Analysis of tuberculosis infection dynamics using Caputo fractional-order models with diagnosis and treatment interventions

This paper develops and analyzes a Caputo fractional-order mathematical model for tuberculosis (TB) transmission that incorporates testing, therapy, isolation, and treatment interventions. The model divides the population into five compartments-susceptible, exposed, infectious, isolated, and recovered-and its qualitative properties, including positivity, boundedness, existence, and uniqueness of solutions, are established. The basic reproduction number R 0 is derived, and sensitivity analysis identifies transmission, progression, testing, and treatment rates as critical drivers of TB dynamics. Using the Laplace-Adomian decomposition method (LADM), numerical simulations are performed to assess the impact of fractional-order derivatives on disease spread and control. The results show that increasing the order of the fractional derivative enhances the accuracy of the model and reveals memory effects in TB dynamics. Moreover, early diagnosis, therapy, and isolation significantly reduce infection levels and improve recovery outcomes. These findings highlight the advantages of fractional-order models over classical approaches and provide valuable insights for designing effective TB control strategies.