Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage
We extend the classical SIRS epidemic model incorporating media coverage from a deterministic framework to a stochastic differential equation (SDE) and focus on how environmental fluctuations of the contact coefficient affect the extinction of the disease. We give the conditions of existence of uniq...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/891765 |
| Summary: | We extend the classical SIRS epidemic model incorporating media coverage
from a deterministic framework to a stochastic differential equation (SDE) and focus
on how environmental fluctuations of the contact coefficient affect the extinction of the
disease. We give the conditions of existence of unique positive solution and the stochastic
extinction of the SDE model and discuss the exponential p-stability and global stability of
the SDE model. One of the most interesting findings is that if the intensity of noise is large,
then the disease is prone to extinction, which can provide us with some useful control strategies
to regulate disease dynamics. |
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| ISSN: | 1085-3375 1687-0409 |