Coronavirus epidemic model with isolation and nonlinear incidence rate

Authors

Afaf Zaghrout, Department of Mathematics, Faculty of Science (Girls), Al-Azhar University, Cairo, EgyptFollow
Youssra Ali, Department of Mathematics, Faculty of Science (Girls), Al-Azhar University, Cairo, EgyptFollow
Doaa Elpagouri, Department of Mathematics, Faculty of Science (Girls), Al-Azhar University, Cairo, EgyptFollow

Corresponding Author

Ali, Youssra

Document Type

Original Article

Subject Areas

Mathematics, Statistics, Computer Science, Physics and Astronomy

Keywords

COVID-19; Epidemiology; Reproduction number; stability; Nonlinear incidence rate; isolation

Abstract

In our article we proposed an epidemiological model consisting of five compartments that describe corona virus disease with isolation. We developed an SEIR system to produce the dynamical behaviour of infection by adding isolation compartment F(t) (that is because of the isolation of the infected individuals will reduce the spread of the disease). We formulated our model with nonlinear incidence rate. First, we discussed the positivity and boundedness of the model. Then we calculated the basic reproduction number of the model under certain conditions. By analysing the local and the global stability of our model, it is noticed that this stability depends on the basic reproductive number. We found that the system has no endemic equilibrium state if R0 < 1. Finally, we discussed the global stability by using Lyapunov function of Goh-volterra type with LaSalle’s invariance principle. It was shown that the system has a unique equilibrium point which is global asymptotically stable.

How to Cite This Article

Zaghrout, Afaf; Ali, Youssra; and Elpagouri, Doaa (2021) "Coronavirus epidemic model with isolation and nonlinear incidence rate," Al-Azhar Bulletin of Science: Vol. 32: Iss. 2, Article 7.
DOI: https://doi.org/10.21608/absb.2021.84983.1126