We first verify that the time from the emergence of larva to the emergence of pupa (i.e., the duration of the larva stage) for Aedes aegypti is approximately gamma distributed, provided that the pupation process is successful. This is illustrated by fitting a multi-stage model to temperature-controlled pupation rate data of Aedes aegypti. We then determine the temperature dependent gamma distribution parameters, and found that both the shape and rate parameters and the survival probability are unimodal functions of temperature. We then use a Gaussian unimodal function to describe the dependence of these parameters on temperature, and fit the model to the pupation rate data. We found that the optimal pupation temperature is about 28℃, with a mean time from the emergence of larva to the emergence of pupa about 3.8 days, and standard deviation of 0.5 days. For very high and very low temperatures, the death rate is 1.
Keywords: Gaussian function; developmental time; gamma distribution; maximum likelihood estimation.