Artificial Neural Network Driven Computational Modeling of Naegleria fowleri Epidemics Using Variational Optimization

This study presents a mathematical framework to analyze the transmission dynamics of an amoeba‐induced central nervous system infection. The population is divided into compartments including susceptible, exposed, infected, quarantined, hospitalized, recovered, protected, and deceased. A system of nonlinear ordinary differential equations models disease progression and intervention effects. The models qualitative behavior is examined through equilibrium analysis. The disease‐free equilibrium is derived, and its local and global stability are established using the Jacobian matrix, Lyapunov function, and LaSalles invariance principle. The basic reproduction number is identified as a key threshold governing disease extinction or persistence. Due to nonlinearity, numerical solutions are obtained using the fourth‐order Runge Kutta method and an artificial neural network approach. Comparative analyzes based on error metrics, regression, and correlation measures show strong agreement between both methods. The results validate the model and demonstrate the effectiveness of neural networks for solving complex epidemic systems.