A novel HIV/AIDS infection model incorporating memory and media coverage effect is formulated. First, we introduce fractional-order derivative to the model. The basic reproduction number $\mathfrak{R}$ ₀ is calculated using the next generation matrix method. Existence, uniqueness, and positivity of the solution of the model are investigated. Existence and local stability analysis of the equilibria of the model are discussed. The disease dies out when $\mathfrak{R}$ ${}_0<1$ at which the disease-free equilibrium is locally asymptotically stable. While the disease persists if $\mathfrak{R}$ ${}_0>1$ at which the disease-free equilibrium becomes unstable and the endemic equilibrium point emerges. Second, a time-delay, $\tau$, is introduced to model the effect of the delayed-induced treatment. The disease-free equilibrium is locally asymptotically stable for all $\tau >0$.

建立了一种新的结合记忆和媒体覆盖作用的HIV / AIDS感染模型。首先，我们将分数阶导数引入模型。基本复制数$\mathfrak{[R}$ 使用下一代矩阵方法计算₀。研究了模型解的存在性，唯一性和正性。讨论了模型平衡性的存在性和局部稳定性。该病何时消失$\mathfrak{[R}$ ${}_0<\mathrm{1个}$无病平衡在局部渐近稳定。如果疾病持续存在，$\mathfrak{[R}$ ${}_0>\mathrm{1个}$无病平衡变得不稳定，地方性平衡点出现。第二，延时$\tau$引入来模拟延迟诱导治疗的效果。对所有人而言，无病平衡是局部渐近稳定的$\tau >0$。