Optimal control analysis of a tuberculosis model

• Published in: Applied Mathematical Modelling Vol. 58; pp. 47 - 64
• Main Authors: Gao, Da-peng, Huang, Nan-jing
• Format: Journal Article
• Language: English
• Published: England Elsevier Inc 01.06.2018; Elsevier BV
• Subjects: Case finding; Case holding; Control theory; Disease control; Disease management; Mathematical models; Maximum principle; Numerical analysis; Optimal control; Pontryagin’s Maximum Principle; Tuberculosis; 92D30; Tuberculosis; Pontryagin’s Maximum Principle; Optimal control; Case finding; 34D30; 49J15; Case holding; 92A30
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2017.12.027

•A new TB model with the 4-order cost function is introduced and investigated.•The method for the proof of uniqueness of optimal control for the model is new.•The numerical results show that the model considered in this paper are effective. In this paper, we extend the model of Liu and Zhang (Math Comput Model 54:836-845, 2011) by incorporating three control terms and apply optimal control theory to the resulting model. Optimal control strategies are proposed to minimize both the disease burden and the intervention cost. We prove the existence and uniqueness of optimal control paths and obtain these optimal paths analytically using Pontryagin’s Maximum Principle. We analyse our results numerically to compare various strategies of proposed controls. It is observed that implementation of three controls is most effective and less expensive among all the strategies. Thus, we conclude that in order to reduce tuberculosis threat all the three controls must be taken into consideration concurrently.