Optimal control for variable order fractional HIV/AIDS and malaria mathematical models with multi-time delay

• Main Authors: N.H. Sweilam, S.M. AL-Mekhlafi, Z.N. Mohammed, D. Baleanu
• Format: Article
• Language: English
• Published: Elsevier 2020-10-01
• Series: Alexandria Engineering Journal
• Subjects: Variable order fractional multi-delay differential equations; Grünwald-Letnikov nonstandard finite difference method; HIV/AIDS and malaria mathematical models; Optimal control theory
• Online Access: http://www.sciencedirect.com/science/article/pii/S1110016820303446

In this article, optimal control for variable order fractional multi-delay mathematical model for the co-infection of HIV/AIDS and malaria is presented. This model consists of twelve differential equations, where the variable order derivative are in the sense of Caputo. Three control variables are presented in this model to minimize the number of the co-infected individuals showing no symptoms of AIDS, the infected individuals with malaria, and the individuals asymptomatically infected with HIV/AIDS. Necessary conditions for the control problem are derived. The Grünwald-Letnikov nonstandard finite difference scheme is constructed to simulating the proposed optimal control system. The stability of the proposed scheme is proved. In order to validate the theoretical results numerical simulations and comparative studies are given.