Modeling the Transmission Dynamics of Coronavirus Using Nonstandard Finite Difference Scheme
A nonlinear mathematical model of COVID-19 containing asymptomatic as well as symptomatic classes of infected individuals is considered and examined in the current paper. The largest eigenvalue of the next-generation matrix known as the reproductive number is obtained for the model, and serves as an...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/6/451 |
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| author | Ihsan Ullah Khan Amjid Hussain Shuo Li Ali Shokri |
| author_facet | Ihsan Ullah Khan Amjid Hussain Shuo Li Ali Shokri |
| author_sort | Ihsan Ullah Khan |
| collection | DOAJ |
| description | A nonlinear mathematical model of COVID-19 containing asymptomatic as well as symptomatic classes of infected individuals is considered and examined in the current paper. The largest eigenvalue of the next-generation matrix known as the reproductive number is obtained for the model, and serves as an epidemic indicator. To better understand the dynamic behavior of the continuous model, the unconditionally stable nonstandard finite difference (NSFD) scheme is constructed. The aim of developing the NSFD scheme for differential equations is its dynamic reliability, which means discretizing the continuous model that retains important dynamic properties such as positivity of solutions and its convergence to equilibria of the continuous model for all finite step sizes. The Schur–Cohn criterion is used to address the local stability of disease-free and endemic equilibria for the NSFD scheme; however, global stability is determined by using Lyapunov function theory. We perform numerical simulations using various values of some key parameters to see more characteristics of the state variables and to support our theoretical findings. The numerical simulations confirm that the discrete NSFD scheme maintains all the dynamic features of the continuous model. |
| first_indexed | 2024-03-11T02:27:48Z |
| format | Article |
| id | doaj.art-987a0a56e9a54d178c9875e3e7dd31ce |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T02:27:48Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-987a0a56e9a54d178c9875e3e7dd31ce2023-11-18T10:29:29ZengMDPI AGFractal and Fractional2504-31102023-05-017645110.3390/fractalfract7060451Modeling the Transmission Dynamics of Coronavirus Using Nonstandard Finite Difference SchemeIhsan Ullah Khan0Amjid Hussain1Shuo Li2Ali Shokri3Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, PakistanDepartment of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, PakistanSchool of Mathematics and Data Sciences, Changji University, Changji 831100, ChinaDepartment of Mathematics, Faculty of Science, University of Maragheh, Maragheh 83111-55181, IranA nonlinear mathematical model of COVID-19 containing asymptomatic as well as symptomatic classes of infected individuals is considered and examined in the current paper. The largest eigenvalue of the next-generation matrix known as the reproductive number is obtained for the model, and serves as an epidemic indicator. To better understand the dynamic behavior of the continuous model, the unconditionally stable nonstandard finite difference (NSFD) scheme is constructed. The aim of developing the NSFD scheme for differential equations is its dynamic reliability, which means discretizing the continuous model that retains important dynamic properties such as positivity of solutions and its convergence to equilibria of the continuous model for all finite step sizes. The Schur–Cohn criterion is used to address the local stability of disease-free and endemic equilibria for the NSFD scheme; however, global stability is determined by using Lyapunov function theory. We perform numerical simulations using various values of some key parameters to see more characteristics of the state variables and to support our theoretical findings. The numerical simulations confirm that the discrete NSFD scheme maintains all the dynamic features of the continuous model.https://www.mdpi.com/2504-3110/7/6/451COVID-19 modelreproduction numberNSFD schemeLyapunov functionSchur–Cohn criterionlocal and global stability |
| spellingShingle | Ihsan Ullah Khan Amjid Hussain Shuo Li Ali Shokri Modeling the Transmission Dynamics of Coronavirus Using Nonstandard Finite Difference Scheme Fractal and Fractional COVID-19 model reproduction number NSFD scheme Lyapunov function Schur–Cohn criterion local and global stability |
| title | Modeling the Transmission Dynamics of Coronavirus Using Nonstandard Finite Difference Scheme |
| title_full | Modeling the Transmission Dynamics of Coronavirus Using Nonstandard Finite Difference Scheme |
| title_fullStr | Modeling the Transmission Dynamics of Coronavirus Using Nonstandard Finite Difference Scheme |
| title_full_unstemmed | Modeling the Transmission Dynamics of Coronavirus Using Nonstandard Finite Difference Scheme |
| title_short | Modeling the Transmission Dynamics of Coronavirus Using Nonstandard Finite Difference Scheme |
| title_sort | modeling the transmission dynamics of coronavirus using nonstandard finite difference scheme |
| topic | COVID-19 model reproduction number NSFD scheme Lyapunov function Schur–Cohn criterion local and global stability |
| url | https://www.mdpi.com/2504-3110/7/6/451 |
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