Set-Valued Control Approach Applied to a COVID-19 Model with Screening and Saturated Treatment Function

The purpose of this paper is modelling and controlling the spread of COVID-19 disease in Morocco. A nonlinear mathematical model with two subclasses of infectious individuals is proposed. The population is divided into five classes, namely, susceptible (S), exposed (E), undiagnosed infectious (Inc),...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2020, Vol.2020 (2020), p.1-15
Main Authors: Balatif, Omar, Alkama, Meryem, Boujallal, Lahoucine, Elhia, Mohamed, Rachik, Mostafa
Format: Article
Language:English
Subjects:
Coronaviruses
COVID-19
Disease control
Disease transmission
Epidemiology
Liapunov functions
Mathematical models
Media coverage
Pandemics
Parameter estimation
Population
Quarantine
Severe acute respiratory syndrome coronavirus 2
Social distancing
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Summary:The purpose of this paper is modelling and controlling the spread of COVID-19 disease in Morocco. A nonlinear mathematical model with two subclasses of infectious individuals is proposed. The population is divided into five classes, namely, susceptible (S), exposed (E), undiagnosed infectious (Inc), diagnosed patients (Ic), and removed individuals. To reflect the real dynamic of the COVID-19 transmission in Morocco, the real reported data are used for estimating model parameters. Two controls representing screening effort and limited treatment are considered. Based on viability theory and set-valued analysis, a Lyapunov function is constructed such that both exposed and infected populations are decreased to zero asymptotically. The corresponding controls are derived via a continuous selection of adequately designed feedback map. Numerical simulations are presented with three scenarios (cases when each control is used alone and the case when two controls are combined). Our results show that when only one control is to be applied, screening is the most effective in decreasing the number of people in the three infected compartments, whereas combining both controls is found to be highly effective and leads to a significant improvement in the epidemiological situation of Morocco. To the best of our knowledge, this work is the first one that applies the set-valued approach to a controlled COVID-19 model which agrees with the observed cases in Morocco.
ISSN:1076-2787
1099-0526
DOI:10.1155/2020/9501028