Optimal control of hybrid variable-order fractional coronavirus (2019-nCov) mathematical model; numerical treatments

• Published in: Ecological complexity 2022-03, Vol.49, p.100983-100983, Article 100983
• Main Authors: Sweilam, N.H., AL-Mekhlafi, S.M., Al-Ajami, T.M.
• Format: Article
• Language: English
• Subjects: Caputo proportional constant finite difference method; Coronavirus diseases; Generalized fourth order Runge-Kutta method; Hybrid variable-order operator; Optimal control problems
• ISSN: 1476-945X; 1476-945X
• DOI: 10.1016/j.ecocom.2022.100983

•Optimal control of the hybrid variable-order fractional model of Coronavirus is presented.•Existence, uniqueness, boundedness, positivity, local and global stability of the solutions of the proposed model problem are proved.•Two control variables are considered to reduce the transmission of infection into healthy people.•Necessary conditions for the control problem are given.•Finite difference method with a hybrid variable-order operator and generalized fourth order Runge-Kutta method are used to study the optimality systems.•Stability analysis and convergence for the proposed method are proved.•Comparative studies between the obtained approximate solutions and the WHO real data for Egypt are given.•Numerical simulations are given. A novel coronavirus is a serious global issue and has a negative impact on the economy of Egypt. According to the publicly reported data, the first case of the novel corona virus in Egypt was reported on 14 February 2020. Total of 96753 cases were recorded in Egypt from the beginning of the pandemic until the eighteenth of August, where 96, 581 individuals were Egyptians and 172 were foreigners. Recently, many mathematical models have been considered to better understand coronavirus infection. Most of these models are based on classical integer-order derivatives which can not capture the fading memory and crossover behavior found in many biological phenomena. Therefore, we study the coronavirus disease in this paper by exploring the dynamics of COVID-19 infection using new variable-order fractional derivatives. This paper presents an optimal control problem of the hybrid variable-order fractional model of Coronavirus. The variable-order fractional operator is modified by an auxiliary parameter in order to satisfy the dimensional matching between the both sides of the resultant variable-order fractional equations. Existence, uniqueness, boundedness, positivity, local and global stability of the solutions are proved. Two control variables are considered to reduce the transmission of infection into healthy people. To approximate the new hybrid variable-order operator, Grünwald-Letnikov approximation is used. Finite difference method with a hybrid variable-order operator and generalized fourth order Runge-Kutta method are used to solve the optimality system. Numerical examples and comparative studies for testing the applicability of the utilized methods and to show the simplicity of these approximation approaches are presented. Mor