Dynamics of Stochastically Perturbed SIS Epidemic Model with Vaccination
We introduce stochasticity into an SIS epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction number R0 is a threshold which determines the persistence or extinction of the diseas...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/517439 |
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| Summary: | We introduce stochasticity into an SIS epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction number R0 is a threshold which determines the persistence or extinction of the disease. When the perturbation and the disease-related death rate are small, we carry out a detailed analysis on the dynamical behavior of the stochastic model, also regarding of the value of R0. If R0≤1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, if R0>1, there is a stationary distribution, which means that the disease will prevail. The results are illustrated by computer simulations. |
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| ISSN: | 1085-3375 1687-0409 |