The study extends the classical SIR epidemic model by incorporating a hearing impairment (H) compartment, which accounts for individuals who suffer from long-term auditory complications due to infection. The proposed SIR-H model includes one more $H$ compartment to study the effect of infectious diseases on long-term disability. The model is expressed in terms of fractional-order differential equations to better capture the memory and hereditary nature of disease processes. A stability analysis is conducted to find the equilibrium points along with the basic reproduction number $R_0$ that governs the disease spread. Numerical solutions are derived using the Laplace Residual Power Series (LRPS) approach, and a comparative analysis with the Runge-Kutta method guarantees accuracy and efficiency. The Simulation results demonstrate how different values for the fractional order $\alpha$ influence the disease dynamics, with smaller values reflecting higher memory effects. Additionally, machine learning algorithms such as Sequential Neural Networks are used to enhance the predictive capability and identify long-term epidemiological trends. The findings highlight the importance of incorporating disability-related compartments into epidemic models in order to aid public health strategies and policy formation.