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Robust uniform persistence and competitive exclusion in a nonautonomous multi-strain SIR epidemic model with

Azmy S Ackleh1, Paul L Salceanu

  • 1Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70504-1010, USA, ackleh@louisiana.edu.

Journal of Mathematical Biology
|January 2, 2013
PubMed

Insights

This study analyzes a nonautonomous SIR epidemic model with multiple infection strains. Disease-induced mortality and model dynamics suggest that many strains can coexist, challenging competitive exclusion principles.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Population Dynamics

Background:

  • The SIR (Susceptible-Infected-Recovered) model is a fundamental tool in epidemiology.
  • Nonautonomous models incorporate time-varying parameters, reflecting real-world environmental changes.
  • Understanding pathogen competition is crucial for predicting disease dynamics.

Purpose of the Study:

  • To investigate the dynamics of multiple infection strains competing within a host population using a nonautonomous SIR model.
  • To determine conditions for the robust uniform persistence of host and infected subpopulations.
  • To analyze the phenomenon of competitive exclusion versus strain coexistence.

Main Methods:

  • Development and analysis of a nonautonomous SIR epidemic model.
  • Derivation of sufficient conditions for population persistence.
  • Exploration of competitive exclusion principles.
  • Numerical simulations to investigate complex dynamics.

Main Results:

  • Sufficient conditions for the uniform persistence of the total population and subpopulations were established.
  • Population persistence is influenced by growth rates from extinction and vertical disease transmission.
  • Numerical simulations indicate that many strains can coexist, contrary to simple competitive exclusion.

Conclusions:

  • The nonautonomous nature of the model and disease-induced mortality can promote the coexistence of multiple infection strains.
  • The theoretical framework is applicable to other nonautonomous epidemic models.
  • Findings challenge traditional competitive exclusion predictions in complex epidemic scenarios.

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