Approach and analysis of a mathematical model in ordinary differential equations, applied to HIV transmission, considering protection strategies.

Throughout the years, since 1981 approximately, the virus HIV marked its presence in the humanity razing with a large number of lives in which children, teenagers, and adults were involved. Although the rates of death caused by HIV have reduced notably because of antiretroviral drugs, the HIV continues spreading in the population. Due to above, in this research HIV spreading is modelled, in special in the city of Pasto, Nariño in Colombia, where thanks to the review of data provided by the NDHI (Nariño departmental health institute) was evident that in recent years, exactly between 2008 and 2018 the number of infected people increased. Then, this fact lead the study of the dynamics of HIV transmission in Pasto, where is necessary a search for information of strategies applied to control the infection, which give bases to propose a mathematical model which initially describes the dynamics of transmission of said epidemic and, finally, it will have a theoretical control incorporated based on sex education campaigns, which pretends to maximize the number of protected people against HIV and clearly avoid the number of people with HIV increases.