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.
Highlights
The struggle for finding an effective and permanent cure for tumor continues to challenge scientists has been made by a lot of progresses in discovering new methodologies which are helpful in successful treatments to reduce and even clear tumors
We focused on numerical solutions of carcinogenesis mutations models that are based on reaction-diffusion systems and Lotka-Volterra food chains
The immune response to tumors depends on how antigenic the tumor is
Summary
The struggle for finding an effective and permanent cure for tumor continues to challenge scientists has been made by a lot of progresses in discovering new methodologies which are helpful in successful treatments to reduce and even clear tumors. We study a simple model of carcinogenesis mutations of DNA, which originally comes from [3]. Was studied in [4,5,6,7,8,9], which describe a process of carcinogenesis mutations with n different steps of mutations (from normal to malignant cells). The model is expressed in terms of system of partial differential equation, in which the latest stage of mutation has different forms depending on whether it has growth advantage in favorable or competitive conditions or disadvantage of growth in unfavorable and competitive conditions. For simplicity in this paper, we only consider the latest stage in unfavorable conditions, as in the case of favorable conditions there is no possibility to cure the disease without any treatment.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
