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Epidemic Models with Population Dispersal

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Mathematics for Life Science and Medicine

Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

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Summary

The purpose of this chapter is to outline recent advances of mathematical models in the studies of epidemic diseases in heterogeneous geography. Section 4.1 presents a model with the immigration of infectives from outside the population. Section 4.2 introduces multi patches into epidemic models but assume that the population size in each patch is constant in time. One objective is to discuss conditions under which patches become synchronised. The second objective is to consider the invasion of malaria into a population distributed in distinct patches. In Sect. 4.3, a demographic structure is incorporated into the epidemic models with multi patches. The basic reproduction number of the model is established. Section 4.4 changes the mass action incidence to a standard incidence. Section 4.5 further considers the residence of individuals, which make mathematical models more accurate.

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Authors and Affiliations

  1. Department of Mathematics, Southwest China Normal University, China

    Wendi Wang

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  1. Wendi Wang
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Editors and Affiliations

  1. Faculty of Engineering, Department of Systems Engineering, Shizuoka University, Hamamatsu 3-5-1, 432-8561, Shizuoka, Japan

    Yasuhiro Takeuchi  & Kazunori Sato  & 

  2. Department of Biology, Kyushu University, 812-8581, Fukuoka, Japan

    Yoh Iwasa

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Wang, W. (2007). Epidemic Models with Population Dispersal. In: Takeuchi, Y., Iwasa, Y., Sato, K. (eds) Mathematics for Life Science and Medicine. Biological and Medical Physics, Biomedical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34426-1_4

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