年龄-环境耦合的两阶段结核病传播动力学模型的稳定性与预设目标控制OA

By incorporating both the age structure of the susceptible population and Mycobacterium tuberculosis in environment,we construct a two-stage dynamical model of tuberculosis transmission and systematically ana-lyze its stability.A preset target control strategy is further developed.First,we derive an explicit expression for the basic reproduction number and prove the globally asymptotic stability of both the disease-free and endemic equilibria using Lyapunov theory.Next,we formulate and solve a preset-target control problem that treats vaccination and the DOTS(directly observed treatment,short-course)strategy as control variables.Numerical simulations show that the combined implementation of vaccination and DOTS can maintain the num-ber of active TB cases below the preset target and yields a significantly higher infection-avoidance rate than either measure used alone,providing a theoretical basis for optimizing tuberculosis prevention and control strate-gies.