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Mathematical Medicine and Biology Advance Access originally published online on September 29, 2006
Mathematical Medicine and Biology 2007 24(1):17-34; doi:10.1093/imammb/dql021
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Disease emergence in multi-host epidemic models

Robert K. McCormack** and Linda J. S. Allen

Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA

** Email: rmccormack16{at}hotmail.com


  Abstract

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

Accepted on 25 August 2006.


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