一类随机SICR丙肝模型的动力学分析

Dynamic Analysis of an SICR Hepatitis C Infection Model with Stochastic Effects

为了研究现实中不确定因素对丙肝的影响,考虑了一类具有急性与慢性感染的随机SICR丙肝模型。首先,依据停时理论证明了全局正解的存在唯一性;其次,通过构造Lyapunov函数并结合伊藤公式,讨论了随机模型的解在确定模型的无病平衡点和正平衡点附近的振荡行为,并给出了随机模型解的平均持续和疾病灭绝的充分条件。最后,数值模拟考虑了噪声对模型的影响,结果表明:随机模型在确定模型的平衡点附近扰动,扰动强度与噪声强度成正相关,并且足够大的噪声使疾病灭绝,进一步证实了理论结果。

In order to study the influence of uncertain factors on hepatitis C in reality,a randomized SICR hepatitis C model with acute and chronic infection was considered.Firstly,the existence and uniqueness of global positive solutions are proved according to the stopping time theory;secondly,by constructing Lyapunov function and combining Ito formula,the oscillation behavior of the solution of the stochastic model near the disease-free equilibrium point and the positive equilibrium point of the model is discussed,and then the sufficient conditions for the average persistence and disease extinction of the solution of the stochastic model are given.Finally,the numerical simulation considers the influence of noise on the model.The results show that the stochastic model is disturbed near the equilibrium point of the determined model,and the disturbance intensity is positively correlated with the noise intensity.Moreover,the noise is large enough to make the disease extinct,which further confirms the theoretical results.