Stochastic modeling of the insecticide fenitrothion in water and sediment compartments of a stagnant pond

Abstract

A stochastic model is developed for the behavior of the insecticide fenitrothion's decomposition in a New Brunswick (Canada) stagnant pond after aerial spraying. The concentrations of fenitrothion are modeled in two pond compartments: water and bottom sediments. Assuming first‐order kinetics, a mass balance equation of fenitrothion is written for each of the compartments. The deterministic model is obtained by integrating the linear system of differential equations. The stochastic model arises by considering both the initial condition in the water compartment and the input term in the sediment compartment to be stochastic, which results in a stochastic differential equation (SDE). The moment equation, derived from the Itô stochastic differential rule, provides the moment solution to the SDE. Temporal expectations and heteroscedastic variance models are thus obtained. The model is calibrated using observations obtained from fenitrothion sampling at three different locations in each of the pond's compartments. The stochastic model performs satisfactorily.