摘要
对在白噪声干预下的随机SIQS传染病模型的持久性与灭绝性进行了分析。通过构造合适的Lyapunov函数,利用Ito公式和Markov半群理论等相关随机微分方程的理论知识,研究了随机SIQS传染病模型的动力学行为,得到了传染病模型全局正解的存在唯一性以及疾病持久和灭绝的条件。同时探讨了环境白噪声对疾病爆发的影响,环境噪声会影响疾病的流行,大的白噪声强度会抑制疾病的爆发,并且通过数值模拟验证了所得结果。
In this paper,the extinction and persistence of stochastic SIQS epidemic model under white noise intervention is analyzed.Dynamics behavior of stochastic SIQS epidemic model is studied by constructing suitable Lyapunov function and employing related theoretic knowledge of stochastic differential equations like Ito formula,Markov semigroup theory and so on.The unique existence of global positive solutions and the conditions of disease persistence and extinction are obtained.Meanwhile,the impact of environmental white noise on disease outbreak is explored.The results show that environmental noise will affect the prevalence of disease and higher intensity white noise will suppress disease outbreak.Some numerical simulations are carried out to support the results.
作者
李海燕
韦煜明
彭华勤
LI Haiyan;WEI Yuming;PENG Huaqin(College of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541004,China)
出处
《西华师范大学学报（自然科学版）》
2019年第4期359-366,共8页
Journal of China West Normal University(Natural Sciences)
基金
国家自然科学基金项目(11771104,11701113)
广西自然基金资助项目(2018GXNSFAA294084,2018GXNSFBA281140)
广西研究生教育创新计划项目(XYCSZ2019083,JGY2019030)
