Bifurcation and chaos in S-I-S epidemic model

Prasenjit Das, Zindoga Mukandavire, Christinah Chiyaka, Ayan Sen, Debasis Mukherjee

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We present a Susceptible-Infective-Susceptible (S-I-S) model with two distinct discrete time delays representing a period of temporary immunity of newborns and a disease incubation period with randomly fluctuating environment. The stability of the equilibria is robustly investigated for the case with and without delay. Conditions for supercritical and subcritical Hopf bifurcation are derived. Comprehensive numerical simulations show that adding delay to an epidemic model could change the asymptotic stability of the system, altering the location of (stable or unstable) endemic equilibrium, or even leading to chaotic behavior. Further, simulation results illustrate that, in some cases where the disease becomes endemic in the model system without delay, addition of delays for temporary immunity and incubation period facilitates smaller final infective population sizes, even if endemicity is still maintained. Effects of randomness of the environment in terms of white noise are thoroughly investigated jointly with delay. The results demonstrate that there are no significant differences in dynamical behaviour of the system when considering delay solely or jointly with stochasticity.

Original languageEnglish
Pages (from-to)393-417
Number of pages25
JournalDifferential Equations and Dynamical Systems
Volume17
Issue number4
DOIs
Publication statusPublished - 1 Sep 2009
Externally publishedYes

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Bifurcation and Chaos
Epidemic Model
Chaos theory
Hopf bifurcation
White noise
Asymptotic stability
Immunity
Time delay
Computer simulation
Endemic Equilibrium
Stochasticity
Chaotic Behavior
Population Size
Dynamical Behavior
Hopf Bifurcation
Asymptotic Stability
Randomness
Discrete-time
Unstable
Distinct

Keywords

  • Delay
  • Equilibria
  • SIS model
  • Stability
  • Stochasticity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Bifurcation and chaos in S-I-S epidemic model. / Das, Prasenjit; Mukandavire, Zindoga; Chiyaka, Christinah; Sen, Ayan; Mukherjee, Debasis.

In: Differential Equations and Dynamical Systems, Vol. 17, No. 4, 01.09.2009, p. 393-417.

Research output: Contribution to journalArticle

Das, Prasenjit ; Mukandavire, Zindoga ; Chiyaka, Christinah ; Sen, Ayan ; Mukherjee, Debasis. / Bifurcation and chaos in S-I-S epidemic model. In: Differential Equations and Dynamical Systems. 2009 ; Vol. 17, No. 4. pp. 393-417.
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