A Mathematical Study of Tuberculosis Spread in Saudi Arabia: Insights From Real-World Data

This paper considers the modeling of tuberculosis in Saudi Arabia based on disease progression status using yearly reported data. We first formulate a classical TB model and then extend it using Caputo fractional operators that incorporate hereditary memory in disease transmission. We show that the fractional TB model is non-negative and that its solutions remain in the feasible region. The existence and uniqueness of the TB model are established, and it is confirmed that the model has a unique solution. The equilibrium points of the TB model are computed, and the corresponding stability outcomes for the disease-free equilibrium and the endemic case are presented. The disease-free equilibrium is locally and globally asymptotically stable when R0 1. Real TB cases reported yearly in the Kingdom of Saudi Arabia for the period 2000–2023 are considered, and the data fitting is performed using a nonlinear least-squares approach, through which we obtain the numerical value of R0=2.2618. Various results are presented under the proposed numerical scheme for disease elimination in the Kingdom of Saudi Arabia based on the given recommendations.