Optimal Control and Sensitivity Analysis of a Fractional Order TB Model

TL;DR

This paper develops a fractional-order TB transmission model, performs sensitivity and cost-effectiveness analyses, and compares fractional optimal control with classical methods to improve intervention strategies.

Contribution

It introduces a fractional optimal control framework for TB, highlighting its advantages over classical models in treatment strategy optimization.

Findings

Sensitivity analysis emphasizes parameter importance.

Fractional control improves intervention cost-effectiveness.

Fractional models outperform classical models under certain conditions.

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.