  In this paper, the mathematical model of HIV infection for CD8+ T-cells is
illustrated. The homotopy analysis method and the Laplace transformations are
combined for solving this model. Also, the convergence theorem is proved to
demonstrate the abilities of presented method for solving non-linear
mathematical models. The numerical results for N = 5, 10 are presented. Several
h-curves are plotted to show the convergence regions of solutions. The plots of
residual error functions indicate the precision of presented method.
