We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stability of the disease-free equilibrium point is investigated. We prove the existence of solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. In the numerical section, we present a simulation to examine the system, in which we calculate equilibrium points of the system and examine the behavior of the resulting functions at the equilibrium points. By calculating the results of the model for different fractional order, we examine the effect of the derivative order on the behavior of the resulting functions and obtained numerical values. We also calculate the results of the integer-order model and examine their differences with the results of the fractional-order model.

我们使用Caputo–Fabrizio分数阶导数研究AH1N1流感传播的SEIR流行病模型。计算系统和平衡点的繁殖数，并研究无病平衡点的稳定性。利用定点理论证明了该模型解的存在性。使用分数欧拉方法，我们得到了模型的近似解。在数值部分，我们提供了一个模拟系统以检查系统，在该系统中，我们计算系统的平衡点并检查结果函数在平衡点处的行为。通过计算不同分数阶模型的结果，我们检查了导数阶对结果函数行为的影响并获得了数值。