1. Optimal Control and Sensitivity Analysis of a Fractional Order TB Model
- Author
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Rosa, Silvério, Torres, Delfim F. M., and uBibliorum
- Subjects
Statistics and Probability ,Control and Optimization ,Fractional optimal control ,Control variable ,01 natural sciences ,010305 fluids & plasmas ,Artificial Intelligence ,0103 physical sciences ,FOS: Mathematics ,Tuberculosis ,Order (group theory) ,Applied mathematics ,Sensitivity (control systems) ,Mathematics - Optimization and Control ,010301 acoustics ,Mathematics ,Optimal control ,Compartmental mathematical models ,3. Good health ,Transmission (telecommunications) ,Optimization and Control (math.OC) ,34A08, 49M05, 92C60 ,Signal Processing ,Computer Vision and Pattern Recognition ,Statistics, Probability and Uncertainty ,Information Systems - Abstract
A Caputo fractional-order mathematical model for the transmission dynamics of tuberculosis (TB) was recently proposed in [Math. Model. Nat. Phenom. 13 (2018), no. 1, Art. 9]. Here, a sensitivity analysis of that model is done, showing the importance of accuracy of parameter values. A fractional optimal control (FOC) problem is then formulated and solved, with the rate of treatment as the control variable. Finally, a cost-effectiveness analysis is performed to assess the cost and the effectiveness of the control measures during the intervention, showing in which conditions FOC is useful with respect to classical (integer-order) optimal control., Comment: This is a preprint of a paper whose final and definite form is with 'Statistics Opt. Inform. Comput.', Vol. 7, No 2 (2019). See [http://www.IAPress.org]. Submitted 09/Sept/2018; Revised 10/Dec/2018; Accepted 11/Dec/2018. arXiv admin note: text overlap with arXiv:1801.09634, arXiv:1810.06900
- Published
- 2019