# Optimal Control and Sensitivity Analysis of a Fractional Order TB Model

• Silvério Rosa Department of Mathematics and Instituto de Telecomunicacoes (IT), University of Beira Interior, 6201-001 Covilh˜ a, Portugal
• Delfim F. M. Torres Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Keywords: Tuberculosis, Compartmental mathematical models, Fractional optimal control.

### 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.

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Published
2019-08-17
How to Cite
Rosa, S., & Torres, D. F. M. (2019). Optimal Control and Sensitivity Analysis of a Fractional Order TB Model. Statistics, Optimization & Information Computing, 7(3), 617-625. https://doi.org/10.19139/soic.v7i3.836
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Section
Research Articles