Parameter Estimation of Two Mathematical Models for the Dynamics of Dengue and its Vector in Cali, Colombia

Dengue is a viral infection transmitted by the female Aedes aegypti mosquito that lives in all tropical and subtropical regions of the planet. In Cali, Colombia, despite the controls that health officials say they are doing, this year, there have been more than 9,000 cases of dengue, of which some have been serious and others have become lethal. For the case of dengue virus transmission, mathematical models to simulate the dynamics of the infected population, either human or mosquito or both, allow a good understanding of the dynamics of the virus, so they are a good tool for monitoring and controlling the disease. However, for this tool to be really useful in a specific case, the models must be tailored to the particular characteristics of the region where you want to use them. In this paper, we present the fitting of two mathematical models to the urban area of Cali, Colombia. Initially, based on the natural behavior of the Aedes aegypti mosquito in a region as the area of interest, we estimate some of the parameters of the models, taking into account the existing literature on this topic. Subsequently, we estimate the others parameters as the (non-linear) least squares solution that best fits the output of the models to the data of reported cases of dengue, according to the Municipal Secretary of Cali, in 2010