“A Stability Study by Routh-Hurwitz Criterion and Gershgorin Circles for Covid-19”

Authors: Bedia Akyar, Ayse Kara Hansen and Sultan Selcuk Sutlu,
Affiliation: University of Southern Denmark, Aarhus University and Halic University
Reference: 2024, Vol 45, No 3, pp. 97-103.

Keywords: Routh-Hurwitz criterion, stability, unstability, Gershgorin circle

Abstract: In this paper, we study stabilization problem on a model for covid-19 by using Routh-Hurwitz criterion and Gershgorin circles. Using Routh-Hurwitz criterion, we prove the necessity of unstability and stability conditions for the model that we extend from an existing one. We give the necessary conditions for stability on this model by using the Gershgorin Circle Theorem and give examples.

PDF PDF (257 Kb)        DOI: 10.4173/mic.2024.3.2

References:
[1] Adom-Konadu, A., Sackitey, A.L., and Anokye, M. (2022). Local stability analysis of epidemic models using a corollary of gershgorin’s circle theorem, Applied Mathematics E-Notes, Research Square. doi:https://doi.org/10.21203/rs.3.rs-1909006/v1
[2] Bejarano, D., E., I.-M., and G´omez-Hern´andez, E. (2018). A stability test for non linear systems of ordinary differential equations based on the gershgorin circles, Contemporary Engineering Science. 11(91):4541--4548. doi:10.12988/ces.2018.89504
[3] Bernoulli, D. (1766). Essai d’une nouvelle analyse de la mortalite causee par la petite verole, Mem. Math. Phys. Acad. Roy.Sci., Paris. pages 1, (Reprinted in: L.P. Bouckaert, B.L. van der Waerden (Eds.), Die Werke von Daniel Bernoulli, Bd. 2 Analysis und Wahrscheinlichkeitsrechnung, Birkh€auser, Basel, 1982, p. 235. English translation entitled ‘An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it’ in: L. Bradley, Smallpox Inoculation: An Eighteenth Century Mathematical Controversy, Adult Education Department, Nottingham, 1971, p. 21. Reprinted in: S. Haberman, T.A. Sibbett (Eds.) History of Actuarial Science, vol. VIII, Multiple Decrement and Multiple State Models, William Pickering, London, 1995, p. 1.).
[4] Dietz, K. and Heesterbeek, J. (2002). Daniel bernoulli’s epidemiological model revisited, Mathematical Biosciences. 180(1:-2):1--21. doi:10.12988/ces.2018.89504
[5] Hethcote, H.W. (2000). The mathematics of infectious diseases, Society for Industrial and Applied Mathematics. 42(4):599--653. doi:10.1137/S0036144500371907
[6] Kermack, W. and Mckendrick, A. (1927). The mathematics of infectious diseases, A Contribution to the Mathematical Theory of Epidemics,Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Characters. 115(772):700--721. doi:10.1098/rspa.1927.01187
[7] Koker, N. and Gozukizil, O. (2021). Application of an epidemic model to turkey data and stability analysis for the covid-19 pandemic, Sakarya University Journal of Science SAUJS. 25(6):1438--1445. doi:10.16984/saufenbilder.980797


BibTeX:
@article{MIC-2024-3-2,
  title={{A Stability Study by Routh-Hurwitz Criterion and Gershgorin Circles for Covid-19}},
  author={Akyar, Bedia and Hansen, Ayse Kara and Sutlu, Sultan Selcuk},
  journal={Modeling, Identification and Control},
  volume={45},
  number={3},
  pages={97--103},
  year={2024},
  doi={10.4173/mic.2024.3.2},
  publisher={Norwegian Society of Automatic Control}
};