Stability of a novel stochastic epidemic model with double epidemic hypothesis

In this paper, a novel SIR disease transmission model is formulated under double epidemic hypothesis and stochastic perturbation. We present the stability conditions of the disease-free equilibrium of the SIR model without stochastic perturbation and with stochastic perturbation. We obtain the deter...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-09, Vol.217 (2), p.506-515
Main Author: Meng, Xin-zhu
Format: Article
Language:English
Subjects:
Double epidemic hypothesis
Dynamics
Epidemics
Exact sciences and technology
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Perturbation methods
Probability theory
Sciences and techniques of general use
Stability
Stochastic epidemic model
Stochastic stability
Stochasticity
Time delay
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Summary:In this paper, a novel SIR disease transmission model is formulated under double epidemic hypothesis and stochastic perturbation. We present the stability conditions of the disease-free equilibrium of the SIR model without stochastic perturbation and with stochastic perturbation. We obtain the deterministic stability threshold β 1 ∗ ∗ and β 2 ∗ ∗ of the disease-free equilibrium, under which the disease-free equilibrium is stochastically stable such that the disease will disappear finally leaving all the population susceptible. The results show that double epidemic hypothesis and stochastic perturbation have significant effects on the dynamics behaviors of the model.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.05.083