Optimization and control in rubella transmission dynamics: A boundedness-preserving numerical model with vaccination

Rubella is an infectious disease that can spread globally. It spreads in the subtropics as well as the tropics. Although it is commonly thought to be a non-fatal condition, there are several circumstances in which it can be fatal. Pregnant women infected with the Rubella virus face a high risk of fe...

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Main Authors: Samiullah Salim, Fazal Dayan, Muhammad Aziz ur Rehman, Husam A. Neamah
Format: Article
Language:English
Published: Elsevier 2024-01-01
Series:Informatics in Medicine Unlocked
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Online Access:http://www.sciencedirect.com/science/article/pii/S2352914824001527
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author Samiullah Salim
Fazal Dayan
Muhammad Aziz ur Rehman
Husam A. Neamah
author_facet Samiullah Salim
Fazal Dayan
Muhammad Aziz ur Rehman
Husam A. Neamah
author_sort Samiullah Salim
collection DOAJ
description Rubella is an infectious disease that can spread globally. It spreads in the subtropics as well as the tropics. Although it is commonly thought to be a non-fatal condition, there are several circumstances in which it can be fatal. Pregnant women infected with the Rubella virus face a high risk of fetal development. The main goal of this study is to look into a model for the spread of Rubella while considering a vaccination campaign as a control measure. The positivity and boundedness of the re-infection rubella transmission and vaccination model are investigated. The local and global stability of the equilibrium points is examined. The sensitivity of parameters is also investigated. Three different techniques forward Euler, RK-4, and non-standard finite difference (NSFD) method are developed for the numerical solution, and their simulation results are examined. Among these three, the NSFD method is superior due to its convergence and positive behavior for all step size values. For some values of the step size, the other two techniques failed to produce positivity and convergent solutions. Analytically, the proposed model's convergence, positivity, boundedness, and consistency are investigated. Finally, the impact of the Rubella vaccine on infected populations has been examined, revealing that vaccination is one of the most effective ways to prevent rubella transmission.
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issn 2352-9148
language English
publishDate 2024-01-01
publisher Elsevier
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spelling doaj-art-30975c79dc0f452cb7c4afd3e563b7022025-08-20T02:21:07ZengElsevierInformatics in Medicine Unlocked2352-91482024-01-015110159510.1016/j.imu.2024.101595Optimization and control in rubella transmission dynamics: A boundedness-preserving numerical model with vaccinationSamiullah Salim0Fazal Dayan1Muhammad Aziz ur Rehman2Husam A. Neamah3Department of Mathematics, School of Science, University of Management and Technology, Lahore, 54000, PakistanDepartment of Mathematics, School of Science, University of Management and Technology, Lahore, 54000, PakistanDepartment of Mathematics, School of Science, University of Management and Technology, Lahore, 54000, PakistanDepartment of Electrical Engineering and Mechatronics, Faculty of Engineering, University of Debrecen, Òtemetö Utca 2-4, 4028, Debrecen, Hungary; Technical Engineering College, Al-Ayen University, Thi-Qar 64001, Iraq; Department of Business Management, Al-imam University College, Balad, Iraq; Corresponding author.Rubella is an infectious disease that can spread globally. It spreads in the subtropics as well as the tropics. Although it is commonly thought to be a non-fatal condition, there are several circumstances in which it can be fatal. Pregnant women infected with the Rubella virus face a high risk of fetal development. The main goal of this study is to look into a model for the spread of Rubella while considering a vaccination campaign as a control measure. The positivity and boundedness of the re-infection rubella transmission and vaccination model are investigated. The local and global stability of the equilibrium points is examined. The sensitivity of parameters is also investigated. Three different techniques forward Euler, RK-4, and non-standard finite difference (NSFD) method are developed for the numerical solution, and their simulation results are examined. Among these three, the NSFD method is superior due to its convergence and positive behavior for all step size values. For some values of the step size, the other two techniques failed to produce positivity and convergent solutions. Analytically, the proposed model's convergence, positivity, boundedness, and consistency are investigated. Finally, the impact of the Rubella vaccine on infected populations has been examined, revealing that vaccination is one of the most effective ways to prevent rubella transmission.http://www.sciencedirect.com/science/article/pii/S2352914824001527RubellaSensitivityStabilityConvergenceConsistencyPositivity
spellingShingle Samiullah Salim
Fazal Dayan
Muhammad Aziz ur Rehman
Husam A. Neamah
Optimization and control in rubella transmission dynamics: A boundedness-preserving numerical model with vaccination
Informatics in Medicine Unlocked
Rubella
Sensitivity
Stability
Convergence
Consistency
Positivity
title Optimization and control in rubella transmission dynamics: A boundedness-preserving numerical model with vaccination
title_full Optimization and control in rubella transmission dynamics: A boundedness-preserving numerical model with vaccination
title_fullStr Optimization and control in rubella transmission dynamics: A boundedness-preserving numerical model with vaccination
title_full_unstemmed Optimization and control in rubella transmission dynamics: A boundedness-preserving numerical model with vaccination
title_short Optimization and control in rubella transmission dynamics: A boundedness-preserving numerical model with vaccination
title_sort optimization and control in rubella transmission dynamics a boundedness preserving numerical model with vaccination
topic Rubella
Sensitivity
Stability
Convergence
Consistency
Positivity
url http://www.sciencedirect.com/science/article/pii/S2352914824001527
work_keys_str_mv AT samiullahsalim optimizationandcontrolinrubellatransmissiondynamicsaboundednesspreservingnumericalmodelwithvaccination
AT fazaldayan optimizationandcontrolinrubellatransmissiondynamicsaboundednesspreservingnumericalmodelwithvaccination
AT muhammadazizurrehman optimizationandcontrolinrubellatransmissiondynamicsaboundednesspreservingnumericalmodelwithvaccination
AT husamaneamah optimizationandcontrolinrubellatransmissiondynamicsaboundednesspreservingnumericalmodelwithvaccination