乙型肝炎疫苗接种-治疗模型的阈值几何、分岔与数据驱动分析
Threshold Geometry, Bifurcation, and Data-Driven Analysis of a Vaccination-Treatment Model for Hepatitis B
中文总结 AI 辅助
本研究构建HBV疫苗接种-治疗模型，通过基本再生数阈值和分岔分析，结合印度数据校准与敏感性分析，揭示干预效果与参数不确定性，为乙肝防控提供定量框架。
中文摘要 AI 辅助
尽管已有优秀的疫苗和抗病毒药物，乙型肝炎病毒（HBV）仍然是重大的公共卫生问题。本研究构建了一个针对HBV传播的数学疫苗接种-治疗模型，以探究疾病持续存在的阈值条件及干预水平。分析给出了无病平衡点和地方病平衡点的特征，并通过下一代矩阵方法确定了基本再生数$\mathcal{R}_0$。模型表明$\mathcal{R}_0=1$是区分无病状态与地方病状态的关键阈值，并刻画了关于传播参数的前向跨临界分岔。数值平衡延续和稳定性评估证实了分析结果。对传播率和疫苗接种率进行的双参数研究确定了阈值几何形状，并通过敏感性分析评估了重要参数的影响。模型使用印度特定数据（如HBsAg流行率、HBV发病率和死亡率）进行校准，通过有限的非线性校准紧密拟合流行病学目标。此外，采用多起点优化和实际可辨识性分析来研究参数不确定性。稳健性分析显示，校准的$\mathcal{R}_0^*=1.1744$对应超阈值状态；然而，参数灵活性允许亚阈值和超阈值状态共存。这一结合分析与数据驱动的框架连接了流行病阈值、分岔结构、干预效果和参数不确定性，为分析HBV持续存在和评估控制策略提供了定量框架，尤其在缺乏流行病学证据的情况下。
英文摘要
Despite the availability of excellent vaccines and antiviral medicines, hepatitis B virus (HBV) remains a major public health problem. In this work, we develop a mathematical vaccination-treatment model for HBV transmission to investigate threshold conditions for illness persistence as well as the level of intervention. The analysis gives the characterisation of both disease-free and endemic equilibria and determines the basic reproduction number, $\mathcal{R}_0$, by the next-generation matrix approach. The model indicates that $\mathcal{R}_0=1$ is a critical threshold dividing disease-free from endemic states and characterises a forward transcritical bifurcation regarding the transmission parameter. Numerical equilibrium continuation and stability assessments confirm the analytical results. A two-parameter study of transmission and vaccination rates identifies threshold geometries and assesses impacts of important parameters using sensitivity analysis. The model is calibrated with India-specific data, such as HBsAg prevalence, HBV incidence and mortality rates and fits epidemiological targets closely through limited nonlinear calibration. Additionally, multi-start optimisation and practical identifiability profiling are used to investigate parameter uncertainty. Robustness analyses reveal that the calibrated $\mathcal{R}_0^*=1.1744$ is associated with a super-threshold regime; however, parameter flexibility permits both sub-threshold and super-threshold regimes. This combined analytical and data-driven framework connects epidemic thresholds, bifurcation structures, intervention efficacy, and parameter uncertainty. It provides a quantitative framework for analysing HBV persistence and evaluating control options, especially in the absence of epidemiological evidence.
