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Stochastic epidemics in growing populations.

Tom Britton1, Pieter Trapman

  • 1Department of Mathematics, Stockholm University, 106 91, Stockholm, Sweden, tom.britton@math.su.se.

Bulletin of Mathematical Biology
|March 13, 2014
PubMed
Summary

This study models infectious disease spread in a growing population. Depending on parameters, epidemics may never start, grow slowly, or lead to endemic equilibrium.

Area of Science:

  • Mathematical epidemiology
  • Population dynamics
  • Stochastic processes

Background:

  • Super-critical linear birth and death processes model population growth.
  • Infectious disease dynamics (SIR/SEIR) are introduced into growing populations.
  • Understanding epidemic behavior in dynamic populations is crucial.

Purpose of the Study:

  • To analyze the potential outcomes of infectious disease introduction in a growing population.
  • To identify conditions leading to different epidemic scenarios.
  • To investigate the interplay between population growth and disease spread.

Main Methods:

  • Modeling a uniformly mixing population with a linear birth and death process.
  • Introducing an infectious disease (SIR or SEIR type) via a single infected individual.

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  • Analyzing three distinct epidemic scenarios: no takeoff, slow growth, or endemic equilibrium.

    • Main Results:

    • Three possible outcomes for epidemic spread were identified: never taking off, growing slower than the population, or outgrowing the population to an endemic equilibrium.
    • The specific scenario depends on the model's parameter values.
    • Parameter values determine if only no takeoff is possible, or if no takeoff and slow growth are possible, or if no takeoff and endemic equilibrium are possible.

    Conclusions:

    • The dynamics of infectious disease spread are highly sensitive to population growth rates and disease parameters.
    • Epidemic potential can range from complete absence to establishing a persistent endemic state.
    • Mathematical modeling provides insights into the complex interactions governing disease emergence in growing communities.