Publication Date:
2015-10-24
Description:
In this paper, we introduce stochasticity into a model of SIR with density dependent birth rate. We show that the model possesses non-negative solutions as desired in any population dynamics. We also carry out the globally asymptotical stability of the equilibrium through the stochastic Lyapunov functional method if R 0 ≤ 1 . Furthermore, when R 0 〉 1 , we give the asymptotic behavior of the stochastic system around the endemic equilibrium of the deterministic model and show that the solution will oscillate around the endemic equilibrium. We consider that the disease will prevail when the white noise is small and the death rate due to disease is limited.
Print ISSN:
1687-1839
Electronic ISSN:
1687-1847
Topics:
Mathematics
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