Modeling the complex hatching and development of Aedes aegypti in temperate climates

Here, we present and discuss a compartmental stochastic model for Aedes aegypti conceived as a mathematical structure able to interpolate and extrapolate (predict) biological phenomena, and direct the attention to biological matters that need experimental elucidation. The model incorporates weather information in the form of daily temperatures and rain and pays particular attention to determining factors in temperate climates. Sufficiently large rains trigger egg hatching, which in turn leads to peaks in larval densities. Hatching is inhibited by the absence of bacteria (Gillett effect), a mechanism of relevance during the winter season and in seasons with isolated rains. The model also incorporates egg hatching independent of rains. Both egg hatching and larval development depend on the availability of food, which is modeled as bacteria produced at rates that depend on the temperature. Larval mortality and pupation rates depend on the larvae to bacteria ratio. The results of the model for egg laying activity were compared with field records during a normal season and a drought. Both the model and the records indicate that the egg laying activity of Ae. aegypti is not zero during the drought and recovers quickly when normal weather is reestablished. We studied the sensitivity of the model to different sets of physiological parameters published for a few different local populations of this species, and found that there is an important sensitivity to local characteristics that will affect some predictions of the model. We emphasize that if the information is going to be used to evaluate control methods, the life cycle of the mosquito must be studied for the local strain under the local environmental conditions (including food). We showed that the adult populations produced by the model are insensitive to certain combinations of parameters and that this insensitivity is related to the variability reported for different strains obtained from closely located places. When the model is considered in a larger biological context, it indicates that some standard procedures performed to measure the life cycle of Ae. aegypti in the laboratory might have a determining influence in the results.