An explicit unconditionally stable scheme: application to diffusive Covid-19 epidemic model

Yasir Nawaz,Kamaleldin Abodayeh,Muhammad Shoaib Arif,Wasfi Shatanawi

doi:10.1186/s13662-021-03513-7

Abstract

An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This scheme is first-order accurate in time and second-order accurate in space and provides the conditions to get a positive solution for the considered type of epidemic model. Furthermore, the scheme’s stability for the general type of parabolic equation with source term is proved by employing von Neumann stability analysis. Furthermore, the consistency of the scheme is verified for the category of susceptible individuals. In addition to this, the convergence of the proposed scheme is discussed for the considered mathematical model.

Highlights

Mathematical modeling of epidemic diseases is one of the branches of modeling concerned with somehow estimating and predicting some insight into actual disease
The constructed mathematical models for epidemic diseases were the first-order differential equations system that might have been constructed on some assumptions
SIR models belong to the constructed mathematical models of epidemic diseases that can describe some relationships between susceptible, infected, and recovered individuals in COVID-19 epidemic disease

Summary

Introduction

Mathematical modeling of epidemic diseases is one of the branches of modeling concerned with somehow estimating and predicting some insight into actual disease. The mathematical model considered in [6] has consisted of susceptible, exposed, asymptomatic, infected, and recovered individuals. The susceptible, exposed, infected, diagnosed, recovered (SEIJR) epidemic model was considered in [12] with effects of net inflow of people into a region.

Results

Conclusion