Qualitative and sensitivity analysis on simple epidemic model (SIR-MODEL): ensuring well-posedness and stability

Authors

  • Auwal Lawan Department of Mathematics, University of Verona, Italy https://orcid.org/0009-0000-8244-7786
  • Abubakar Salihu Department of Mathematics, Aliko Dangote University of Science and Technology, Wudil, Nigeria
  • Ismail Ahmad Federal University Dutse, Nigeria
  • Jibril Abdullahi Department of Physics, Aliko Dangote University of Science and Technology, Wudil, Nigeria
  • Umar Abdullahi Department of Mathematics, Aliko Dangote University of Science and Technology, Wudil, Nigeria

DOI:

https://doi.org/10.64497/jssci.49

Keywords:

model, stability, equilibrium, next-generation matrix, sensitivity

Abstract

This study investigates the dynamics of infectious disease transmission using an SIR (Susceptible-Infected-Recovered) model. We examine the model’s positivity, equilibrium points, basic reproduction number using the next generation matrix method, and sensitivity to key parameters using the sensitivity index method. Our findings reveal the equilibrium point, basic reproduction number, and most sensitive parameter, , which significantly influences the infectious rate. By identifying the effective control measures, particularly targeting,  we can reduce the spread of the disease. This research highlights the importance of understanding infectious disease dynamics and informs strategies for disease control and prevention.   

Downloads

Download data is not yet available.

Author Biography

Auwal Lawan, Department of Mathematics, University of Verona, Italy

Auwal Lawan is a graduate of mathematics from Aliko Dangote University of Science and Technology, Wudil Kano, Nigeria, Auwal graduated as the best students in his department, and was selected as the first and only African student for the Maths-Disc master degree program as a scholarship holder starting at University of Verona, Italy.

He is also a data scientist, machine learning, and AI practitioner.

References

[1] Zaman, Gul, Yong han Kang. (2008). S. Stability analysis and vaccination of an SIR epidemic model. Biosystems, 93(3), 240-249.

[2] Boris Shulgin. (1998). Pulse vaccination strategy in the SIR epidemic model. Bulletin of mathematical biology, 60, 1123-1148. DOI: https://doi.org/10.1016/S0092-8240(98)90005-2

[3] Gul Zaman, Yong Han Kang, Il Hyo Jung. (2018). Stability Analysis and Optimal Vacination on SIR Model. Biosystems, 93(3), 240-249. DOI: https://doi.org/10.1016/j.biosystems.2008.05.004

[4] Settapat Chinviriyasit. (2010). Numerical modelling of an SIR epidemic model with diffusion. Applied mathematics and computation, 216(2), 394-409. DOI: https://doi.org/10.1016/j.amc.2010.01.028

[5] Simon Merkt. (2025). Integrating Complex Biomedical Datasets into Differential Equation Models, . - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn. Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-83675.

[6] Winnie Kulei, Amos Kipkorir Langat, David Chepkonga, John Kamwele Mutinda (2025). Optimizing Control Measures for a Vector-Host Epidemic Model: A Mathematical Analysis Applied Mathematics on Science and Engineering, 2(1):57-82, 2025.

[7] Ihor, K., Mykhailovych, C. I., & Dmytro, S. Mathematical analysis of SIR models of epidemiology processes. Bukovinian Mathematical Journal, 13(1), 83-91 DOI: https://doi.org/10.31861/bmj2025.01.07

[8] Herdicho, F. F., Hakim, N. A., Fatmawati, F., Alfiniyah, C., & Akanni, J. O. (2025). Mathematical Model Of Dengue Hemorrhagic Fever Spread With Different Levels Of Transmission Risk. Barekeng: Jurnal Ilmu Matematika dan Terapan, 19(3), 1649-1666 DOI: https://doi.org/10.30598/barekengvol19iss3pp1649-1666

[9] Yu, Gouzhi, and Houhui Huang. Mathematical modelling of the heterogeneity of disease progression an d treatment outcomes in patients with COVID-19. Frontiers in Microbiology 16:1551320. DOI: https://doi.org/10.3389/fmicb.2025.1551320

[10] John Boscoh H Njagarah and Farai Nyabadza. Modelling the role of drug barons on the prevalence of drug epidemics. Mathematical Biosciences & Engineering, 10(3):843–860, 2013. DOI: https://doi.org/10.3934/mbe.2013.10.843

[11] Karl Peltzer, Shandir Ramlagan, Bruce D Johnson, and Nancy Phaswana Mafuya. Illicit drug use and treatment in south africa: a review. Substance use & misuse, 45(13):2221–2243, 2010. DOI: https://doi.org/10.3109/10826084.2010.481594

[12] Charles Parry, Andreas Pl¨ uddemann, and Arvin Bhana. Monitoring alcohol and drug abuse trends in South Africa (1996–2006): reflections on treatment demand trends. Contemporary Drug Problems, 36(3-4):685–703, 2009. DOI: https://doi.org/10.1177/009145090903600319

[13] John Olajide Akanni and Afeez Abidemi. Mathematical analysis of the concomitance of illicit drug use and banditry in a population. 2021. DOI: https://doi.org/10.21203/rs.3.rs-1089919/v1

Downloads

Published

2025-10-29

How to Cite

Lawan, A., Salihu, A., Ahmad, I., Abdullahi, J., & Abdullahi, U. (2025). Qualitative and sensitivity analysis on simple epidemic model (SIR-MODEL): ensuring well-posedness and stability. Journal of Statistical Sciences and Computational Intelligence, 1(4), 312–320. https://doi.org/10.64497/jssci.49

Issue

Vol. 1 No. 4 (2025): Volume 1, Issue 4 (October – December 2025)

Section

Articles

License

Copyright (c) 2025 Auwal Lawan, Abubakar Salihu, Ismail Ahmad, Jibril Abdullahi, Umar Abdullahi

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Views
  • Abstract 477
  • PDF 157

Similar Articles

1 2 3 4 > >> 

You may also start an advanced similarity search for this article.