Theoretical investigation of tuberculosis transmission dynamics: A soft computing–integrated mathematical approach

This study methodically examines the contagion dynamics of tuberculosis (TB) through the synergistic integration of artificial intelligence methodologies into a mathematical modeling framework. Incorporating the effects of the media awareness campaigns and treatment control strategies on both smear-positive and smear-negative individuals, we design a five-compartment TB model. The basic reproduction number R0 is analytically computed using the next-generation matrix method, along with the existence of equilibria and their local asymptotic stability. Changes in the system’s dynamical behavior across varying parameter regimes reveal the occurrence of bifurcations at the critical value R0=1, specifically transcritical and backward bifurcations. Therefore, we conduct an LHS-PRCC (Latin Hypercube Sampling-Partial Rank Correlation Coefficients) based global sensitivity analysis on R0 to identify the most influential parameters. Numerical simulation further demonstrates how variations in these sensitive parameters drive bifurcation transitions. Moreover, the dynamical behavior of the proposed model is assessed by implementing a surrogate hybrid AI-ODE framework based on a Multilayer Perceptron Neural Network (MLPNN), whose computational efficiency and lower MSE values across training, testing, and validation sets confirm its ability to accurately mimic the underlying nonlinear dynamics. The proposed framework’s robustness is reviewed through the perturbation of key sensitive parameters and evaluation under varying model configurations. Coupled with this, the study advances the optimization technique using an evolutionary-based optimization technique, the Genetic Algorithm (GA). It minimizes the threshold value R0 by optimally adjusting the most influential parameters, offering insights into intervention strategies to control the disease.