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

  • Mohammad Soleh Department of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Sultan Syarif Kasim Riau, Indonesia https://orcid.org/0009-0001-3805-574X
  • Mutia Nazvira Department of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Sultan Syarif Kasim Riau, Indonesia https://orcid.org/0009-0006-4280-6573
  • Wartono Wartono Department of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Sultan Syarif Kasim Riau, Indonesia https://orcid.org/0009-0003-2283-1729
  • Elfira Safitri Department of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Sultan Syarif Kasim Riau, Indonesia https://orcid.org/0009-0002-9179-0935
  • Riry Sriningsih Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Padang, Indonesia https://orcid.org/0000-0002-3849-5032
DOI: https://doi.org/10.30598/barekengvol19iss1pp173-184
Keywords: Stability Analysis, SIQR Model, Diphtheria Disease, Equilibrium State, Asymptotically Stable

Abstract

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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Published
2025-01-13
How to Cite
[1]
M. Soleh, M. Nazvira, W. Wartono, E. Safitri, and R. Sriningsih, “STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT”, BAREKENG: J. Math. & App., vol. 19, no. 1, pp. 173-184, Jan. 2025.
Issue
Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2025 Mohammad Soleh, Mutia Nazvira, Wartono Wartono, Elfira Safitri, Riry Sriningsih

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