Geodesic
Some remarks on a mathematical model of COVID-19 pandemic with health care capacity
Mathematica Applicanda, Tome 50 (2022) no. 1, pp. 23-42.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

In this paper, a SEIR model proposed in an article “Dynamic analysis of mathematical model with health care capacity for COVID-19 pandemic” by S. Çakan (2020) is analysed. The model describes COVID-19 pandemic spread affected by healthcare capacity and is expressed by a system of delay differential equations. To prove the local stability of stationary states, S. Çakan uses linearization technique, though she does this as if the equations did not depend on the delay. Additionally, it is shown that the crucial argument used by S. Çakan to prove boundedness of the solutions is not correct, which implies that the proofs of global stability in the original article are not correct either. In this paper, improved proofs of local and global stability of the stationary states are provided. For local stability of the stationary states a standard linearization technique is used. Global stability of the stationary states is proved based on Lyapunov’s functionals. Although the functionals are the same as those proposed by S. Çakan, additional properties of the solutions (in the case of disease–free stationary state) and the functional (in the case of the endemic stationary state) are proved.
DOI : 10.14708/ma.v50i1.7113
Classification : 34K20, 34K21, 37N25
Mots-clés : delay differential equations, Lyapunov's functional, COVID-19 spread model, healthcare capacity, stationary states, local and global stability 
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Joanna Krawczyk; Agnieszka Kowalewska; Marek Bodnar. Some remarks on a mathematical model of COVID-19 pandemic with health care capacity. Mathematica Applicanda, Tome 50 (2022) no. 1, pp.  23-42. doi : 10.14708/ma.v50i1.7113. http://geodesic.mathdoc.fr/articles/10.14708/ma.v50i1.7113/

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