STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT

Diphtheria is an acute disease that affects the upper respiratory tract caused by Corynebacterium diphtheriae, which can also affect the skin, eyes, and other organs. This article analyzes the stability of the SIQR model of diphtheria disease spread in Mandau District by considering the migration fa...

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Main Authors: Mohammad Soleh, Mutia Nazvira, Wartono Wartono, Elfira Safitri, Riry Sriningsih
Format: Article
Language:English
Published: Universitas Pattimura 2025-01-01
Series:Barekeng
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Online Access:https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13060
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author Mohammad Soleh
Mutia Nazvira
Wartono Wartono
Elfira Safitri
Riry Sriningsih
author_facet Mohammad Soleh
Mutia Nazvira
Wartono Wartono
Elfira Safitri
Riry Sriningsih
author_sort Mohammad Soleh
collection DOAJ
description Diphtheria is an acute disease that affects the upper respiratory tract caused by Corynebacterium diphtheriae, which can also affect the skin, eyes, and other organs. This article analyzes the stability of the SIQR model of diphtheria disease spread in Mandau District by considering the migration factor. The SIQR model is a development of the SIR model by incorporating the quarantine process as an alternative to reduce morbidity. The purpose of this study is to see the effect of migration on the spread of diphtheria disease in Mandau District through mathematical model simulation. We calculated the disease-free and endemic equilibrium points and the basic reproduction number ( ) of the model. Model parameters were obtained using data from BPS Bengkalis Regency and UPTD Puskesmas Mandau. The calculation resulted in one disease-free equilibrium point and one endemic equilibrium point. If  < 1, then the disease-free equilibrium point is asymptotically stable, and if  > 1, then the endemic equilibrium point is also asymptotically stable. Based on the results of the data analysis, the value of. This value is less than 1, so the equilibrium point obtained is a disease-free and asymptotically stable equilibrium point. This means that the population will be free from diphtheria and the level of migration affects the presence of diphtheria disease in Mandau District.
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spelling doaj-art-ddc802965e424e88acf6fd5cf73f50232025-08-20T03:41:56ZengUniversitas PattimuraBarekeng1978-72272615-30172025-01-0119117318410.30598/barekengvol19iss1pp173-18413060STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACTMohammad Soleh0Mutia Nazvira1Wartono Wartono2Elfira Safitri3Riry Sriningsih4Department of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Sultan Syarif Kasim Riau, IndonesiaDepartment of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Sultan Syarif Kasim Riau, IndonesiaDepartment of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Sultan Syarif Kasim Riau, IndonesiaDepartment of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Sultan Syarif Kasim Riau, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Padang, IndonesiaDiphtheria is an acute disease that affects the upper respiratory tract caused by Corynebacterium diphtheriae, which can also affect the skin, eyes, and other organs. This article analyzes the stability of the SIQR model of diphtheria disease spread in Mandau District by considering the migration factor. The SIQR model is a development of the SIR model by incorporating the quarantine process as an alternative to reduce morbidity. The purpose of this study is to see the effect of migration on the spread of diphtheria disease in Mandau District through mathematical model simulation. We calculated the disease-free and endemic equilibrium points and the basic reproduction number ( ) of the model. Model parameters were obtained using data from BPS Bengkalis Regency and UPTD Puskesmas Mandau. The calculation resulted in one disease-free equilibrium point and one endemic equilibrium point. If  < 1, then the disease-free equilibrium point is asymptotically stable, and if  > 1, then the endemic equilibrium point is also asymptotically stable. Based on the results of the data analysis, the value of. This value is less than 1, so the equilibrium point obtained is a disease-free and asymptotically stable equilibrium point. This means that the population will be free from diphtheria and the level of migration affects the presence of diphtheria disease in Mandau District.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13060stability analysissiqr modeldiphtheria diseaseequilibrium stateasymptotically stable
spellingShingle Mohammad Soleh
Mutia Nazvira
Wartono Wartono
Elfira Safitri
Riry Sriningsih
STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT
Barekeng
stability analysis
siqr model
diphtheria disease
equilibrium state
asymptotically stable
title STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT
title_full STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT
title_fullStr STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT
title_full_unstemmed STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT
title_short STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT
title_sort stability analysis of the siqr model of diphtheria disease spread and migration impact
topic stability analysis
siqr model
diphtheria disease
equilibrium state
asymptotically stable
url https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13060
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