Estimación de los parámetros de dos modelos para la dinámica del dengue y su vector en Cali, Colombia

Abstract

El dengue es una infección viral transmitida por la hembra del mosquito Aedes aegypti que se presenta en todas las regiones tropicales y subtropicales del planeta. En Cali, Colombia, a pesar de los controles que las autoridades de salud dicen estar haciendo, durante el año 2013, se reportaron más de 9.000 casos de dengue, de los cuales algunos han sido graves y otros han llegado a ser letales. Para la transmisión del virus del dengue, los modelos matemáticos que simulan la dinámica de la población infectada, bien sea de humanos, de mosquitos o de ambos, permiten una buena comprensión de la dinámica del virus, por lo que son una excelente herramienta para el seguimiento y control de la enfermedad causada por ellos. Sin embargo, para que esta herramienta sea realmente útil en casos concretos, los modelos deben ser ajustados a las características particulares de la región donde se quieren utilizar. En este artículo, queremos presentar el ajuste de dos modelos matemáticos al área urbana de la ciudad de Cali, Colombia. Inicialmente, con base en el comportamiento natural del mosquito Aedes aegypti en una región como el área de interés, estimamos algunos de los parámetros de los modelos, teniendo en cuenta la literatura existente sobre este tema. Posteriormente, estimamos el resto de parámetros como la solución de mínimos cuadrados que mejor ajusta los resultados de los modelos a los datos de los casos reportados de dengue, según la Secretaria Municipal de Salud de Cali, durante el año 2010.

Optimal control of dengue epidemic outbreaks under limited resources

“…In particular, and are entomological parameters and their values are during the 2010 dengue outbreak affected by the temperature and humidity variations. [28][29][30] Parameters and related to the disease transmission may vary with the virulence of circulating DENV strains. 31,32 Finally, the average vectorial density depends on the total size of the vector population (assuming that the total number of human residents remain invariable), and its value is affected not only by the climatic changes, [28][29][30] but also by the efficiency of routinary control actions, such as periodical treatment of mosquito breeding sites with larvicides, and by inflow and outflow of daily commuters.…”

“…[28][29][30] Parameters and related to the disease transmission may vary with the virulence of circulating DENV strains. 31,32 Finally, the average vectorial density depends on the total size of the vector population (assuming that the total number of human residents remain invariable), and its value is affected not only by the climatic changes, [28][29][30] but also by the efficiency of routinary control actions, such as periodical treatment of mosquito breeding sites with larvicides, and by inflow and outflow of daily commuters. 31,33 Furthermore, it is worthwhile to note that the values of parameters ( , , , , , ) given in Table 2 bear little difference with other estimations obtained from the incidence datasets collected in Cali, Colombia during different years.…”

“…31,33 Furthermore, it is worthwhile to note that the values of parameters ( , , , , , ) given in Table 2 bear little difference with other estimations obtained from the incidence datasets collected in Cali, Colombia during different years. 28,31,34,35 Figure 4 displays the daily incidence (new dengue cases registered on a daily basis) reported to the MSPH (Cali, Colombia) during the whole year 2010, and our observation period corresponds to the epidemics peak.…”

Biological and Chemical Control of Mosquito Population by Optimal Control Approach

“…In accordance with estimations performed in Reference [32] for average daily temperature (23.9 • C) in the city of Cali, Colombia, and other data found in scientific literature, Table 2 displays numerical values assigned to all constant parameters of the dynamical system (1) which will be kept unaltered during the computational experiments involving numerical solutions of the optimal control problem (10).…”

“…It also holds that Q 0 < Q, which is in line with common sense. Using the values of parameters of the model (1) without predacious species (x(t) = 0, t ≥ 0, see also Table 2 ahead) estimated for the climatic conditions of the city of Cali, Colombia [32], it had been shown that Q > 1 for all temperature ranges. This explains durable persistence of the mosquito population in Cali, Colombia all the year around.…”