On the Effectiveness of Fractional-Order Modeling of Tuberculosis using Optimal Control

Abstract

A fractional-order Tuberculosis (TB) SEITR model with Caputo derivatives has been analyzed to illustrate the dynamics of tuberculosis transmission, incorporating memory effects which make the model more realistic. The treatment initiation rateand distancing compliance have been incorporated as control measures, along with baseline parameters such as the transmission rate, recovery rate , and waning immunity rate . The local stability of the disease-free equilibrium (DFE) is verified under the condition. Sensitivity analysis also revealed that and  are the most significant parameters, because increases in  directly enhance the spread of infection, whereas improvements in  significantly diminish the infection.For the computation purpose, the Adams–Bashforth–Moulton method has been utilized andthe results indicate that the combination of control strategies produces the most substantial impact. Also illustrates that treatment has a moderate effect on decreasing infection while distancing prolongs the duration of transmission. Moreover, the efficacy of fractional order rather than a SIR model has been emphasized in enhancing predictive accuracy and supporting control strategies for tuberculosis in high-prevalence areas.