An analytical approach to transmission dynamics of infectious diseases with waning immunity

A Yildirim, Hüseyin Koçak

Research output: Contribution to journalArticlepeer-review

4 Citations (SciVal)

Abstract

In this study, we present a mathematical model that describes the dynamics of reinfection under the assumption that the vaccine-induced immune protection may wane over time. The qualitative analysis reveals that the disease eradication depends on vaccination coverage as well as on vaccine efficacy. Using an appropriate Lyapunov function, we established that the disease-free equilibrium is globally asymptotically stable if the vaccination coverage level exceeds a certain threshold value. We combined homotopy perturbation method (HPM) and Pade approximation technique for this problem. Numerical simulations support our analytical conclusions and illustrate possible behavior scenarios of the model.
Original languageEnglish
Pages (from-to)929-940
Number of pages12
JournalJournal of Mechanics in Medicine and Biology
Volume11
Issue number4
DOIs
Publication statusPublished - Sep 2011

Keywords

  • homotopy perturbation method
  • vaccination coverage
  • Lyapunov function
  • epidemic model
  • waning immunity
  • pade technique

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