Estudio de un modelo determinista SI (Susceptibles-Infectados) para el comportamiento del VIH en una población sexualmente activa de la Universidad Distrital Francisco José de Caldas

Abstract

Human Immunodeficiency Virus (HIV) remains one of the greatest threats to public health worldwide, especially in vulnerable populations. public health threats worldwide, especially in vulnerable populations. HIV transmission is multifactorial HIV transmission is multifactorial and is influenced by a variety of social, cultural and behavioral factors that may vary by gender and sexuality of the behavioral factors that may vary according to the gender and sexuality of the people involved. The objective of this study is to analyze the situation of HIV infection in a sexually active population of the Universidad population of the Universidad Distrital Francisco José de Caldas (UDFJC) and to develop a simulation model for the simulation model (Susceptible-Infected) to predict the behavior of the virus in the university. virus in the university. To achieve this purpose, an exhaustive survey was carried out among students, faculty and staff of the students, faculty and administrative staff, in order to assess their level of knowledge about HIV, their HIV knowledge about HIV, their sexual protection practices and their attitudes towards HIV prevention. prevention of the virus. Thus, with this research, we seek to obtain a clearer perspective of the current situation of HIV infection in the studied population, as well as to project its evolution in the future. of HIV infection in the population studied, as well as to project its evolution in the future (a few years). (a few years). It also aims to better understand the factors that influence the spread of the virus within the university. The creation of an IS simulation model will make it possible to make predictions about the behavior of the virus in the university. predictions about the behavior of the virus in the university, taking into account various variables that influence its spread. that influence the spread of the virus. On the other hand, this work also addresses the importance of sex education in the prevention of HIV and highlights the imperative need to HIV prevention and highlights the imperative need for more effective prevention programs within the university setting. within the university setting. The research aims to make a significant contribution to the understanding of the factors to the understanding of the factors that influence the spread of HIV in universities, as well as to the universities, as well as in the implementation of effective measures to prevent its transmission. In this regard, the creation of the SI model adapted to the educational needs discussed The creation of the SI model, adapted to the educational needs discussed since 2022, plays a fundamental role in promoting a more solid and evidence-based educational and preventive approach. and based on real data; in this way, it is expected to have a positive impact on the reduction of HIV infections in the the reduction of HIV infections in the university community. It also aims to promote a culture of awareness and responsibility regarding sexual health, contributing to the creation of a safer and healthier environment for all members of the Universidad Distrital Francisco José de Caldas. Additionally, it is necessary to mention that the mathematical process carried out in this work began once the relevant variables of the problem were identified and the relationships between them were defined. Then, equations, formulas and mathematical models were constructed to represent the relationships between the variables. Thus, the process of mathematization in an investigation of HIV infections in the UDFJC can be summarized in the following steps: Identification of relevant variables: In the first instance, the crucial variables of the problem were identified, such as the total population of the university, the HIV transmission rate, the recovery rate, as well as the mortality and undetectability rates. 2. Definition of the relationships between the variables: subsequently, the relationships between the variables are defined, such as the infection rate depending on the transmission rate and the proportion of susceptible and infected persons in the population. 3. Creation of a survey for the university population: A survey was designed to collect information on age, sex and general knowledge about HIV transmission and prevention in the student community. Systematization of the survey data: A process of organization and analysis of the data provided by the survey was carried out in order to obtain relevant information about the population studied. 5. Creation of the mathematical model: A deterministic mathematical model of the SI type is constructed, which describes the dynamics of HIV transmission in the university population, based on the relationships identified in the previous step and the analysis of the data provided in the survey described above. The model describes how the population evolves over time, taking into account the interaction between susceptible and infected individuals. 6. Model validation: The validity of the model is verified by comparing the model results with empirical data, such as the number of HIV cases reported in Colombia. 7. Analysis of results: The results of the model and the behavior of the virus for each of the related variables are analyzed. Conclusions and recommendations: From the analysis of the model results, fundamental conclusions were obtained and specific recommendations were formulated for the prevention and control of HIV at the university. In summary, the mathematization of the dynamics of HIV infection at the Universidad Distrital Francisco José de Caldas by means of a deterministic IS model allows the rigorous analysis of the spread of the virus and the evaluation of different prevention and control strategies. Detailed information on this process will be presented in the course of this work.