OPTIMAL CONTROL OF A TUBERCULOSIS TRANSMISSION MODEL WITH AGE STRUCTURE AND TIME DELAYS

Tuberculosis remains a critical global health challenge. We develop an age-structured delayed model to identify cost-effective control strategies, proving the existence and uniqueness of a non-negative solution to the model and demonstrating the continuous dependence of solutions on control variables. Through optimal control theory, we derive necessary conditions for minimizing intervention costs during the implementation of treatment programs for active tuberculosis cases and public health education campaigns. By combining theoretical analysis with simulations, we propose integrated interventions to accelerate China's progress toward achieving the WHO 2035 target (90% reduction in new cases compared to 2015).