Stability and bifurcations in an epidemic model with varying immunity period

  • Blyuss K
  • Kyrychko Y
  • 38

    Readers

    Mendeley users who have this article in their library.
  • 41

    Citations

    Citations of this article.

Abstract

An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists, it is possible to analytically prove its local and global stability using Lyapunov functionals. Bifurcation analysis is performed using DDE-BIFTOOL and traceDDE to investigate different dynamical regimes in the model using numerical continuation for different values of system parameters and different integral kernels.

Author-supplied keywords

  • Delay differential equations
  • Epidemic model
  • Varying temporary immunity

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free