Modeling the dynamics of COVID-19 Epidemic with a reaction-diffusion framework: a case study from Thailand

This paper introduces a novel mathematical framework to examine the spread of COVID-19 using a two-dimensional reaction-diffusion epidemic model. The model is structured into six compartments, which account for different stages of the disease and its transmission: (S) Susceptible, (E) Exposed, (Ia\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_a$$\end{document}) Asymptomatic, (Is\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_s$$\end{document}) Symptomatic, (Q) Quarantined, and (R) Recovered, forming the SEQIa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_a$$\end{document}Is\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_s$$\end{document}R structure. The basic reproduction number, R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}, is derived through the next-generation matrix method, providing insights into the potential for disease outbreak. Model parameters are estimated using least squares curve fitting to match observed data accurately. To solve the model equations, a combination of explicit finite difference methods and an operator splitting technique is employed, effectively capturing both time and spatial dynamics. The stability of the disease-free and endemic equilibrium states is rigorously analyzed to understand the conditions under which the disease can persist or be eradicated. The study also presents comprehensive simulations that compare scenarios with and without spatial diffusion, offering a robust verification of the model's accuracy through numerical and theoretical validation. The findings provide a deeper understanding of the spatial and temporal dynamics of COVID-19 spread and suggest potential strategies for controlling the epidemic.