Optimal control of a fractional order model for granular SEIR epidemic with uncertainty

•Optimal control problem governed by fuzzy fractional differential systems.•Granular SIR and SEIR epidemic models are introduced.•A Numerical Scheme to Solve Fractional Optimal Control Problems.•An application of real data extracted from COVID-19 pandemic. In this study, we present a general formula...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2020-09, Vol.88, p.105312-105312, Article 105312
Main Authors: Dong, Nguyen Phuong, Long, Hoang Viet, Khastan, Alireza
Format: Article
Language:English
Subjects:
COVID-19
Differential equations
Diseases modeling
Environment models
Epidemics
Fractional optimal control
Fuzzy logic
Fuzzy systems
Granular differentiability
Matrix Mittag-Leffler function
Optimal control
Optimization
Pandemics
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Summary:•Optimal control problem governed by fuzzy fractional differential systems.•Granular SIR and SEIR epidemic models are introduced.•A Numerical Scheme to Solve Fractional Optimal Control Problems.•An application of real data extracted from COVID-19 pandemic. In this study, we present a general formulation for the optimal control problem to a class of fuzzy fractional differential systems relating to SIR and SEIR epidemic models. In particular, we investigate these epidemic models in the uncertain environment of fuzzy numbers with the rate of change expressed by granular Caputo fuzzy fractional derivatives of order β ∈ (0, 1]. Firstly, the existence and uniqueness of solution to the abstract fractional differential systems with fuzzy parameters and initial data are proved. Next, the optimal control problem for this fractional system is proposed and a necessary condition for the optimality is obtained. Finally, some examples of the fractional SIR and SEIR models are presented and tested with real data extracted from COVID-19 pandemic in Italy and South Korea.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2020.105312