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

作　　者：李琳娜[1] 王欢 黄琼丹 仝秋娟 LI Lin-na;WANG Huan;HUANG Qun-dan;TONG Qiu-juan(Alumni office, Xi’an University of Post and Telecommunications, Xi’an 710121, China;School of Communication and Information Engineering, Xi'an University of Post and Telecommunications, Xi’an 710121, China;School of Science, Xi’an University of Post and Telecommunications, Xi’an 710121, China)

机构地区：[1]西安邮电大学校友办公室,陕西西安710121 [2]西安邮电大学通信与信息工程学院,陕西西安710121 [3]西安邮电大学理学院,陕西西安710121

出　　处：《数学的实践与认识》2019年第15期306-317,共12页Mathematics in Practice and Theory

基　　金：国家民委民族研究项目(2018-GME-010);陕西省重点研发计划(2018GY-150);西安市科技计划项目(201805040YD18CG24-3)

摘　　要：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.

关 键 词：分数阶SEIR模型 残差幂级数法 CAPUTO导数 

分 类 号：O172[理学—数学] R181[理学—基础数学]