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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
Bifurcation and chaos in S-I-S epidemic model
Differential Equations and Dynamical Systems, Volume 17, No. 4, Year 2009
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Description
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. © 2009 Foundation for Scientific Research and Technological Innovation.
Authors & Co-Authors
Das, Prasenjit
India, Kolkata
Kidderpore Academy
Mukandavire, Zindoga
Taiwan, Taichung
China Medical University
Chiyaka, Christinah
Taiwan, Taichung
China Medical University
Statistics
Citations: 14
Authors: 3
Affiliations: 3
Identifiers
Doi:
10.1007/s12591-009-0028-4
ISSN:
09746870
Study Design
Cross Sectional Study