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Journal of Mathematical Biology

, Volume 66, Issue 6, pp 1123–1153 | Cite as

High host density favors greater virulence: a model of parasite–host dynamics based on multi-type branching processes

  • K. Borovkov
  • R. Day
  • T. Rice
Article

Abstract

We use a multitype continuous time Markov branching process model to describe the dynamics of the spread of parasites of two types that can mutate into each other in a common host population. While most mathematical models for the virulence of infectious diseases focus on the interplay between the dynamics of host populations and the optimal characteristics for the success of the pathogen, our model focuses on how pathogen characteristics may change at the start of an epidemic, before the density of susceptible hosts decline. We envisage animal husbandry situations where hosts are at very high density and epidemics are curtailed before host densities are much reduced. The use of three pathogen characteristics: lethality, transmissibility and mutability allows us to investigate the interplay of these in relation to host density. We provide some numerical illustrations and discuss the effects of the size of the enclosure containing the host population on the encounter rate in our model that plays the key role in determining what pathogen type will eventually prevail. We also present a multistage extension of the model to situations where there are several populations and parasites can be transmitted from one of them to another. We conclude that animal husbandry situations with high stock densities will lead to very rapid increases in virulence, where virulent strains are either more transmissible or favoured by mutation. Further the process is affected by the nature of the farm enclosures.

Keywords

Epidemics Virulence Multitype branching process 

Mathematics Subject Classification

Primary 60J85 Secondary 90D30 60J80 92B99 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe University of MelbourneParkvilleAustralia
  2. 2.Department of ZoologyThe University of MelbourneParkvilleAustralia

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