SI_cICR急慢性乙肝传染病模型的动力学分析和最优控制

Dynamical Analysis and Optimal Control of an SI_cICR Model for the Transmission of Acute and Chronic Hepatitis B

摘要: 本文构建了一类包含携带者、急性乙肝患者和慢性乙肝患者人群的乙肝传播动力学模型，真实地刻画了乙肝在人群中的传播机制。首先，借助LaSalle不变性原理和Lyapunov函数方法，分析了模型平衡点的存在性及其全局稳定性；其次，运用Pontryagin最大值原理对最优控制问题进行分析研究，得出最优控制策略；最后，结合数值模拟与敏感性分析，探讨了关键参数对乙肝传播动态的影响。研究结果表明，提高对乙肝病毒携带者的诊断率、降低感染者与易感者的有效接触率和提高疫苗接种率是遏制乙肝传播的关键策略。该研究为优化乙肝防控措施和制定科学的公共卫生政策提供了理论依据与决策参考。

Abstract: This study develops a hepatitis B transmission dynamics model that includes carriers, acute hepatitis B patients, and chronic hepatitis B patients, aiming to realistically capture the transmission mechanism of hepatitis B within the population. Firstly, the existence and global stability of the model’s equilibrium points are analyzed using LaSalle’s invariance principle and the Lyapunov function method. Secondly, the Pontryagin Maximum Principle is applied to investigate the optimal control problem, and the corresponding optimal control strategies are obtained. Finally, numerical simulations and sensitivity analysis are conducted to examine the influence of key parameters on the transmission dynamics of hepatitis B. The results indicate that improving the diagnosis rate of HBV carriers, reducing the effective contact rate between infectious and susceptible individuals, and increasing the vaccination rate are key strategies for controlling the spread of hepatitis B. This study provides a theoretical foundation and practical reference for optimizing hepatitis B prevention and control measures and formulating sound public health policies.