Soluciones aproximadas de la dinámica de infección de VIH-1 con tasa de curación

Héctor Vázquez Leal,K Boubaker,J Huerta-Chua,A Marin-Hernandez

doi:10.21640/ns.v7i13.2

Héctor Vázquez Leal, K Boubaker + Show 2 more

Open Access

https://doi.org/10.21640/ns.v7i13.2

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Journal: Nova Scientia	Publication Date: Sep 3, 2014
License type: CC BY-NC 4.0

Affiliation: Tunis University, Universidad Veracruzana

Abstract

En este trabajo, se presentan dos soluciones aproximadas del modelo de la dinámica de infección de VIH-1 con tasa de curación. Las soluciones propuestas se obtienen usando el método de perturbación homotópica, por sus siglas en inglés (HPM) y el esquema de expansión polinomial de Boubaker por sus siglas en inglés (BPES). Al comparar las soluciones obtenidas vemos que HPM y BPES son herramientas muy potentes para resolver modelos no lineales de infecciones virales.

Highlights

In the last three decades, tremendous attention had been paid to establishing mathematical models to Human Immune-deficiency Virus type 1 (HIV-1) proliferation dynamics as AIDS (Acquired Immune Deficiency Syndrome) agent [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
The homotopy perturbation method (HPM) method can be considered as a combination of the classical perturbation technique [37,38] and the homotopy [39,40], but not restricted to a small parameter like traditional perturbation methods
Further research is required in order to obtain solutions with even larger domain of convergence that can lead to a better understanding of the dynamics of the HIV infection and its relationship with the parameters of Table 1

Summary

Introduction

In the last three decades, tremendous attention had been paid to establishing mathematical models to Human Immune-deficiency Virus type 1 (HIV-1) proliferation dynamics as AIDS (Acquired Immune Deficiency Syndrome) agent [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. The models for describing the dynamics of HIV infection for CD4+ cells are usually nonlinear differential equations with no known exact solution. 2. Governing equations and general assumptions Simple and standard classic models for HIV-1 proliferation dynamics [7,9,10,11,12,13,14,15] are generally based on interacting features between three components like: infected and uninfected CD4+ Tcells along with virus population (Fig. 1). It expresses that the process of infection to the uninfected CD4+ T-cells is in concordance to the mass action principle under mixing homogeneity In this case, the concentration of new infected cells is proportional to the product x(t) y(t).

Basic concept of HPM method

Resolution using the Boubaker Polynomials Expansion Scheme BPES

Results and analysis

Conclusion