Modelado y análisis de la epidemia de VIH-SIDA en Cuba

58 páginasPremio de Estudios Iberoamericanos La Rábida. Área Científico-Técnica 2007 (II Edición). En este trabajo se estudia la epidemia VIH-SIDA en Cuba desde una triple perspectiva: I) se analiza su dinámica de evolución a partir de un modelo de epidemia en Ecuaciones Diferenciales Ordinaria; II) se estiman los principales parámetros de la epidemia; y III) se lleva a cabo un análisis exploratorio de datos para evaluar la incidencia de la epidemia sobre determinados grupos de la población

The HIV/AIDS epidemic in Cuba: description and tentative explanation of its low HIV prevalence

<p>Abstract</p> <p>Background</p> <p>The Cuban HIV/AIDS epidemic has the lowest prevalence rate of the Caribbean region. The objective of this paper is to give an overview of the HIV/AIDS epidemic in Cuba and to explore the reasons for this low prevalence.</p> <p>Methods</p> <p>Data were obtained from the Cuban HIV/AIDS programme established in 1983. This programme has an extensive adult HIV testing policy, including testing of all pregnant women. HIV and AIDS cases have been recorded since 1986. Persons found to be HIV-positive are interviewed on their sexual behaviour and partners. Tracing and voluntary testing of these partners are organised. Epidemiological description of this epidemic was obtained from analysis of this data set. Using elementary mathematical analyses, we estimated the coverage of the detection system (percentage of HIV-positive adults detected) and the average period between HIV infection and detection. Estimated HIV prevalence rates were corrected to account for the coverage.</p> <p>Results</p> <p>HIV prevalence has increased since 1996. In 2005, the prevalence among pregnant women was 1.2 per 10,000 (16/137000). Estimated HIV prevalence among 15- to 49-year-olds was 8.1 per 10,000 (4913/6065000; 95%CI: 7.9 per 10,000 – 8.3 per 10,000). Most (77%) of the HIV-positive adults were men, most (85.1%) of the detected HIV-positive men were reported as having sex with men (MSM), and most of the HIV-positive women reported having had sex with MSM. The average period between HIV infection and detection was estimated to be 2.1 years (IQR = 1.7 – 2.2 years). We estimated that, for the year 2005, 79.6% (IQR: 77.3 – 81.4%) of the HIV-positive persons were detected.</p> <p>Conclusion</p> <p>MSM drive the HIV epidemic in Cuba. The extensive HIV testing policy may be an important factor in explaining the low HIV prevalence. To reduce the HIV epidemic in Cuba, the epidemic among MSM should be addressed. To understand this epidemic further, data on sexual behaviour should be collected. Now that antiretroviral therapy is more widely available, the Cuban policy, based on intensive HIV testing and tracing of partners, may be considered as a possible policy to control HIV/AIDS epidemics in other countries.</p

Estimación de parámetros en modelos epidemiológicos de VIH/SIDA.

The validation process of mathematical models that describe practical applications usually implies the estimation of the unknown parameters that are involved. In this work, in order to estimates these parameters in the HIV/AIDS models of [7], the problem of estimatingthe parameters in first order ordinary differential equations with known start point is formulated and a strategy of solution is presented. It is verified as well, which is the model of HIV/AIDS that represents best the real data according with the strategy of solution.El proceso de validación de modelos matemáticos que describen aplicaciones prácticas implica, generalmente, la estimación de los parámetros desconocidos que en ellos intervienen. En este trabajo, con el fin de estimar estos parámetros en los modelos de VIH/SIDA de [7], se formula el problema de estimación de parámetros en ecuacionesdiferenciales ordinarias de primer orden con punto inicial conocido y se presenta una estrategia de solución al mismo. Se verifica, además, cuál es, en algún sentido, el modelo de VIH/SIDA que mejor representa los datos reales existentes según la estrategia de solución

A model for HIV - AIDS epidemic in Cuba. Numerical approaches.

From the beginning of the HIV/AIDS epidemic in Cuba a system for detection of persons living with HIV was put in place. A nonlinear model is developed for the detection system considering different types of searches, some random and others non-random, the model is based on another one studied before by some of the present authors. We study the dynamics of the system. Using the data from the Cuban HIV/AIDS epidemic, we fit the model to the data. For this, as not all types of searches were introduced at the same time, we consider the parameters of the system to be step functions. We obtain estimates for the size of the Cuban HIV epidemic, and for the mean time for detecting a person that is infected with HIV. Also the basic reproduction number is computed for each set of values of the parameters

La complejidad en la propagación del VIH y sus modelos matemáticos

Resumen | Este trabajo ofrece una panorámica de la complejidad que representa la modelación matemática de la propagación, detección y control de la epidemia de VIH en el contexto cubano, partiendo del enfoque sanitario y social hasta llegar a una aproximación matemática que incluye modelos definidos por ecuaciones diferenciales ordinarias y por inclusiones diferenciales, que permitieron manejar la calidad de incertidumbre e imprecisión en los valores que toman los parámetros esenciales que describen la dinámica de dichos modelos. Se comentan algunas ilustraciones producto de simulaciones que validan dichos modelos y se hace un análisis de la importancia de este tipo de trabajo para las políticas estratégicas que deben establecer los sistemas de salud

Estimación de parámetros en modelos epidemiológicos de VIH/SIDA.

The validation process of mathematical models that describe practical applications usually implies the estimation of the unknown parameters that are involved. In this work, in order to estimates these parameters in the HIV/AIDS models of [7], the problem of estimatingthe parameters in first order ordinary differential equations with known start point is formulated and a strategy of solution is presented. It is verified as well, which is the model of HIV/AIDS that represents best the real data according with the strategy of solution.El proceso de validación de modelos matemáticos que describen aplicaciones prácticas implica, generalmente, la estimación de los parámetros desconocidos que en ellos intervienen. En este trabajo, con el fin de estimar estos parámetros en los modelos de VIH/SIDA de [7], se formula el problema de estimación de parámetros en ecuacionesdiferenciales ordinarias de primer orden con punto inicial conocido y se presenta una estrategia de solución al mismo. Se verifica, además, cuál es, en algún sentido, el modelo de VIH/SIDA que mejor representa los datos reales existentes según la estrategia de solución