This talk gives a novel age-structured tuberculosis (TB) model to evaluate the impact of pre- and post-exposure vaccinations on TB control, explicitly incorporating the waning of vaccine-induced efficacy over time. Mathematically, we establish a broadly applicable analytical frame-work for rigorously proving the global stability of steady states in the age-structured model. Furthermore, we formulate an optimal control problem with time-dependent vaccination schedules, identifying cost-effective vaccination strategies under realistic resource constraints. Epidemiologically, our analysis indicates that a combined vaccination strategy is most effective overall. While pre-exposure vaccination proves superior for long-term outbreak control, high-intensity post-exposure vaccination is crucial in high-exposure scenarios to rapidly reduce infected cases. This offers valuable insights for evaluating vaccination-based prevention and control strategies.

报告人简介：刘志军教授，湖北民族大学二级教授，四川大学数学学院博士研究生导师。长期从事非线性生物动力系统和控制理论学术研究。主持在研或结题国家自然科学基金3项；以第一作者或通讯作者在国内外学术刊物SIAM J Control Optim、IEEE TAC、IMA J Appl Math、Appl Math Model等期刊上发表论文80余篇；获得湖北省自然科学奖三等奖1项。