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An SIS epidemic model with individual variation.

Philip K Pollett1

  • 1School of Mathematics and Physics, The University of Queensland, Qld 4072, Australia.

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Summary

This study extends the stochastic Susceptible-Infectious-Susceptible (SIS) model to include individual variations. We identified conditions under which an infection can become endemic in a growing population.

Keywords:
EpidemicsMarkov processesSIS Modellimit theoremsquasi stationarity

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Stochastic Processes

Background:

  • The standard Susceptible-Infectious-Susceptible (SIS) model is a foundational tool in epidemiology.
  • However, it often assumes homogeneous mixing and identical individuals, which may not reflect real-world scenarios.
  • Accounting for individual variation is crucial for accurate disease modeling.

Purpose of the Study:

  • To extend the continuous-time stochastic SIS model by incorporating heterogeneity among individuals.
  • To analyze the large population limit of this extended model.
  • To determine the conditions necessary for an infectious disease to become endemic.

Main Methods:

  • Development of a continuous-time stochastic SIS model with individual-based variations.
  • Mathematical analysis of the model's behavior in the limit of large population sizes.
  • Derivation of endemicity conditions based on model parameters and population dynamics.

Main Results:

  • The extended stochastic SIS model successfully incorporates individual variability.
  • The analysis of the large population limit provides insights into disease persistence.
  • Specific conditions for the establishment and maintenance of endemic infections were derived.

Conclusions:

  • Individual variation significantly influences disease dynamics and endemicity thresholds.
  • The developed model offers a more realistic framework for studying infectious disease spread.
  • This work contributes to understanding the factors that sustain epidemics in heterogeneous populations.