Stochastic Milstein computing driven autoregressive exogenous neuro-architecture for chaotic nonlinear measles transmission system with impact of immunization

Measles continues to be a significant contributor to child mortality worldwide, causing thousands of deaths each year, even though a safe and effective vaccine is available. In recent years, global measles cases have risen significantly, with the majority of infections occurring in children under 5 years old and immunocompromised adults. The presented study introduces a novel autoregressive exogenous neuro-computing framework, enhanced through optimization by the Levenberg–Marquardt scheme, to model the dynamics of nonlinear stochastic measles transmission epidemic systems, considering the effects of immunization. The mathematical representations are formulated using multi-class stochastic differential compartments, describing the susceptible, immunized, exposed, infected, recovered individuals, and hospitalized cases. Synthetic data for executing the multi-layer structure of the autoregressive exogenous neuro-computing framework model are created using the Milstein method across various scenarios of the stochastic measles model, involving variation in key parameters such as rates of susceptible individuals, contact among susceptible people, immunization, mortality, infection, medical treatment, recovery, and natural death. The generated data are randomly partitioned into response and prediction sets for use in the testing, validation, and training phases of the autoregressive exogenous neuro-computing networks. The results from the designed approach exhibit a close correlation with the reference solutions, with negligible error magnitudes across all scenarios of the stochastic measles transmission model. The proposed approach is validated through convergence analyses using mean squared error, visual representations of adaptive governing parameters, error histograms, and regression indices for various nonlinear stochastic measles transmission models within mathematical biology.