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.
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Acknowledgements
A. Dénes was supported by Hungarian Scientific Research Fund OTKA PD and National Research, Development and Innovation Office NKFIH KH 125628 and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. G. Röst was supported by the EU-funded Hungarian grant EFOP-3.6.1-16-2016-00008 and Marie Sklodowska-Curie Grant No. 748193.
A. Dénes thanks to the International Union of Biological Sciences (IUBS) for partial support of living expenses in Moscow, during the 17th BIOMAT International Symposium, October 29–November 04, 2017.
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Dénes, A., Röst, G. (2018). Dynamics of an Infectious Disease Including Ectoparasites, Rodents and Humans. In: Mondaini, R. (eds) Trends in Biomathematics: Modeling, Optimization and Computational Problems. Springer, Cham. https://doi.org/10.1007/978-3-319-91092-5_5
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DOI: https://doi.org/10.1007/978-3-319-91092-5_5
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