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.

在本文中，提出了针对HIV / AIDS和疟疾共同感染的可变阶数分数阶多延迟数学模型的最优控制。该模型由十二个微分方程组成，其中变量阶导数在Caputo的意义上。在该模型中提供了三个控制变量，以最大程度地减少无艾滋病症状的合并感染患者，感染疟疾的患者以及无症状感染艾滋病毒/艾滋病的患者的数量。得出控制问题的必要条件。构建了Grünwald-Letnikov非标准有限差分方案，以模拟所提出的最优控制系统。证明了所提方案的稳定性。为了验证理论结果，给出了数值模拟和比较研究。