<p>Infectious diseases characterized by high fatality rates and recurrent outbreaks continue to pose a serious challenge to global public health. In this work, we develop a mathematical framework for the transmission dynamics of the Nipah virus by incorporating three interacting populations: humans, pigs, and bats. The resulting system of nonlinear ordinary differential equations, formulated in both integer-order and fractional-order settings, is solved numerically using the Hermite Wavelet Collocation Method (HWCM). By employing the operational matrix of integration for fractional derivatives together with a collocation strategy, the model is reduced to a system of algebraic equations. The unknown coefficients are determined using the Newton–Raphson iterative scheme. To evaluate the accuracy and computational efficiency of the proposed approach, the numerical solutions are compared with those obtained via the Runge–Kutta method, the NDSolver, and the Haar Wavelet Method. The temporal behavior of the state variables illustrates the progression of the infection within the populations. Furthermore, numerical experiments conducted under different parameter scenarios validate the robustness, accuracy, and reliability of the method, highlighting its capability to effectively capture the influence of parameter variations.</p>