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Stochastic models for competing species with a shared pathogen.

Linda J S Allen1, Vrushali A Bokil

  • 1Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States. lallen@math.ttu.edu

Mathematical Biosciences and Engineering : MBE
|August 14, 2012
PubMed
Summary
This summary is machine-generated.

Pathogens can alter species competition, leading to invasions or population declines. This study models pathogen dynamics in competing species, revealing how random chance influences invasion success and disease spread.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Epidemiology

Background:

  • Pathogens significantly impact ecological communities by altering competitive dynamics between species.
  • Stochastic (random) variations in birth, death, and transmission processes are crucial for invasion success and disease spread.
  • Understanding these dynamics is vital for predicting species coexistence and community stability.

Purpose of the Study:

  • To investigate the ecological implications of a shared pathogen in a system of n competing species.
  • To analyze both deterministic and stochastic models of disease dynamics in multispecies competition.
  • To explore how stochasticity affects species invasion, pathogen persistence, and overall community structure.

Main Methods:

  • Developed a deterministic model using ordinary differential equations for n competing species with an SIS (Susceptible-Infected-Susceptible) disease model.
  • Formulated new stochastic models using continuous-time Markov chains and stochastic differential equations.
  • Applied branching process theory to Markov chain models for estimating extinction and invasion probabilities; conducted numerical simulations.

Main Results:

  • Summarized analytical results for pathogen persistence/extinction in 2- and 3-species deterministic models.
  • Obtained new results on the stability of the infection-free state and invasion dynamics in n-1 species systems.
  • Numerical simulations illustrated disease effects on two-species competition and highlighted differences between stochastic and deterministic models.

Conclusions:

  • Stochastic variability plays a critical role in determining species invasion success and pathogen establishment in competitive systems.
  • Both deterministic and stochastic models provide insights into disease-driven ecological dynamics, with stochasticity offering a more nuanced view of invasion probabilities.
  • The findings contribute to a better understanding of how infectious diseases shape biodiversity and community structure.