Stability and Numerical Analysis of SEIVR COVID-19 Fractional and Integral Order Model under Saturated Incidence Rate

被引：0

作者：

Shahid Ullah ^{[1
]}

Muhammad Shoaib Arif ^{[3
]}

Rahim Ud Din ^{[2
]}

Ikram Ullah ^{[1
]}

机构：

[1] University of Engineering and Technology Mardan,Department of Natural Sciences and Humanities

[2] Air University,Department of Mathematics

[3] College of Humanities and Sciences,Department of Mathematics and Sciences

[4] Prince Sultan University,undefined

来源：

International Journal of Applied and Computational Mathematics | 2025年 / 11卷 / 3期

关键词：

Fractional order model; Stability; Reproduction number; Local stability; Non-standard finite difference scheme; Fractional simulation;

D O I：

10.1007/s40819-025-01914-w

中图分类号：

学科分类号：

摘要：

In this manuscript, we introduce an SEIVR model for COVID-19 and conduct a stability and numerical analysis. The stability of the integral-order system is examined using the Routh-Hurwitz criterion for local stability and the Lyapunov function for global stability. 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 using the next-generation matrix approach. Additionally, a sensitivity analysis is performed to identify the most influential parameters affecting disease dynamics. To enhance the model’s accuracy, the integer-order system is extended to a fractional-order framework using fractional derivatives. Numerical simulations are carried out using the non-standard finite difference scheme for the integral-order model and the RK2 method for the fractional-order system. Finally, a comparative analysis of both numerical methods are presented in the last diagrams.

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