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Un enfoque bayesiano para el estudio de la propagación temprana de brotes de enfermedades de carácter epidémico
Díaz Portillo, Jimmy Olmedo
Díaz Portillo, Jimmy Olmedo
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Abstract
Estudiar y predecir el comportamiento de los brotes de enfermedades infecciosas desde las fases tempranas de transmisión han sido objetos de permanente atención a lo largo de las décadas. Diversos investigadores han abordado estos aspectos, estudiando tanto las tasas de contagio en tiempo real, como los registros de epidemias pasadas. En este sentido, los modelos clásicos asumían tasas de contagio exponenciales, pero estudios recientes han considerado otros modelos matemáticos, como los que se presentan en este trabajo, que permiten cuanti car dinámicas de contagios con cierta desviación del modelo exponencial. Dos enfoques se han tenido en cuenta en este estudio, uno bayesiano y otro, cuasi-estocástico, para la estimación de los parámetros en los modelos matemáticos considerados. En un estudio de simulación, el enfoque bayesiano reveló ser menos susceptible a valores iniciales de los parámetros y a tamaños de muestra. Se analizaron conjuntos de datos de in uenza del 1918 en San Francisco, de Fiebre Aftosa de 2001 en Uruguay y de COVID-19 de 2020 en Puerto Rico. Los resultados obtenidos con los modelos presentados en este trabajo para in uenza y ebre aftosa concuerdan con los publicados en la literatura. Para COVID-19 en Puerto Rico se observa un patrón de crecimiento exponencial en la etapa temprana de la epidemia. Se logró estudiar la evolución de los parámetros del modelo matemático en el tiempo, lo que permitiría estudiar el comportamiento de epidemias en tiempo real.
Studying and predicting the behavior of infectious disease outbreaks from the early stages of transmission have been subjects of constant attention over the decades. Various researchers have addressed these aspects, studying both real-time infection rates and records of past epidemics. In this regard, classical models assumed exponential infection rates, but recent studies have considered other mathematical models, such as those presented in this work, which allow quantifying infection dynamics with some deviation from the exponential model. Two approaches have been considered in this study, one Bayesian and the other quasi-stochastic, for the estimation of parameters in the considered mathematical models. In a simulation study, the Bayesian approach proved to be less susceptible to initial parameter values and sample sizes. Data sets from the 1918 influenza outbreak in San Francisco, the 2001 Foot-and-mouth disease outbreak in Uruguay, and the 2020 Covid-19 outbreak in Puerto Rico were analyzed. The results obtained with the models presented in this work for influenza and foot-and-mouth disease agree with those published in the literature. For Covid-19 in Puerto Rico, an exponential growth pattern is observed in the early stage of the epidemic. It was possible to study the evolution of the parameters of the mathematical model over time, which would allow studying the behavior of epidemics in real-time.
Studying and predicting the behavior of infectious disease outbreaks from the early stages of transmission have been subjects of constant attention over the decades. Various researchers have addressed these aspects, studying both real-time infection rates and records of past epidemics. In this regard, classical models assumed exponential infection rates, but recent studies have considered other mathematical models, such as those presented in this work, which allow quantifying infection dynamics with some deviation from the exponential model. Two approaches have been considered in this study, one Bayesian and the other quasi-stochastic, for the estimation of parameters in the considered mathematical models. In a simulation study, the Bayesian approach proved to be less susceptible to initial parameter values and sample sizes. Data sets from the 1918 influenza outbreak in San Francisco, the 2001 Foot-and-mouth disease outbreak in Uruguay, and the 2020 Covid-19 outbreak in Puerto Rico were analyzed. The results obtained with the models presented in this work for influenza and foot-and-mouth disease agree with those published in the literature. For Covid-19 in Puerto Rico, an exponential growth pattern is observed in the early stage of the epidemic. It was possible to study the evolution of the parameters of the mathematical model over time, which would allow studying the behavior of epidemics in real-time.
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2024-05-10
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Modelos, Bayesianos, Incidencias, Estimación, Parámetros