We investigate the celebrated mathematical SICA model but using fractional differential equations in order to better describe the dynamics of HIV-AIDS infection. The infection process is modelled by a general functional response, and the memory effect is described by the Caputo fractional derivative. Stability and instability of equilibrium points are determined in terms of the basic reproduction number. Furthermore, a fractional optimal control system is formulated and the best strategy for minimizing the spread of the disease into the population is determined through numerical simulations based on the derived necessary optimality conditions.

中文翻译：

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具有记忆和一般发生率的艾滋病毒/艾滋病分流行模型的稳定性分析和最优控制

我们调查了著名的数学SICA模型，但使用分数微分方程以更好地描述HIV-AIDS感染的动态。感染过程以一般的功能反应为模型，记忆效果用Caputo分数导数描述。平衡点的稳定性和不稳定性根据基本再生数确定。此外，制定了分数最优控制系统，并根据导出的必要最优条件，通过数值模拟确定了最小化疾病向人群传播的最佳策略。