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Dynamics of an Infectious Disease Including Ectoparasites, Rodents and Humans

In: Trends in Biomathematics: Modeling, Optimization and Computational Problems

Author

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  • A. Dénes

    (University of Szeged, Bolyai Institute)

  • G. Röst

    (University of Szeged, Bolyai Institute)

Abstract

We present a mathematical model describing the spread of an infectious disease spread by ectoparasites which are harboured by rodents (e.g. plague transmitted by fleas spread by rats). We identify three reproduction numbers for the rodent subsystem and show that these three reproduction numbers completely characterize the global dynamics of this subsystem. Depending on which of the four equilibria of the rodent subsystem is globally attractive, we determine the possible equilibria of the human subsystem and show that one of the equilibria of this subsystem is always globally attractive. Hence we completely describe the global dynamics of the full system.

Suggested Citation

  • A. Dénes & G. Röst, 2018. "Dynamics of an Infectious Disease Including Ectoparasites, Rodents and Humans," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling, Optimization and Computational Problems, pages 59-73, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-91092-5_5
    DOI: 10.1007/978-3-319-91092-5_5
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