A Deep Learning Approach for Modeling Tuberculosis with Differential Infectivity

Tuberculosis (TB) continues to be a serious global health issue, and building accurate models to understand and predict its spread is critical for controlling outbreaks. This work introduces a deep learning methodology for modeling tuberculosis with differential infectivity. Specifically, a system of nonlinear ordinary differential equations (ODEs) for TB dynamics is solved using two numerical methods (the classical fourth-order Runge–Kutta (RK4) and the adaptive Runge–Kutta methods), alongside two deep learning models: Physics-informed Neural Networks (PINN) and DeepONets. In comparison to a reference high-accuracy method, each model is evaluated in terms of accuracy (using the Pearson correlation coefficient and the mean-squared error (MSE)), and the computational efficiency (using the execution time). The results indicate that RK4 provides the highest accuracy, while the adaptive RK method achieves faster performance with acceptable precision. Unlike the numerical solvers, the learning-based solvers are trained to generalize beyond a single initial condition, enabling them to accurately and efficiently predict solutions for a wide range of initial states. In fact, the PINN and DeepONets models were approximately 17 and 12 times faster than the classical RK4 method, respectively.