Analysis of the invasion of a city by Aedes aegypti via mathematical models and Bayesian statistics

Abstract

We analysed data from the invasion of a city by Aedes aegypti by using a series of models based on Fisher’s reaction–diffusion equation with Richard’s growth model and Bayesian statistics. The model that best explains the invasion of the city was defined through a step-by-step process of model selection based on a series of candidate models. As explanatory variables, we used the effect of urbanization type and climate variables on the parameters of Fisher’s equation: carrying capacity (K), population growth rate (r), and the diffusion coefficient (D). The resulting model is a reaction–diffusion equation with a near-zero shape parameter, similar to a Gompertz-type growth. The population advance rate of 60.19 m/day allowed Aedes aegypti to fully occupy a medium-sized city in 5 months from the estimated date of colonization. We found that the carrying capacity was dependent on temperature and urbanization type. While the results are coherent with existing literature on this species, most of the theory on population dynamics of Aedes aegypti usually assumes a logistic growth instead of Gompertz population dynamics. This type of growth is faster than logistic at densities lower than the inflexion point but slower at higher densities. Therefore, it is possible that in a regime in which the K depends on the climate, Gompertz dynamics could stabilize the population of this species of mosquito faster than assumed by the existing theory.