Infection Eradication Criterion in a General Epidemic Model with Logistic Growth, Quarantine Strategy, Media Intrusion, and Quadratic Perturbation

Yassine Sabbar, Mehmet Yavuz () and Fatma Özköse
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Yassine Sabbar: LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez 30050, Morocco
Mehmet Yavuz: Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, Konya 42090, Turkey
Fatma Özköse: Department of Mathematics, Faculty of Science, Erciyes University, Kayseri 38039, Turkey

Mathematics, 2022, vol. 10, issue 22, 1-16

Abstract: This article explores and highlights the effect of stochasticity on the extinction behavior of a disease in a general epidemic model. Specifically, we consider a sophisticated dynamical model that combines logistic growth, quarantine strategy, media intrusion, and quadratic noise. The amalgamation of all these hypotheses makes our model more practical and realistic. By adopting new analytical techniques, we provide a sharp criterion for disease eradication. The theoretical results show that the extinction criterion of our general perturbed model is mainly determined by the parameters closely related to the linear and quadratic perturbations as well as other deterministic parameters of the system. In order to clearly show the strength of our new result in a practical way, we perform numerical examples using the case of herpes simplex virus (HSV) in the USA. We conclude that a great amount of quadratic noise minimizes the period of HSV and affects its eradication time.

Keywords: epidemic model; logistic growth; quarantine strategy; media intrusion; quadratic noise (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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