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

doi:10.1093/imammb/dqq013

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 journal › Article › peer-review

5 Scopus citations

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 language	English
Pages (from-to)	287-333
Number of pages	47
Journal	Mathematical Medicine and Biology
Volume	28
Issue number	4
DOIs	https://doi.org/10.1093/imammb/dqq013
State	Published - Dec 2011

Funding

University of Montana faculty exchange grant (to L. K.); National Academy for Integration of Research and Teaching and Learning (NAIRTL) Grant ‘Development and implementation of two project based courses “Mathematical Modelling for Biologists’ (to T.K., M.O. and A.P.); Federal Programme ‘Scientists of Innovative Russia’ (Grant 2009-1.5-507-007 to A.P.).

Funder number
2009-1.5-507-007

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 13 Climate Action

Keywords

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

Access to Document

10.1093/imammb/dqq013

Cite this

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

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.",

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note = "Funding Information: University of Montana faculty exchange grant (to L. K.); National Academy for Integration of Research and Teaching and Learning (NAIRTL) Grant {\textquoteleft}Development and implementation of two project based courses “Mathematical Modelling for Biologists{\textquoteright} (to T.K., M.O. and A.P.); Federal Programme {\textquoteleft}Scientists of Innovative Russia{\textquoteright} (Grant 2009-1.5-507-007 to A.P.).",

year = "2011",

month = dec,

doi = "10.1093/imammb/dqq013",

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volume = "28",

pages = "287--333",

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AU - Kelly, T. C.

AU - O'callaghan, M. J.

AU - Pokrovskii, A. V.

AU - Pokrovskiy, A. V.

N1 - Funding Information: University of Montana faculty exchange grant (to L. K.); National Academy for Integration of Research and Teaching and Learning (NAIRTL) Grant ‘Development and implementation of two project based courses “Mathematical Modelling for Biologists’ (to T.K., M.O. and A.P.); Federal Programme ‘Scientists of Innovative Russia’ (Grant 2009-1.5-507-007 to A.P.).

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N2 - 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.

AB - 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.

KW - Birds-ticks interaction

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KW - Population dynamics

KW - Thresholds

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

Abstract

Funding

UN SDGs

Keywords

Access to Document

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