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An analysis of the coexistence of two host species with a shared pathogen

Zhi-Min Chen1, W G Price

  • 1School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK. zhimin@soton.ac.uk

Journal of Mathematical Biology
|November 6, 2007
PubMed

Insights

A shared pathogen can enable two host species to coexist persistently or periodically. Intrinsic growth rates significantly influence these population dynamics, with very small rates potentially causing weak, unobservable periodicity.

Area of Science:

  • Mathematical Biology
  • Epidemiology
  • Population Ecology

Background:

  • Infectious diseases and pathogens significantly impact host population dynamics.
  • Understanding interspecies interactions under disease pressure is crucial for ecological stability.
  • Mathematical models are essential tools for analyzing complex population dynamics.

Purpose of the Study:

  • To investigate the population dynamics of two host species sharing a pathogen.
  • To determine conditions for host species coexistence (persistent or periodic) under disease transmission.
  • To analyze the role of intrinsic growth rates in shaping these dynamics.

Main Methods:

  • Utilized the Holt-Pickering mathematical model for population dynamics.
  • Employed rigorous mathematical analysis and a numerical scheme.
  • Focused on direct pathogen transmission between the two host species.

Main Results:

  • Identified specific circumstances where a shared pathogen promotes two-host species coexistence.
  • Demonstrated that intrinsic growth rates (birth rate minus death rate) are key factors controlling coexistence.
  • Observed that very small positive intrinsic growth rates can lead to weak, potentially unobservable periodicity.

Conclusions:

  • Shared pathogens can be a driver for the stable coexistence of multiple host species.
  • Intrinsic growth rates critically modulate the stability and nature (persistent vs. periodic) of host populations.
  • The model suggests that weak periodic dynamics might occur but may be difficult to detect empirically.

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