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

Jing-Yang Hou; Zhong-Kai Guo

doi:10.11948/20240575

2025 Volume 15 Issue 6

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Jing-Yang Hou, Zhong-Kai Guo. OPTIMAL CONTROL OF A TUBERCULOSIS TRANSMISSION MODEL WITH AGE STRUCTURE AND TIME DELAYS[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3246-3269. doi: 10.11948/20240575

Citation:

Jing-Yang Hou, Zhong-Kai Guo. OPTIMAL CONTROL OF A TUBERCULOSIS TRANSMISSION MODEL WITH AGE STRUCTURE AND TIME DELAYS[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3246-3269. doi: 10.11948/20240575

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

Jing-Yang Hou^1,,
Zhong-Kai Guo^1, ,

1.
School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China

Author Bio: Email: 805012545@qq.com(J.-Y. Hou)
Corresponding author: Email: guozhonkai@lzjtu.edu.cn(Z.-K. Guo)
Fund Project: The authors were supported by the Young Scholars Science Fundation of Lanzhou Jiaotong University (2020030) and the Scientific Research Foundation of Lanzhou Jiaotong University (1520020410)

Abstract

Abstract

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).
- Tuberculosis /
- age structure /
- time delays /
- optimal control
MSC: 35B35, 35B40

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