Stability analysis of COVID-19 model with fractional-order derivative and a delay in implementing the quarantine strategy

M M Hikal; M M A Elsheikh; W K Zahra

doi:10.1007/s12190-021-01515-y

Stability analysis of COVID-19 model with fractional-order derivative and a delay in implementing the quarantine strategy

J Appl Math Comput. 2022;68(1):295-321. doi: 10.1007/s12190-021-01515-y. Epub 2021 Mar 22.

Authors

M M Hikal^{1

2}, M M A Elsheikh³, W K Zahra^{1

4}

Affiliations

¹ Departement of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt.
² Department of Basic Sciences, Higher Institute of Engineering and Technology Kafrelsheikh, Kafr El Sheikh, Egypt.
³ Departement of Mathematics, Faculty of Science, Menofia University, Shebin El-Koom, Egypt.
⁴ Department of Mathematics, Institute of Basic and Applied Sciences, Egypt-Japan University of Science and Technology (E-JUST), New Borg El-Arab City, 21934 Alexandria Egypt.

Abstract

This study presents methods of hygiene and the use of masks to control the disease. The zero basic reproduction number can be achieved by taking the necessary precautionary measures that prevent the transmission of infection, especially from uninfected virus carriers. The existence of time delay in implementing the quarantine strategy and the threshold values of the time delay that keeping the stability of the system are established. Also, it is found that keeping the infected people quarantined immediately is very important in combating and controlling the spread of the disease. Also, for special cases of the system parameters, the time delay can not affect the asymptotic behavior of the disease. Finally, numerical simulations have been illustrated to validate the theoretical analysis of the proposed model.

Keywords: Caputo fractional derivative; SEIRUS covid-19 epidemic model; Stability analysis.