Bayesian inference of a dynamical model evaluating Deltamethrin effect on Daphnia survival

Abstract

The estimation of toxicokinetic and toxicodynamic (TK-TD) models parameters is a real problem in research. These models highlight a dynamics of internalisation of a toxic compound and a dynamics of the damage that this contaminant will cause on an organism and of possible repairs on the latter. This coupling TK-TD makes it possible to connect these measurements at different times with the same set of parameters sometimes very important in number. In this paper, the focus is on assessing the long-term impact of deltamethrin effects on a sample of daphnia magna survival. For this purpose we fit our TK-TD model of deltamethrin bio-accumuluation and daphnia survival to our experimental data by using bayesian inference algorithm developed in the package deBinfer of R. This bayesian inference method allows estimate simultaneously all the parameters of deltamethrin bio-accumuluation and daphnia survival dynamical system. For the estimation of the environmental risks, our results show that whatever the concentration or duration of exposure, the concentration of bioaccumulated deltamerin should not exceed on average 6.188 ng/L, at the risk of observing the deadly effects