AI 中文总结
本研究构建了含调和平均发生率和垂直传播的HBV隔室模型，结合LHS、PRCC及庞特里亚金最大值原理分析其动力学，经数值模拟发现联合治疗与疫苗接种可有效减少HBV感染。
AI 中文摘要
乙型肝炎（HBV）是一种潜在致命的肝脏感染性疾病，尽管已有疫苗可用，但由于垂直传播、治疗延迟等持续存在的障碍，它仍然是全球范围内主要的广泛流行疾病。本研究提出了一种考虑垂直传播和调和平均型发生率影响的隔室数学模型，用于分析HBV的传播动力学。通过基本再生数$R_0$研究该模型的阈值行为，分析无病平衡点和地方病平衡点附近的定性动力学，以确定其渐近局部和全局稳定性的条件。为识别关键流行病学驱动因素，结合拉丁超立方抽样（LHS）和偏秩相关系数（PRCC）方法对系统进行全局敏感性分析。利用庞特里亚金最大值原理构建最优控制问题，通过数值模拟强调减少HBV流行的有效策略。数值模拟表明，优化的控制措施在减少感染者数量、增加康复人群方面发挥重要作用。此外，我们确定了三种不同的减少感染策略，发现每种策略在消除感染方面均存在局限性，但同时实施治疗和疫苗接种对减少HBV感染是有用且有效的。
英文摘要
Hepatitis B (HBV) is a potentially fatal liver infection that remains a primary widespread disease around the globe, despite the availability of vaccinations, owing to ongoing obstacles such as vertical transmission and delayed treatment. In the present study, a compartmental mathematical model that accounts for the effects of vertical transmission and harmonic mean type incidence is put forward for the analysis of the transmission dynamics of HBV. The model's threshold behavior is investigated through the basic reproduction number $R_0$, and the qualitative dynamics around the disease-free and endemic equilibria are examined to establish conditions for their asymptotic local and global stability. To identify key epidemiological drivers, the global sensitivity analysis of the system is performed through the incorporation of Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficient (PRCC) methodologies. We formulate the optimal control problem using Pontryagin's maximum principle. Effective strategies for diminishing the prevalence of HBV are emphasized through numerical simulations. Numerical simulations demonstrated that optimized control measures play a significant role in reducing the number of infected individuals and increasing the recovered population. In addition, we have characterized three distinct strategies for reducing infection and observed that each has limitations in eliminating infections. However, the simultaneous administration of treatment and vaccination is useful and effective for the reduction of HBV infection.
Comments31 pages, 19 figures
Journal refBoletim da Sociedade Paranaense de Matematica (3s.), 2026, 44(12), 1-30
