Forward-backward and period doubling bifurcations in a discrete epidemic model with vaccination and limited medical resources

Yu Jhe Huang*, Jonq Juang, Tai Yi Kuo, Yu Hao Liang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A discrete epidemic model with vaccination and limited medical resources is proposed to understand its underlying dynamics. The model induces a nonsmooth two dimensional map that exhibits a surprising array of dynamical behavior including the phenomena of the forward-backward bifurcation and period doubling route to chaos with feasible parameters in an invariant region. We demonstrate, among other things, that the model generates the above described phenomena as the transmission rate or the basic reproduction number of the disease gradually increases provided that the immunization rate is low, the vaccine failure rate is high and the medical resources are limited. Finally, the numerical simulations are provided to illustrate our main results.

Original languageEnglish
Article number77
JournalJournal of Mathematical Biology
Volume86
Issue number5
DOIs
StatePublished - May 2023

Keywords

  • A Nonsmooth two dimensional map
  • Forward-backward bifurcation
  • Limited medical resources
  • Period doubling route to Chaos
  • Vaccination

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