The Stability of SI Epidemic Model in Complex Networks with Stochastic Perturbation
We investigate a stochastic SI epidemic model in the complex networks. We show that this model has a unique global positive solution. Then we consider the asymptotic behavior of the model around the disease-free equilibrium and show that the solution will oscillate around the disease-free equilibriu...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/610959 |
| Summary: | We investigate a stochastic SI epidemic model in the complex networks. We show that
this model has a unique global positive solution. Then we consider the asymptotic behavior of the model
around the disease-free equilibrium and show that the solution will oscillate around the disease-free
equilibrium of deterministic system when R0≤1. Furthermore, we derive that the disease will be persistent
when R0>1. Finally, a series of numerical simulations are presented to illustrate our mathematical
findings. A new result is given such that, when R0≤1, with the increase of noise intensity the solution of
stochastic system converging to the disease-free equilibrium is faster than that of the deterministic
system. |
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| ISSN: | 1085-3375 1687-0409 |