal rate.

Two examples are given to illustrate that population dispersal plays an important role for the disease spread. The first one shows that population dispersal can intensify the disease spread if the reproduction number for one patch is large, and can reduce the disease spread if the reproduction numbers for all patches are suitable and the population dispersal rate is strong. The second example indicates that a population dispersal results in the spread of the disease in all patches, even though the disease can not spread in each isolated patch.

Two examples are given to illustrate that population dispersal plays an important role for the disease spread. The first one shows that population dispersal can intensify the disease spread if the reproduction number for one patch is large, and can reduce the disease spread if the reproduction numbers for all patches are suitable and the population dispersal rate is strong. The second example indicates that a population dispersal results in the spread of the disease in all patches, even though the disease can not spread in each isolated patch.

### MSC:

92D30 | Epidemiology |

37N25 | Dynamical systems in biology |

34C60 | Qualitative investigation and simulation of ordinary differential equation models |

34D99 | Stability theory for ordinary differential equations |

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\textit{W. Wang} and \textit{X.-Q. Zhao}, Math. Biosci. 190, No. 1, 97--112 (2004; Zbl 1048.92030)

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