Shifted Boubaker Lagrangian approach for solving biological systems

Abstract

Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many mathematical models in biology can be formulated by a nonlinear system of ordinary differential equations. This work deals with the numerical solution of the hantavirus infection model, the human immunodeficiency virus (HIV) infection model of CD4[Formula: see text]T cells and the susceptible–infected–removed (SIR) epidemic model using a new reliable algorithm based on shifted Boubaker Lagrangian (SBL) method. This method reduces the solution of such system to a system of linear or nonlinear algebraic equations which are solved using the Newton iteration method. The obtained results of the proposed method show highly accurate and valid for an arbitrary finite interval. Also, those are compared with fourth-order Runge–Kutta (RK4) method and with the solutions obtained by some other methods in the literature.