一类HCV模型的随机稳定性和分岔分析

Stochastic Dynamics Analysis of HCV Virus Model

摘要: 在HCV模型中加入高斯白噪声，建立带有随机激励的非线性微分方程组，应用随机降阶和随机平均法相关定理将原方程化为二维的伊藤微分方程。然后，本文应用最大Lyapunov指数和奇异边界理论分析了该随机系统平凡解的局部和全局稳定性，得到了相应的稳定性条件；利用Hamilton理论中的随机平均法，对HCV系统的动态分岔和唯象分岔行为做了研究。最后，通过数值模拟得到HCV流行病在噪声的影响下传染速率会有明显的变化。

Abstract: Gauss white noise was added into the nonlinear HCV model, nonlinear differential equations were established, and the original equation was reduced to a two-dimensional Ito ̂ differential equation by applying the theorem of stochastic central manifold and the correlation theorem of stochastic average method. Then, the maximum Lyapunov index and singular boundary theory are applied to analyze the local stochastic stability and global stochastic stability of the stochastic system respectively, and the stability conditions are obtained. The dynamic bifurcation and phenomenological bifurcation behavior of systems are studied by using stochastic average method for quasi-integrable Hamiltonian systems. Finally, the numerical simulation shows that the infection rate of HCV epidemic will change obviously under the influence of noise.