Journal of Guangxi Normal University(Natural Science Edition) ›› 2015, Vol. 33 ›› Issue (4): 81-86.doi: 10.16088/j.issn.1001-6600.2015.04.014

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Dynamics Analysis of a Stochastic SIS Epidemic Model with Birth Pulses

YANG Kun, LIN Jiao, JIANG Gui-rong   

  1. School of Mathematics and Computing Science, Guilin University of Electronic Technology,Guilin Guangxi 541004, China
  • Received:2015-04-01 Online:2015-12-25 Published:2018-09-21

Abstract: A class of SIS epidemic model with birth pulse and random disturbance is investigated in this paper. The sufficient condition for the stochastic stability of trivial solution is obtained by applying the theory of stochastic differential equation. The sufficient condition for the exponentially asymptotical stability of infection-free solution is obtained by using the Lyapunov exponent. By applying It$\widehat{o}$ formula and the theory of impulsive differential equations, the global existence of positive solution is proved. Moreover, the theoretical results are finally confirmed by numerical simulations.

Key words: stochastic SIS epidemic model, birth pulses, Lyapunov exponent

CLC Number: 

  • O175
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