Modeling the dynamics of Covid-19 in Japan: employing data-driven deep learning approach

This paper aims to build the SVIHRD model for COVID-19 and it also simultaneously conduct stability and numerical analysis on the transmission of COVID-19. Here we do a mathematical analysis for the SVIHRD model, which involves positivity, boundedness, uniqueness, and proving both global and local stability. In the process of numerical simulation, we use real-world data for COVID-19 cases in Japan. An important feature presents in this paper, is that we replace the usual numerical solving technique for obtaining the parameters with a Physics Informed Neural Network (PINN). This PINN needs an order of time instances as input and the number of Susceptible (S), Vaccinated (V), Infected (I), Hospitalized (H), Recovered (R), and Death (D) people per time instances to learn specific parameters of the model using loss functions. We developed three different PINN setups-the baseline model, configuration-I, and configuration-II-to explore and optimize these parameters for modeling COVID-19 dynamics in Japan. During the validation process, we evaluated how well the learned parameters from these three PINN architectures predicted real infection data for the next two months. The baseline model, with four hidden layers and 32 neurons each, performed well with an R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R<^>{2}$$\end{document} value of 0.8038 and a Wilcoxon signed-rank test p value of 0.001556, closely matching actual infection data. A sensitivity analysis of the baseline model's parameters showed that the vaccination rate sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma$$\end{document} is the most sensitive.