中文摘要：

在经典的SIR,SIRS,SIS流行病模型基础上引入关于时间的分数阶导数,并利用同伦摄动方法分别求出这3个模型的近似解析解,而且应用数值实验结果印证了FDEs的记忆特征.改进和推广了一些已有的成果,且对深入研究分数阶流行病模型有很好的启示作用.

英文摘要：

By the homotopy perturbation method（ HPM）,the approximate analytic solutions of fractional-order time derivatives are presented for the classical SIR,SIRS and SIS epidemic models with initial values. Besides,the numerical simulation results illustrate the memory character of FDEs,which improves and expands current results for epidemic dynamic. It will inspire further research on the fractional epidemic systems.