Numerical simulation process and HIV infection control in the action antiretrovials

Abstract

This paper considers the proposal, development and numerical simulation of a system that models the behavior of the treatment of HIV-1 using antiretrovirals. The system defined for three dependent variables of the variable t, denoted by X(t)=(x1 (t), x2 (t), x3 (t)) represent the amount of T Lymphocytes "Helpers" (CD4), number of Cytotoxic T Lymphocytes (CD8) Viral load and infection process of HIV-1 at any time t, respectively. The assembly consists of a Nonlinear Ordinary Differential Equations system whose existential domain represents time system evaluation process of infection and viral clearance in a patient with HIV-1. This set of states of Nonlinear Dynamic System, associated with the initial value condition is called Cauchy problem. There are few studies related to the solution of this system, found some of the study are reduced to two variables and others without obtaining the explicit solution. Equivalence of the solution of the system linearization, phase diagram, qualitative stability, existence and uniqueness of analytic solution, where test: In this paper contributes to the study of the system for three variables, and qualitative and quantitative analysis comprising nonlinear the linearized system. The equivalence is based on Theorem Grobman - Hartman and explicit solution by the Runge Kutta 4th order, thus the model results and whose convergence is obtained is, is guaranteed by the consistency and stability of the numerical scheme.