Numerical study for multi-strain tuberculosis (TB) model of variable-order fractional derivatives
نویسندگان
چکیده
In this paper, we presented a novel multi-strain TB model of variable-order fractional derivatives, which incorporates three strains: drug-sensitive, emerging multi-drug resistant (MDR) and extensively drug-resistant (XDR), as an extension for multi-strain TB model of nonlinear ordinary differential equations which developed in 2014 by Arino and Soliman [1]. Numerical simulations for this variable-order fractional model are the main aim of this work, where the variable-order fractional derivative is defined in the sense of Grünwald-Letnikov definition. Two numerical methods are presented for this model, the standard finite difference method (SFDM) and nonstandard finite difference method (NSFDM). Numerical comparison between SFDM and NSFDM is presented. It is concluded that, NSFDM preserves the positivity of the solutions and numerically stable in large regions than SFDM.
منابع مشابه
Implicit RBF Meshless Method for the Solution of Two-dimensional Variable Order Fractional Cable Equation
In the present work, the numerical solution of two-dimensional variable-order fractional cable (VOFC) equation using meshless collocation methods with thin plate spline radial basis functions is considered. In the proposed methods, we first use two schemes of order O(τ2) for the time derivatives and then meshless approach is applied to the space component. Numerical results obtained ...
متن کاملOn modeling two immune effectors two strain antigen interaction
In this paper we consider the fractional order model with two immune effectors interacting with two strain antigen. The systems may explain the recurrence of some diseases e.g. tuberculosis (TB). The stability of equilibrium points are studied. Numerical solutions of this model are given. Using integer order system the system oscillates. Using fractional order system the system converges to a s...
متن کاملA numerical method for discrete fractional--order chemostat model derived from nonstandard numerical scheme
In this paper, the fractional--order form of three dimensional chemostat model with variable yields is introduced. The stability analysis of this fractional system is discussed in detail. In order to study the dynamic behaviours of the mentioned fractional system, the well known nonstandard (NSFD) scheme is implemented. The proposed NSFD scheme is compared with the forward Euler and ...
متن کاملStudy on multi-order fractional differential equations via operational matrix of hybrid basis functions
In this paper we apply hybrid functions of general block-pulse functions and Legendre polynomials for solving linear and nonlinear multi-order fractional differential equations (FDEs). Our approach is based on incorporating operational matrices of FDEs with hybrid functions that reduces the FDEs problems to the solution of algebraic systems. Error estimate that verifies a converge...
متن کاملA study of a Stefan problem governed with space–time fractional derivatives
This paper presents a fractional mathematical model of a one-dimensional phase-change problem (Stefan problem) with a variable latent-heat (a power function of position). This model includes space–time fractional derivatives in the Caputo sense and time-dependent surface-heat flux. An approximate solution of this model is obtained by using the optimal homotopy asymptotic method to find the solu...
متن کامل