Keywords:Caputo fractional derivative
,
Generalized Euler method
,
HIV model
,
Homotopy analysis method
,
Numerical solution
,
Caputo fractional derivatives
,
Euler method
,
HIV models
,
Homotopy analysis methods
,
Numerical solution
,
Differentiation (calculus)
,
Drug therapy
,
Plasma density
,
Viruses
,
Diseases
Abstract:
In this paper, generalized Euler method (GEM) and homotopy analysis method (HAM) are performed to solve the problem of the population dynamics of the human immunodeficiency type 1 virus (HIV-1). We introduce fractional orders to the model of HIV-1 whose components are plasma densities of uninfected CD4+ T-cells, the infected such cells and the free virus. The effect of the drug treatment of HIV-1 will be discussed in this paper. � 2012 Elsevier Inc.