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Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media
Xiaodong Wang1, Chunxia Wang1, Kai Wang1
1Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, Xinjiang 830011 P.R. China.
Abstract:
In this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.
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