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Related Experiment Videos

An SIS epidemic model with variable population size and a delay

H W Hethcote1, P van den Driessche

  • 1Department of Mathematics, University of Iowa, Iowa City 52242, USA.

Journal of Mathematical Biology
|January 1, 1995
PubMed
Summary

This study analyzes the SIS epidemiological model, revealing how disease persistence and deaths impact population dynamics. Findings show populations can decline, stabilize, or grow, with stability depending on specific disease parameters.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Population Dynamics

Background:

  • The SIS (Susceptible-Infectious-Susceptible) model is a fundamental tool for studying infectious disease dynamics.
  • Understanding disease persistence and its impact on population size is crucial for public health.
  • Previous models often simplify the complexities of disease-induced mortality and population responses.

Purpose of the Study:

  • To analyze the SIS epidemiological model incorporating births, natural deaths, and disease-related deaths.
  • To determine the thresholds for disease persistence, equilibria, and stability.
  • To investigate the long-term effects of disease dynamics on population size and growth.

Main Methods:

  • Mathematical modeling using the SIS framework.

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  • Analysis of differential equations to determine model equilibria and stability.
  • Bifurcation analysis to identify transitions in model behavior, including Hopf bifurcations.

    • Main Results:

    • Disease persistence coupled with disease-related deaths can lead to population extinction, stabilization, or reduced exponential growth.
    • Specific parameter values dictate whether the endemic equilibrium is stable or unstable.
    • Hopf bifurcations can lead to periodic solutions around an unstable endemic equilibrium.

    Conclusions:

    • The SIS model demonstrates complex population dynamics influenced by disease parameters.
    • Disease-induced mortality is a critical factor shaping population trajectories.
    • The model highlights the potential for endemic diseases to cause significant population decline or instability.