ZHAO Jin-qing, LIU Mao-xing, MA Yang-jun, WANG Wan-wan. Stochastic Stability and Bifurcation of an SI Epidemic Model With Double Noises[J]. Applied Mathematics and Mechanics, 2013, 34(12): 1300-1310. doi: 10.3879/j.issn.1000-0887.2013.12.009
Citation: ZHAO Jin-qing, LIU Mao-xing, MA Yang-jun, WANG Wan-wan. Stochastic Stability and Bifurcation of an SI Epidemic Model With Double Noises[J]. Applied Mathematics and Mechanics, 2013, 34(12): 1300-1310. doi: 10.3879/j.issn.1000-0887.2013.12.009

Stochastic Stability and Bifurcation of an SI Epidemic Model With Double Noises

doi: 10.3879/j.issn.1000-0887.2013.12.009
Funds:  The National Natural Science Foundation of China(10901145)
  • Received Date: 2013-05-27
  • Rev Recd Date: 2013-08-28
  • Publish Date: 2013-12-16
  • A stochastic SI epidemic model was proposed with double noises. With the stochastic averaging method and nonlinear dynamic theory, the SI epidemic model was simplified. According to the Lyapunov exponent and singular boundary theory, some new criteria ensuring the model’s local and global stochastic stability were obtained. By dint of the Lyapunov exponent of invariant measure and the stationary probability density, the stochastic bifurcation of the model was explored. Results show that the system under the effect of random factors becomes more sensitive and more unstable.
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