ABSTRACT
This chapter is devoted to presenting some results about the dynamics of the Human immunodeficiency virus (HIV). In Sec. 2.2, we give an overview of the definition of Human immunodeficiency virus (HIV) as a retrovirus. In particular, some statistics are also given and discussed. In Sec. 2.3, we present the standard systems modelling HIV. The dynamics of sexual transmission are presented in Sec. 2.4 via a mathematical distributed delay equation. The effects of variable infectivity on the HIV dynamics are presented in Sec. 2.5. The CD4⁺ Lymphocyte dynamics in HIV infection are discussed in Sec. 2.6, where a model of CD4⁺ lymphocyte dynamics in HIV-infected persons was presented. A mathematical model that tracks both infectious and total viral load was presented in Sec. 2.7 in order to describe the in vitro kinetics of the SHIV-KS661 viral infection. In Sec. 2.8, the effects of morphine on Simian Immunodeficiency Virus Dynamics is presented via a mathematical model that incorporates experimentally observed effects of morphine on inducing HIV-1 co-receptor expression. Finally, the dynamics of an HIV therapy system is presented in Sec. 2.9. We show that the concentrations of the CD4 lymphocyte population converge on a fixed quantity, that the CD8 lymphocyte population converges on another fixed quantity and that the HIV-1 viral load also converges on another fixed quantity. Thus, the system never returns to the normal unperturbed concentrations of the CD4 and CD8 lymphocyte population.
In Sec. 2.10, we present some properties of dynamics of urbanization. In particular, the rural-urban interaction attractor is presented and discussed.
