Cargando…
The stability analysis of a nonlinear mathematical model for typhoid fever disease
Typhoid fever is a contagious disease that is generally caused by bacteria known as Salmonella typhi. This disease spreads through manure contamination of food or water and infects unprotected people. In this work, our focus is to numerically examine the dynamical behavior of a typhoid fever nonline...
Autores principales: | , , , , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2023
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10504385/ https://www.ncbi.nlm.nih.gov/pubmed/37714901 http://dx.doi.org/10.1038/s41598-023-42244-5 |
_version_ | 1785106713526927360 |
---|---|
author | Khan, Ihsan Ullah Mustafa, Shahbaz Shokri, Ali Li, Shuo Akgül, Ali Bariq, Abdul |
author_facet | Khan, Ihsan Ullah Mustafa, Shahbaz Shokri, Ali Li, Shuo Akgül, Ali Bariq, Abdul |
author_sort | Khan, Ihsan Ullah |
collection | PubMed |
description | Typhoid fever is a contagious disease that is generally caused by bacteria known as Salmonella typhi. This disease spreads through manure contamination of food or water and infects unprotected people. In this work, our focus is to numerically examine the dynamical behavior of a typhoid fever nonlinear mathematical model. To achieve our objective, we utilize a conditionally stable Runge–Kutta scheme of order 4 (RK-4) and an unconditionally stable non-standard finite difference (NSFD) scheme to better understand the dynamical behavior of the continuous model. The primary advantage of using the NSFD scheme to solve differential equations is its capacity to discretize the continuous model while upholding crucial dynamical properties like the solutions convergence to equilibria and its positivity for all finite step sizes. Additionally, the NSFD scheme does not only address the deficiencies of the RK-4 scheme, but also provides results that are consistent with the continuous system's solutions. Our numerical results demonstrate that RK-4 scheme is dynamically reliable only for lower step size and, consequently cannot exactly retain the important features of the original continuous model. The NSFD scheme, on the other hand, is a strong and efficient method that presents an accurate portrayal of the original model. The purpose of developing the NSFD scheme for differential equations is to make sure that it is dynamically consistent, which means to discretize the continuous model while keeping significant dynamical properties including the convergence of equilibria and positivity of solutions for all step sizes. The numerical simulation also indicates that all the dynamical characteristics of the continuous model are conserved by discrete NSFD scheme. The theoretical and numerical results in the current work can be engaged as a useful tool for tracking the occurrence of typhoid fever disease. |
format | Online Article Text |
id | pubmed-10504385 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-105043852023-09-17 The stability analysis of a nonlinear mathematical model for typhoid fever disease Khan, Ihsan Ullah Mustafa, Shahbaz Shokri, Ali Li, Shuo Akgül, Ali Bariq, Abdul Sci Rep Article Typhoid fever is a contagious disease that is generally caused by bacteria known as Salmonella typhi. This disease spreads through manure contamination of food or water and infects unprotected people. In this work, our focus is to numerically examine the dynamical behavior of a typhoid fever nonlinear mathematical model. To achieve our objective, we utilize a conditionally stable Runge–Kutta scheme of order 4 (RK-4) and an unconditionally stable non-standard finite difference (NSFD) scheme to better understand the dynamical behavior of the continuous model. The primary advantage of using the NSFD scheme to solve differential equations is its capacity to discretize the continuous model while upholding crucial dynamical properties like the solutions convergence to equilibria and its positivity for all finite step sizes. Additionally, the NSFD scheme does not only address the deficiencies of the RK-4 scheme, but also provides results that are consistent with the continuous system's solutions. Our numerical results demonstrate that RK-4 scheme is dynamically reliable only for lower step size and, consequently cannot exactly retain the important features of the original continuous model. The NSFD scheme, on the other hand, is a strong and efficient method that presents an accurate portrayal of the original model. The purpose of developing the NSFD scheme for differential equations is to make sure that it is dynamically consistent, which means to discretize the continuous model while keeping significant dynamical properties including the convergence of equilibria and positivity of solutions for all step sizes. The numerical simulation also indicates that all the dynamical characteristics of the continuous model are conserved by discrete NSFD scheme. The theoretical and numerical results in the current work can be engaged as a useful tool for tracking the occurrence of typhoid fever disease. Nature Publishing Group UK 2023-09-15 /pmc/articles/PMC10504385/ /pubmed/37714901 http://dx.doi.org/10.1038/s41598-023-42244-5 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Khan, Ihsan Ullah Mustafa, Shahbaz Shokri, Ali Li, Shuo Akgül, Ali Bariq, Abdul The stability analysis of a nonlinear mathematical model for typhoid fever disease |
title | The stability analysis of a nonlinear mathematical model for typhoid fever disease |
title_full | The stability analysis of a nonlinear mathematical model for typhoid fever disease |
title_fullStr | The stability analysis of a nonlinear mathematical model for typhoid fever disease |
title_full_unstemmed | The stability analysis of a nonlinear mathematical model for typhoid fever disease |
title_short | The stability analysis of a nonlinear mathematical model for typhoid fever disease |
title_sort | stability analysis of a nonlinear mathematical model for typhoid fever disease |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10504385/ https://www.ncbi.nlm.nih.gov/pubmed/37714901 http://dx.doi.org/10.1038/s41598-023-42244-5 |
work_keys_str_mv | AT khanihsanullah thestabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease AT mustafashahbaz thestabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease AT shokriali thestabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease AT lishuo thestabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease AT akgulali thestabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease AT bariqabdul thestabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease AT khanihsanullah stabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease AT mustafashahbaz stabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease AT shokriali stabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease AT lishuo stabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease AT akgulali stabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease AT bariqabdul stabilityanalysisofanonlinearmathematicalmodelfortyphoidfeverdisease |