分数阶SEIR传染病模型的残差幂级数解法

Solution of the fractional SEIR Model of Epidemics Using Residual Power Series Method

SEIR传染病模型在研究传染病和社交网络的信息传播等方面具有重要的应用背景,分数阶SEIR传染病模型对于这些动态系统的传播过程描述更加确切,但是分数阶SEIR模型难于求解.给出一种求解该模型的残差幂级数方法.首先,将分数阶SEIR模型中的S(t)、E(t)、I(t)和R(t)分别用广义泰勒级数展开至k项;再将展开后的表达式带入到分数阶SEIR模型中;利用残差为0来求解未知的系数ak、bk、ck、dk,得到分数阶SEIR模型的一种级数形式的近似解析解.通过与同伦分析变换法得到的解进行对比,结果表明,残差幂级数法在求解分数阶SEIR模型更有效,其误差更小.

The SEIR epidemic model has an important application background in the study of infectious diseases and social network information dissemination. The fractional SEIR epidemic model describes the propagation process of these dynamic systems more accurately, but the fractional SEIR model is difficult to solve. This paper presents a residual power series method for solving the model. First, we use the generalized Taylor series to expand theS(t),E(t),I(t)and R(t)in the fractional SEIR model, we expand them to k term;then the expanded expression is brought into the fractional SEIR model;according to the residual is zero, the unknown coefficients are solved. An approximate analytical solution in the form of a series of fractional SEIR models is obtained. Compared with the solution obtained by the homotopy analysis transformation method, the results show that the residual power series method is more effective in solving the fractional SEIR model, and its error is smaller.