An Efficient Numerical Simulation of a Reaction-Diffusion Malaria Infection Model using B-splines Collocation

Abstract

• Reaction-diffusion malaria infection model • Neumann Boundary Conditions • Cubic B-splines collocation method • Runge-Kutta method Malaria is a potentially life-threatening disease caused by parasite. This disease is more common in countries with tropical climates. Due to chromosomal mutations, the dynamics of malaria parasites are quite complex to study as well as for any predictions. A reaction-diffusion model to characterize the dynamics of within-host malaria infection with adaptive immune responses is studied in this paper. A numerical scheme 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 RK4 method. The non-linearity of the model is being resolved without any transformation or linearization. The computed numerical results are in good agreement with those already available in the literature. Easy to apply and achieving accurate solutions in less CPU time are the strong points of the present method.