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Evolution of Spatial Patterns in Host-Parasitoid Metapopulation Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Dynamics of an Infectious Disease Including Ectoparasites, Rodents and Humans

Authors : A. Dénes, G. Röst

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

Publisher: Springer International Publishing

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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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Literature
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A. Dénes, G. Röst, Biomathematics 1, 1209256, 1–5 (2012)
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Y. Tselentis, A. Gikas, Murine typhus, in Rickettsial Diseases, ed. by D. Raoult, Ph. Parola (CRC Press, New York, 2007)
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G. Watt, P. Kantipong, Orientia tsutsugamushi and scrub typhus, in Rickettsial Diseases, ed. by D. Raoult, Ph. Parola (CRC Press, New York, 2007)
Metadata
Title
Dynamics of an Infectious Disease Including Ectoparasites, Rodents and Humans
Authors
A. Dénes
G. Röst
Copyright Year
2018
Book
Trends in Biomathematics: Modeling, Optimization and Computational Problems

Print ISBN: 978-3-319-91091-8

Electronic ISBN: 978-3-319-91092-5

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91092-5_5

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