Solutions of Fractional model of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells using HAM

Anas Arafa,M Khalil,S Z Rida

doi:10.14419/ijbas.v1i1.15

Abstract

In this paper, we introduce fractional-order model of (HTLV-I) infection of CD 4+ T-cells. Homotopy analysis method (HAM) is implemented to give approximate and analytical solutions of the presented problem. The fractional derivatives are described in the Caputo sense. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. Numerical results show that the approach is easy to implement and accurate when applied to ordinary differential equations of fractional order.

Highlights

Human T-cell lymphotropic virus type I (HTLV-I) infection is associated with a variety of human diseases
Human T-cell lymphotropic virus (HTLV) is a member of the exogeneous human retroviruses that have a tropism for T lymphocytes
fractional ordinary differential equations (FODE) are naturally related to systems with memory which exists in most biological systems

Summary

Introduction

Human T-cell lymphotropic virus type I (HTLV-I) infection is associated with a variety of human diseases. Infection with HTLV-I is a global epidemic, affecting 10 million to 20 million people This virus has been linked to life-threatening, incurable diseases: a) Adult T-cell leukemia (ATL). These syndromes are important causes of mortality and morbidity in the areas where HTLV-I is endemic, mainly in the tropics and subtropics [17]. Infected cells contain the virus, but do not produce DNA and are incapable of contagion. When such cells are stimulated by antigen, they can become active and infect healthy cells.

Fractional Calculus

Model Derivation

Numerical Results and Discussion

Conclusion