Novel analytical and numerical techniques for fractional temporal SEIR measles model

被引:10
作者
Abdullah, F. A. [1 ]
Liu, F. [2 ]
Burrage, P. [2 ]
Burrage, K. [3 ]
Li, T. [4 ]
机构
[1] Univ Sains Malaysia, Sch Math Sci, Usm 11800, Pulau Pinang, Malaysia
[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
[3] Queensland Univ Technol, ACEMS ARC Ctr Excellence, Brisbane, Qld 4001, Australia
[4] Sichuan Univ Sci & Engn, Sch Math & Stat, Zigong 643000, Peoples R China
基金
中国国家自然科学基金;
关键词
Time fractional model; SEIR measles model; Analytical solution; Predictor-corrector method; GMMP Scheme; FOKKER-PLANCK EQUATION; DIFFERENTIAL-EQUATIONS; DIFFUSION; EPIDEMICS;
D O I
10.1007/s11075-017-0426-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, a fractional temporal SEIR measles model is considered. The model consists of four coupled time fractional ordinary differential equations. The time-fractional derivative is defined in the Caputo sense. Firstly, we solve this model by solving an approximate model that linearizes the four time fractional ordinary differential equations (TFODE) at each time step. Secondly, we derive an analytical solution of the single TFODE. Then, we can obtain analytical solutions of the four coupled TFODE at each time step, respectively. Thirdly, a computationally effective fractional Predictor-Corrector method (FPCM) is proposed for simulating the single TFODE. And the error analysis for the fractional predictor-corrector method is also given. It can be shown that the fractional model provides an interesting technique to describe measles spreading dynamics. We conclude that the analytical and Predictor-Corrector schemes derived are easy to implement and can be extended to other fractional models. Fourthly, for demonstrating the accuracy of analytical solution for fractional decoupled measles model, we applied GMMP Scheme (Gorenflo-Mainardi-Moretti-Paradisi) to the original fractional equations. The comparison of the numerical simulations indicates that the solution of the decoupled and linearized system is close enough to the solution of the original system. And it also indicates that the linearizing technique is correct and effective.
引用
收藏
页码:19 / 40
页数:22
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