Hamiltonian and Neural Network-Based Framework for Modeling Conjunctivitis Transmission with Medical Intervention

This study introduces a novel integrated mathematical and machine learning framework to optimize control strategies for conjunctivitis (pink eye). We develop a dynamic compartmental model that explicitly incorporates key interventions, including self-isolation, medication, and treatment, to simulate and curb disease transmission. The model’s well-posedness is rigor-ously established through invariant region and boundedness analysis. Analytical derivation of the basic reproduction number (R0) quantifies the epidemic threshold, while sensitivity analysis identifies critical parameters, incubation rate (ρ), transmission rate of conjunctivitis (κ), and natural birth rate (δ), as primary drivers of disease dynamics. Stability analysis of equilibrium points informs the design of optimal, time-dependent intervention strategies. Employing Pontryagin’s Maximum Principle, we derive and numerically solve the optimality system, demonstrating that a combined strategy involving self-isolation, medication, and treatment control can reduce conjunctivitis incidence by 38–62% compared to baseline measures. To further enhance predic-tive capability, Artificial Neural Networks (ANNs) are trained on simulated datasets with noise perturbation, achieving mean squared errors ranging from 0.19 to 0.98 across test scenarios and confirming robust forecasting accuracy. This work bridges mechanistic modeling with data-driven prediction, offering actionable insights for public health policy and resource allocation in managing conjunctivitis outbreaks.