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

Nguyen Phuong Dong; Hoang Viet Long; Alireza Khastan

doi:10.1016/j.cnsns.2020.105312

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

Commun Nonlinear Sci Numer Simul. 2020 Sep:88:105312. doi: 10.1016/j.cnsns.2020.105312. Epub 2020 Apr 30.

Authors

Nguyen Phuong Dong¹, Hoang Viet Long^{2

3}, Alireza Khastan⁴

Affiliations

¹ Faculty of Mathematics, Hanoi Pedagogical University 2, Vietnam.
² Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
³ Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
⁴ Department of Mathematics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran.

Abstract

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.

Keywords: 28B10; 34A07; 54C60; 58C06; Diseases modeling; Fractional optimal control; Granular differentiability; Matrix Mittag-Leffler function.