https://doi.org/10.1140/epjp/s13360-025-06247-7
Regular Article
Stochastic Milstein computing driven autoregressive exogenous neuro-architecture for chaotic nonlinear measles transmission system with impact of immunization
1
Department of Mathematics, University of Narowal, 51600, Narowal, Pakistan
2
Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, 64002, Douliou, Yunlin, Taiwan
3
Department of Mathematics, University of Gujrat, 50700, Gujrat, Pakistan
4
AI Center, Yuan Ze University, 320, Taoyuan, Taiwan
Received:
15
February
2025
Accepted:
20
March
2025
Published online:
19
April
2025
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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
