一类具有饱和发生率的随机SIRS模型全局正解的渐近行为
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摘要
研究了一类具有饱和发生率并且移出率受到白噪声影响的随机SIRS模型.讨论了系统全局正解的存在唯一性与有界性,并通过构造Lyapunov函数,证明了当基本再生数不大于1时,无病平衡点的随机渐近稳定性,给出基本再生数大于1时,随机模型的解围绕确定性模型地方病平衡点震荡的充分条件,最后通过数值仿真验证结论.
A stochastic SIRS model with saturation incidence was explored,in which the recovery rate is influenced by white noise.The global existence,uniqueness and boundness of the positive solution of the system were discussed-and the stochastical asymptotical stability of disease-free equilibrium was proved when the basic reproduction number is not more than 1 by constructing Lyapunov function.A sufficient criteria for the solution of the stochastic model oscillating around the endemic equilibrium of the deterministic model was also given out while the basic reproduction number is more than 1.Finally,numerical simulations were presented to illustrate the mathematical findings.
A stochastic SIRS model with saturation incidence was explored,in which the recovery rate is influenced by white noise.The global existence,uniqueness and boundness of the positive solution of the system were discussed-and the stochastical asymptotical stability of disease-free equilibrium was proved when the basic reproduction number is not more than 1 by constructing Lyapunov function.A sufficient criteria for the solution of the stochastic model oscillating around the endemic equilibrium of the deterministic model was also given out while the basic reproduction number is more than 1.Finally,numerical simulations were presented to illustrate the mathematical findings.
引文
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[2]胡适耕,黄乘明,吴付科.随机微分方程[M].北京:科学出版社,2008.
[3]Rundnicki R.Long-time behavior of stochastic preypredator model[J].Stoch Proc Appl,2003,108(1):93-107.
[4]Yang Q.Jiang D,Shi N,et al.The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence[J].Math Anal Appl,2012,388(1):248-271.
[5]Mao X,Yuan C,Zou J.Stochastic differential delay equations of population dynamics[J].Math Anal Appl,2002,304(1):296-320.
[6]Carletti M.On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment[J].Math Biosci,2002,175(2):117-131.
[7]Dalai N,Greenhalgh D.Mao X R.A stochastic model for internal HIV dynamics[J].Math Anal Appl,2008,341(2):1084-1101.
[8]Kiouach D,Omari L.Stochastic asymptotic stability of a SIRS epidemic model[J].European Journal of Scientific Research,2008,24(4)s 575-579.
[9]Dalai N,Greenhalgh D,Mao X R.A stochastic model of AIDS and condom use[J].Math Anal Appl,2007,325(1):36-53.
[10]Jiang D Q,Yu J JJi C Y,et al.Asymptotic behavior of global positive solution to a stochastic SIR model[J].Math ComputModelling,2011,54(1/2):221-232.
[11]崔倩倩,张强.一类具有饱和发生率的SIRS传染病模型的全局性分析[J].四川理工学院学报,2012,25(6):83-85.