A new unconditionally stable implicit numerical scheme for fractional diffusive epidemic model

AIMS Mathematics

article

Yasir Nawaz¹  Muhammad Shoaib Arif²  Wasfi Shatanawi²  Muhammad Usman Ashraf⁶ 

[1] Department of Mathematics, Air University;Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University;Stochastic Analysis and Optimization Research Group, Department of Mathematics, Air University;Department of Mathematics, Faculty of Science, The Hashemite University;Department of Medical Research, China Medical University;Department of Sciences and Humanities, National University of Computer and Emerging Sciences

关键词: fractional numerical scheme;    conditionally positivity preserving;    COVID-19 model;    stability;    convergence;   

DOI  :  10.3934/math.2022788

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

This contribution proposes a numerical scheme for solving fractional parabolic partial differential equations (PDEs). One of the advantages of using the proposed scheme is its applicability for fractional and integer order derivatives. The scheme can be useful to get conditions for obtaining a positive solution to epidemic disease models. A COVID-19 mathematical model is constructed, and linear local stability conditions for the model are obtained; afterward, a fractional diffusive epidemic model is constructed. The numerical scheme is constructed by employing the fractional Taylor series approach. The proposed fractional scheme is second-order accurate in space and time and unconditionally stable for parabolic PDEs. In addition to this, convergence conditions are obtained by employing a proposed numerical scheme for the fractional differential equation of susceptible individuals. The scheme is also compared with existing numerical schemes, including the non-standard finite difference method. From theoretical analysis and graphical illustration, it is found that the proposed scheme is more accurate than the so-called existing non-standard finite difference method, which is a method with notably good boundedness and positivity properties.

【 授权许可】

CC BY