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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. [ABSTRACT FROM AUTHOR]

In the present work, a fractional temporal SIR model is considered. The total population is divided into three compartments—susceptible, infected and removed individuals. It generalizes the classical SIR model and consists of three coupled time-fractional ordinary differential equations (ODEs). The fractional derivative is introduced to account for the subdiffusion process of confirmed, cured and deceased people dynamics. Although relatively basic, the model is robust and captures the real dynamics, helped by the memory property of the fractional system. In the paper, the issue of an adequate model reconstruction is addressed, and a coefficient identification inverse problem is solved; in particular, the transition and recovering rates, varying in time, are recovered. A least-squares cost functional is minimized for solving the problem. The time-dependent parameters are reconstructed with an iterative predictor–corrector algorithm. Its application is demonstrated via tests with synthetic and real data. What is more, an approach for economic impact assessment is proposed. [ABSTRACT FROM AUTHOR]