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

作     者：Young Il Seo Anwar Zeb Gul Zaman Il Hyo Jung 

作者机构：Department of Mathematics Pusan National University Busan South Korea Department of Mathematics University of Malakand Chakdara Pakistan National Fisheries Research and Development Institute Busan South Korea 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2012年第3卷第12期

页      面：1882-1887页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Mathematical Model Square Root Dynamics Fractional Derivative Non-Standard Finite Difference Scheme Numerical Analysis 

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.