一种具有垂直传播、自发恢复和最优控制分析的新型乙型肝炎流行模型
A Novel Hepatitis B Epidemic Model with Vertical Transmission, Spontaneous Recovery and Optimal Control Analysis
AI总结：
该研究建立含垂直传播等的乙肝流行模型，用下一代矩阵法得基本再生数\(\mathcal{R}_0\)，经敏感性分析确定关键参数，通过稳定性分析研究模型行为，应用庞特里亚金极大值原理得出三种最优控制策略，为设计HBV传播干预措施提供理论框架。
AI中文摘要：
本研究建立了一个乙型肝炎病毒（HBV）传播的房室流行模型，纳入垂直传播、急性感染个体的自发恢复、慢性感染个体的饱和治疗反应以及易感个体的疫苗接种。用下一代矩阵法推导基本再生数\(\mathcal{R}_0\)，以了解疾病动态。通过拉丁超立方抽样（LHS）和偏秩相关系数（PRCCs）进行敏感性分析来确定最有影响的参数。通过对无病和地方病平衡点的稳定性分析研究模型的定性行为。结果表明，当\(\mathcal{R}_0 < 1\)时无病平衡点全局渐近稳定，当\(\mathcal{R}_0 > 1\)时地方病平衡点全局稳定。应用庞特里亚金极大值原理优化公共卫生干预措施，得出三种旨在降低治疗和疫苗接种综合成本的最优控制策略。研究结果为设计具有成本效益的HBV传播干预措施提供了严格的理论框架。
英文摘要：
This study develops a compartmental epidemic model for Hepatitis B virus (HBV) transmission incorporating vertical transmission, spontaneous recovery in acutely infected individuals, saturated treatment response for chronically infected individuals, and vaccination of susceptible individuals. The basic reproduction number, \(\mathcal{R}_0\), is derived using the next-generation matrix method, providing a threshold quantity for understanding disease dynamics. To identify the most influential parameters, sensitivity analysis is performed using Latin Hypercube Sampling (LHS) together with Partial Rank Correlation Coefficients (PRCCs). The qualitative behavior of the model is investigated through stability analysis of the disease-free and endemic equilibria. It is shown that the disease-free equilibrium is globally asymptotically stable when \(\mathcal{R}_0 < 1\), while the endemic equilibrium is globally stable when \(\mathcal{R}_0 > 1\). Pontryagin's Maximum Principle is applied to optimize public health interventions, leading to three optimal control strategies aimed at reducing the combined cost of treatment and vaccination. The results provide a rigorous theoretical framework for designing cost-effective interventions against HBV transmission.
