A numerical study for covid-19 spatio-temporal lockdown model

Abstract

This article presents a detailed numerical study of lockdown (temporal and spatio-temporal) mathematical models for COVID-19. The temporal model proposed in this study comprises a system of five nonlinear ordinary differential equations, while the spatio-temporal model consists of five nonlinear partial differential equations. The reproduction number is discussed as a means to estimate the spread of the COVID-19 pandemic, and sensitivity analysis is performed to highlight the significance of pandemic parameters. Furthermore, the stability regions of the given models, as well as the Von Neumann stability and consistency of the numerical scheme applied to the spatio-temporal model, are investigated. To analyze the numerical results of the presented models under various parameters and facilitate comparison, effective methods such as the central finite difference (CFD) and Runge-Kutta of fifth order (RK-5) are applied. This comprehensive study provides insights into the dynamics and behavior of the COVID-19 pandemic under different scenarios, shedding light on the effectiveness of lockdown measures and the impact of various parameters on the spread of the disease.