Publication Date:
2014-10-22
Description:
In this paper, we extend the deterministic single-group MSIRS epidemic model to a multi-group model, and we also extend the deterministic multi-group framework to a stochastic one and formulate it as a stochastic differential equation. In the deterministic multi-group model, the basic reproduction number R0 is a threshold that completely determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show that if R0〉1, then the disease will prevail, the infective condition persists and the endemic state is asymptotically stable in a feasible region. If R0⩽1, then the infective condition disappears and the disease dies out. For the stochastic version, we perform a detailed analysis on the asymptotic behavior of the stochastic model, which also depends on the value of R0, when R0〉1, we determine the asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time-averaged data. Numerical methods are used to illustrate the dynamic behavior of the model and to solve the systems.
Print ISSN:
1687-1839
Electronic ISSN:
1687-1847
Topics:
Mathematics
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