Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

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
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Retrospective analysis of age-specific non-pharmaceutical interventions on wild-type SARS-CoV-2 in Canada.

BMC public health·2026
Same author

Estimation of the exponential growth rate of an epidemic.

Infectious Disease Modelling·2026
Same author

Distributions of prevalence and daily new cases in a stochastic linear SEIR model.

Mathematical biosciences·2025
Same author

Estimating the effect of contact tracing during the early stage of an epidemic.

Infectious Disease Modelling·2025
Same author

A selfish supergene causes meiotic drive through both sexes in <i>Drosophila</i>.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

A mathematical model to assess the impact of testing and isolation compliance on the transmission of COVID-19.

Infectious Disease Modelling·2023
Same journal

Phenotypic plasticity trade-offs in an age-structured model of bacterial growth under stress.

Journal of mathematical biology·2026
Same journal

Intraspecific interactions facilitate mutualism across multilayer networks under weak selection.

Journal of mathematical biology·2026
Same journal

A two-species competition model on a compact metric graph for the invasion and competition of Aedes Aegypti and Aedes Albopictus mosquitoes in Florida.

Journal of mathematical biology·2026
Same journal

Superinfection and the hypnozoite reservoir for Plasmodium vivax: a multitype branching process approximation.

Journal of mathematical biology·2026
Same journal

Correction to: Superinfection and the hypnozoite reservoir for Plasmodium vivax: a general framework.

Journal of mathematical biology·2026
Same journal

Stoichiometric balance and sustained rhythms.

Journal of mathematical biology·2026
See all related articles

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.