Aucaille-Quispe, Yetsabel

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    Análisis de incertidumbre y sensibilidad: un modelo de transmisión de VIH/SIDA en Puerto Rico
    (2011-06) Aucaille-Quispe, Yetsabel; Santana-Morant, Dámaris; College of Arts and Sciences - Sciences; Lorenzo González, Edgardo; Ríos Soto, Karen; Quintana Paz, Julio C.; Department of Mathematics; Ortiz, Gloribell
    We studied the behavior of HIV/AIDS in Puerto Rico using epidemiological models. We adjusted the model proposed by Blower et al. (1991) to the data that is available for Puerto Rico to assess the factors that contribute to the prevalence of the virus in Puerto Rico. The model is designed to assess the epidemiological effects of the heterosexual transmission of HIV and the transmission of HIV among intravenous drug users. The model takes into account certain risky behaviors like: the rate of sharing needles per year (for men and women that use intravenous drugs), the rate of change of sex partners per year (for men and women that use intravenous drug and are sexually active), the rate of change of sex partners per year (for men and women that does not use intravenous drugs), and epidemiological parameters like: the heterosexual transmission efficiency per partnership, the HIV transmission efficiency per needle injection, the average adult incubation time, and the average adult survival time. We estimate the cumulative number of AIDS cases after ten years in Puerto Rico and identified the parameters that contributed most to the uncertainty in the estimation using uncertainty analysis and sensitivity analysis. These methods require estimates of the model parameters for Puerto Rico and their performance depends on the efficient exploration of the parameter space. Seaholm et al. (1988) and Blower and Dowlatabadi (1994) proposed the use of Latin Hypercube Sampling for this purpose. We proposed a modification of the Latin Hypercube Sampling Method using randomized Halton sequences. This method wereshown to be more efficient in the sensitivity analysis, in our model for Puerto Rico, in the identification of the parameters that contributed most to the uncertainty of the estimation as well as in the convergence of the mean of some of the distributions of interest. The sensitivity analysis shows that the parameters that affect the cumulative number of AIDS in the next ten years in Puerto Rico are: the heterosexual transmission efficiency per partnership of the HIV virus, the average adult incubation time of the VIH virus and the rate of sex partners per year for women that use intravenous drugs and are sexually active.