Mathematical Analysis and Modeling of Ebola Virus Dynamics via Optimal Control and Neural Network Paradigms

Ebola virus disease is a severe hemorrhagic fever with rapid transmission through infected fluids and surfaces. We develop a fractional-order model using Caputo derivatives to capture memory effects in disease dynamics. An eight-compartment structure distinguishes symptomatic, asymptomatic, and post-mortem transmission pathways. We prove global well-posedness, derive the basic reproduction number $\mathcal{R}_0$, and establish stability theorems. Sensitivity analysis shows $\mathcal{R}_0$ is most sensitive to transmission rate, incubation period, and deceased infectivity. Treatment-safe burial synergy achieves 86.5\% morbidity-mortality control, with safe burial being most effective. Our disease-informed neural network achieves near-perfect predictive accuracy ($R^2$: 0.991-0.999, 99.1-99.9\% accuracy), closely matching real epidemic behavior.