Analysis of threshold-type behaviour in mathematical models of the intrusion of a novel macroparasite in a host colony

L. V. Kalachev, T. C. Kelly, M. J. O'callaghan, A. V. Pokrovskii, A. V. Pokrovskiy

Research output: Contribution to journalArticlepeer-review

Abstract

Macroparasites include worms, ticks, mites, bugs and fleas. These parasites are well known to induce morbidity effects including a reduction in the hosts' reproductive output and survival. An important scenario is the introduction of a new macroparasite into an established host population which may be caused by the climate change and by the transport of domestic animals. The aim of the article is to demonstrate an interesting feature of this scenario using a mathematical model with four dimensionless parameters. Six possible scenarios of introducing a new macroparasite into a host colony, ranging from the elimination of the new pathogen, through guaranteed host and parasite coexistence, to the collapse of the host colony are distinguished. The threshold surfaces in the space of parameters which separate the different scenarios are found. Some special limit cases are discussed.

Original languageEnglish
Pages (from-to)287-333
Number of pages47
JournalMathematical Medicine and Biology
Volume28
Issue number4
DOIs
StatePublished - Dec 2011

Keywords

  • Birds-ticks interaction
  • Introduction of a novel macroparasite
  • Macroparasites
  • Population dynamics
  • Thresholds

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