Mathematical Identification Analysis of a Fractional-Order Delayed Model for Tuberculosis

Abstract

Extensive research was conducted on the transmission dynamics of tuberculosis epidemics during its reemergence from the 1980s to the early 1990s, but this global problem of investigating tuberculosis spread dynamics remains of paramount importance. Our study utilized a fractional-order delay differential model to study tuberculosis transmission, where the time delay in the model was attributed to the disease’s latent period. What is more, this model accounts for endogenous reactivation, exogenous reinfection, and treatment of tuberculosis. The model qualitative properties and the basic reproduction number were analyzed. The primary goal of the study was to recover the important dynamic parameters of tuberculosis. Our understanding of these complex processes leverages the efficacy of efforts for controlling the disease, forecasting future dynamics, and applying further appropriate strategies to prevent its spread.The calibration itself was carried out via minimization of a quadratic cost functional. Computational simulations demonstrated that the algorithm is capable of working with noisy real data.

A Quasilinearization Approach for Identification Control Vectors in Fractional-Order Nonlinear Systems

“…In particular, the solution for HIV-I infection and Hepatitis E virus infection models is investigated. In [45], the author investigate a fractional-order delay nonlinear ODE system to study tuberculosis transmission. A numerical method for recovering dynamic parameters of tuberculosis is developed.…”