https://doi.org/10.1140/epjp/s13360-025-06365-2
Regular Article
A novel intelligent computing approach for modeling the population dynamics of monkeypox infection
1
School of Mathematics and Data Sciences, Changji University, 831100, Changji, Xinjiang, China
2
Department of Natural Sciences and Humanities University of Engineering and Technology, Mardan, Pakistan
3
School of Mathematical Science, Yangzhou University, 225002, Yangzhou, China
4
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
5
Computer Engineering Department, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia
6
Department of Zoology, Abdul Wali Khan University Mardan, Mardan, Pakistan
7
International Business School, Shaanxi Normal University, Shaanxi 710062, Xi′an, P.R. China
Received:
16
January
2025
Accepted:
24
April
2025
Published online:
25
May
2025
In this study, we present a novel intelligent computing framework that integrates a supervised deep neural network (DNN) with a nonstandard finite difference scheme to investigate the dynamics of Monkeypox (Mpox) viral infection. We develop a new mathematical model incorporating key aspects of Mpox virus transmission including vaccination and hospitalization. The fundamental qualitative analysis of the model, such as the existence and uniqueness of solutions, as well as their nonnegativity and boundedness, is established. The basic reproduction number 
is derived, and stability of the infection free steady state is proved. Additionally, a comprehensive normalized sensitivity analysis is conducted to assess the model’s robustness across various parameters. Furthermore, to enhance the biological validity of the model, it is fitted to the reported Mpox incidence data from the USA for the period of May 1, 2022 to March 31, 2023. To ensure the reliability, consistency, and accuracy of the model across various states, we provide a comprehensive numerical analysis with graphical representations of statistical indices such as error distribution assessments, regression analysis, and detailed curve fitting for each solution. The regression value 
across all dataset indicates a perfect correlation between the model predictions and target values. This study contributes to the mathematical modeling of infectious diseases and provides valuable insights for future advancements in the field. Additionally, the methodologies developed here can be applied to other diseases, offering broader benefits beyond the Mpox infection.
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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.
