  The search to understand how the HIV virus spreads inside the human body and
how the immune response works to control it has motivated studies related to
Mathematical Immunology. Actually, researches include the idea of mathematical
models representing the dynamics of healthy and infected cell populations and
focusing on mechanisms used by HIV to invade target-host cells, viral
dissemination (which leads to depletion of the T-cell pool and collapse of the
immune system), and impairment of immune response. In this work, we show the
importance of specific cells of immune response, as infection vectors involved
in the dynamics of viral proliferation within an untreated patient, by using an
ordinary differential equation model in which we considered that the virus
infected target-cells such as macrophages, dendritic cells, and lymphocytes
TCD4 and TCD8 populations. In conclusion, we demonstrate the importance of each
cell-host and the threshold of viral establishment and posterior spread based
on the presence of infected macrophages and dendritic cells in
antigen-presenting processing, which leads to new infections (by wild or mutant
virions) after immune response activation episodes. We presented an $R_0$
expression that provides the major parameters of HIV infection. Additionally,
we suggest some possibilities of new targets for functional vaccines.
