This article investigates a family of approximate solutions for the fractional model (in the Liouville-Caputo sense) of the Ebola virus via an accurate numerical procedure (Chebyshev spectral collocation method). We reduce the proposed epidemiological model to a system of algebraic equations with the help of the properties of the Chebyshev polynomials of the third kind. Some theorems about the convergence analysis and the existence-uniqueness solution are stated. Finally, some numerical simulations are presented for different values of the fractional-order and the other parameters involved in the coefficients. We also note that we can apply the proposed method to solve other models.

本文通过精确的数值程序（切比雪夫谱搭配法）研究了埃博拉病毒分数模型（刘维尔-卡普托意义上）的一系列近似解。我们借助第三类切比雪夫多项式的性质将所提出的流行病学模型简化为代数方程组。给出了收敛性分析和存在唯一性解的一些定理。最后，针对分数阶和系数中涉及的其他参数的不同值进行了一些数值模拟。我们还注意到，我们可以应用所提出的方法来求解其他模型。