Modelling of immune cells as vectors of HIV spread inside a patient human body

Abstract: 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.