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Mathematical Epidemiology pp 179–189Cite as

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Spatial Structure: Patch Models

Spatial Structure: Patch Models

  • P. van den Driessche7 
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Part of the Lecture Notes in Mathematics book series (LNMBIOS,volume 1945)

Discrete spatial heterogenity is introduced into disease transmission models, resulting in large systems of ordinary differential equations. Such metapopulation models describe disease spread on a number of spatial patches. In the first model considered, there is no explicit movement of individuals; rather infectives can pass the disease to susceptibles in other patches. The second type of model explicitly includes rates of travel between patches and also takes account of the resident patch as well as the current patch of individuals. A formula for and useful bounds on the basic reproduction number of the system are determined. Brief descriptions of application of this type of metapopulation model are given to investigate the spread of bovine tuberculosis and the effect of quarantine on the spread of influenza.

Keywords

  • West Nile Virus
  • Reproduction Number
  • Epidemic Model
  • Endemic Equilibrium
  • Basic Reproduction Number

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, 3060 STN CSC, Victoria, BC, V8W 3R4, Canada

    P. van den Driessche

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  1. P. van den Driessche
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Z2, Canada

    Fred Brauer

  2. Department of Mathematics and Statistics, University of Victoria, 3060 STN CSC, Victoria, B.C. V8W 3R4, Canada

    Pauline van den Driessche

  3. Center for Disease Modeling Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

    Jianhong Wu

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van den Driessche, P. (2008). Spatial Structure: Patch Models. In: Brauer, F., van den Driessche, P., Wu, J. (eds) Mathematical Epidemiology. Lecture Notes in Mathematics, vol 1945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78911-6_7

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