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J. C. Arciero, T. L. Jackson and D. E. Kirschner, “A Mathematical Model of Tumor-Immune Evasion and siRNA Treatment,” Discrete and Continuous Dynamical Systems, Series B, Vol. 4, No. 1, 2004, pp. 39-58.

has been cited by the following article:

• TITLE: On the Numerical Solutions of One and Two-Stage Model of Carcinogenesis Mutations with Time Delay and Diffusion

  AUTHORS: Ishtiaq Ali

  KEYWORDS: Carcinogenesis Mutations; Delay and Diffusion; Spectral Postprocessing; Numerical Simulations

  JOURNAL NAME: Applied Mathematics, Vol.4 No.10B, October 16, 2013

  ABSTRACT: In this paper, we focused on numerical solutions of carcinogenesis mutations models that are based on reaction-diffusion systems and Lotka-Volterra food chains. We consider the case with one and two-stages of mutations with appropriate initial conditions and the zero-flux boundary conditions. The main purpose is to construct a stable discretization scheme, which allows much accuracy than those of a standard approach. To this end, we use the spectral method to postprocess numerical solutions for the proposed model by using some classical methods for solving differential equations. The implementation of the algorithm is simple and it does not need to solve the linear or nonlinear system (in case the model is nonlinear). We simulate the one and two-stage carcinogenesis mutations model and compared the results with previously published ones.