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Two SIS epidemiologic models with delays.

H W Hethcote1, P van den Driessche

  • 1Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA. hethcote@math.uiowa.edu

Journal of Mathematical Biology
|February 9, 2000
PubMed
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This study examines Susceptible-Infected-Susceptible (SIS) epidemiologic models with logistic dynamics. It finds that periodic solutions in the infectious fraction can emerge as the population nears extinction under specific parameters.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Susceptible-Infected-Susceptible (SIS) models are crucial for understanding infectious disease dynamics.
  • Incorporating delays and variable population sizes, such as logistic growth, adds complexity to these models.
  • Previous models with exponential dynamics showed delays destabilizing equilibria.

Purpose of the Study:

  • To analyze SIS epidemiologic models with logistic population dynamics and time delays.
  • To determine thresholds and equilibria, and examine their stability.
  • To investigate the conditions under which periodic solutions arise.

Main Methods:

  • Developed SIS models incorporating logistic population dynamics and time delays representing the infectious period and disease-related deaths.

Related Experiment Videos

  • Analyzed model thresholds and equilibria.
  • Examined the stability of these equilibria.
  • Investigated the occurrence of periodic solutions under varying parameter values.

    • Main Results:

    • In SIS models with logistic dynamics, population size is variable due to disease-related deaths.
    • The stability of equilibria was examined.
    • Periodic solutions in the infectious fraction were observed to occur as the population approaches extinction for a specific set of parameter values.

    Conclusions:

    • Time delays in SIS models with logistic dynamics can lead to complex behaviors, including periodic solutions.
    • These periodic solutions are linked to population decline and approach extinction.
    • The findings highlight the importance of considering population dynamics and delays in epidemiologic modeling.