Numerical Simulation of Oncolytic M1 Cancer Virotherapy Reaction-Diffusion Model by Collocation of B-Splines

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Rohit Goel , Prof. R.C. Mittal, Dr. Neha Ahlawat

Abstract

Cancer is a leading cause of death worldwide. Invention of better cancer treatment strategies remained a burning topic of the research since decades. Oncolytic virotherapy being a targeted type therapy is an emerging technology that uses selective engineered viruses to treat cancerous malignancies. The dynamics of oncolytic M1 virotherapy with spatial effects and anti-tumour immune responses cab better be studied and analysed with reaction-diffusion mathematical models. A
reaction-diffusion mathematical model to characterize the dynamics of oncolytic M1 alphavirus in the cancer treatment virotherapy with immune responses is studied in this paper. A numerical simulation technique based on the collocation of cubic B-splines is proposed to approximate the solution of the considered reaction-diffusion model. Collocation forms of the partial differential equation results in a system of first order ordinary differential equations which in turn have been solved by Runge-Kutta method of order 4. The non-linearity of the model is being resolved without any transformation or
linearization. The computed numerical results are in good agreement with those expected. Easy to apply and achieving accurate solutions in less CPU time are the key points of the present approach.

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