摘要
考虑了一类恢复率受到环境噪声影响的随机SIS流行病模型,并研究了其渐近行为.通过停时及Lyapunov分析法,首先证明了模型正解的全局存在惟一性和有界性.其次证明了当基本再生数不大于1时,无病平衡点是随机渐近稳定,此时疾病将绝灭;当基本再生数大于1时,通过计算随机模型的解与确定性模型地方病平衡点之间差距的时间均值,得到了随机模型的解围绕确定性模型地方病平衡点振荡,并得到了系统平均持续和疾病绝灭的充分条件.最后,通过数值仿真验证了本文的理论结果.
In this paper, we consider a stochastic SIS epidemic model in which the recovery rate is influenced by white noise in the environment, and the asymptotic behavior of this model is studied. With the help of stopping time and Lyapunov analysis method, we first show the global existence, uniqueness and boundedness of the positive solution. Then, we prove that： when the basic reproduction number is less than or equal to one, the disease-free equilibrium is stochastically asymptotical stability, which means the disease will die out; on the other hand, when the basic reproduction number is greater than one, the solution is oscillating around the endemic equilibrium of the deterministic model, which is measured by the average difference between the solution of the stochastic model and the endemic equilibrium of the deterministic model. Furthermore, we obtain the sufficient conditions of persistence in the mean and extinction of the disease. Finally, numerical simulations are carried out to verify our theoretical results.
出处
《工程数学学报》
CSCD
北大核心
2013年第6期804-814,共11页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(11271260)
上海市一流学科项目(XTKX2012)
上海市教委科研创新重点项目(13ZZ116)~~
