Square-Root Dynamics of a SIR-Model in Fractional Order

• 作者: Anwar Zeb Gul Zaman Il Hyo Jung Young Il Seo
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Mathematical MODEL SQUARE ROOT Dynamics FRACTIONAL DERIVATIVE Non-Standard Finite Difference Scheme Numerical Analysis
• 年，卷（期）: 2012,（12）
• 页码范围: 1882-1887
• 页数: 6页
• 分类号: O1

摘要

In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented and a discrete-time finite difference scheme is constructed using the nonstandard finite difference (NSFD) method. A comparative study of the classical Runge-Kutta method and ODE45 is presented in the case of integer order derivatives. The solutions obtained are presented graphically.