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Related Experiment Video

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Dynamic analysis of the recurrent epidemic model.

Hui Cao1, Dong Xue Yan2, Ao Li3

  • 1Department of Mathematics, Shaanxi University of Science and Technology, Xi'an, 710021, P.R. China.

Mathematical Biosciences and Engineering : MBE
|September 11, 2019
PubMed
Summary

This study introduces an age-structured SIRS model for recurrent infectious diseases, highlighting the significant impact of temporary immunity and time delays on disease dynamics and population behavior.

Keywords:
C0-semigroupHopf bifurcationage-structured modelasymptotical stabilityrecurrent epidemic

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Area of Science:

  • Mathematical epidemiology
  • Dynamical systems theory
  • Population dynamics

Background:

  • Recurrent infectious diseases pose significant public health challenges.
  • Understanding disease persistence requires models that account for population structure and immunity dynamics.
  • Temporary immunity and time delays are crucial factors in disease transmission.

Purpose of the Study:

  • To propose and analyze a novel SIRS model incorporating age structure and temporary immunity.
  • To investigate the impact of time delays on the stability of disease equilibria.
  • To determine conditions for Hopf bifurcation and explore non-periodic and periodic disease behaviors.

Main Methods:

  • Formulation of the SIRS model as an abstract non-densely defined Cauchy problem.
  • Analysis of global stability for the disease-free equilibrium.
  • Analysis of local stability for the endemic equilibrium.
  • Derivation of conditions for Hopf bifurcation.

Main Results:

  • Established conditions for the global stability of the disease-free equilibrium.
  • Determined the local stability of the endemic equilibrium.
  • Identified conditions for the existence of Hopf bifurcation, indicating potential for oscillations.
  • Demonstrated that time delays significantly influence disease persistence and dynamics, allowing for both non-periodic and periodic outcomes.

Conclusions:

  • The proposed age-structured SIRS model provides a robust framework for studying recurrent infectious diseases.
  • Temporary immunity and time delays are critical parameters influencing disease spread and stability.
  • The model predicts complex dynamics, including oscillations, underscoring the importance of incorporating these factors into epidemiological models.