Numerical Analysis and Artificial Neural Networks for Solving Nonlinear Tuberculosis Model in SEITR Framework

Abstract

This study investigates an epidemiological model of tuberculosis dynamics by classifying the total population into five distinct compartments: susceptible, exposed, infected, treated, and recovered. To solve the system of nonlinear differential equations and obtain approximate solutions for the $SEITR$ tuberculosis model, three analytical methods are utilized: the transcendental-exponential type proposed method (PNM), the Homotopy perturbation method (HPM), and the higher-order inverse polynomial method (HOIPM). Additionally, the study examines the stochastic performance of artificial neural networks trained using the Levenberg–Marquardt algorithm (ANNs-LMB) to offer a comprehensive evaluation of the tuberculosis model. The predictions generated by ANNs-LMB provide valuable benefits for researchers, significantly improving their understanding of infectious tuberculosis dynamics. Furthermore, error estimations demonstrate that the PNM, HOIPM, and ANNs-LMB methods are highly effective in generating accurate solutions, closely matching those obtained from the Runge–Kutta solver, and surpassing the performance of HPM. These methods exhibit strong reliability and efficiency, making them innovative tools for addressing tuberculosis models and simulating epidemiological challenges. Moreover, the analysis of key parameters, including contact rate, infection rate, tuberculosis-related mortality rate, reinfection rate, and treatment rate, provides crucial insights into the model's behavior and dynamics, paving the way for future research and effective intervention strategies.