Journal Article

Disease emergence in multi-host epidemic models

Robert K. McCormack and Linda J. S. Allen

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 24, issue 1, pages 17-34
Published in print March 2007 | ISSN: 1477-8599
Published online March 2007 | e-ISSN: 1477-8602 | DOI:
Disease emergence in multi-host epidemic models

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  • Applied Mathematics
  • Biomathematics and Statistics


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Most pathogens are capable of infecting multiple hosts. These multiple hosts provide many avenues for the disease to emerge. In this investigation, we formulate and analyse multi-host epidemic models and determine conditions under which the disease can emerge. In particular, SIS and SIR epidemic models are formulated for a pathogen that can infect n different hosts. The basic reproduction number is computed and shown to increase with n, the number of hosts that can be infected. Therefore, the possibility of disease emergence increases with the number of hosts infected. The SIS model for two hosts is studied in detail. Necessary and sufficient conditions are derived for the global stability of an endemic equilibrium. Numerical examples illustrate the dynamics of the two- and three-host epidemic models. The models have applications to hantavirus in rodents and other zoonotic diseases with multiple hosts.

Keywords: multi-host epidemic model; basic reproduction number; hantavirus

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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