A novel intelligent computing approach for modeling the population dynamics of monkeypox infection

Abstract

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 \(\mathcal {R}_0\) 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 \(R = 1\) 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.