The kinetics of insecticide action. Part I: The properties of a mathematical model describing insect pharmacokinetics

A simple two-compartment model for the movement of insecticide from the insect surface to the region within the insect (compartment 2) is described, introducing a parameter to represent the relative thermodynamic capacities of the compartments.

Abstract

Abstract A simple two‐compartment model, introducing a parameter (λ) to represent the relative thermodynamic capacities of the compartments, is described for the movement of insecticide from the insect surface (compartment 1) to the region within the insect (compartment 2); loss from compartment 2 is considered. First‐order rate constants are assumed for penetration ( k p ) and elimination ( k e ). The differential equations describing the rates of change of insecticide in each compartment after application of insecticide are solved analytically, and terms describing ( a ) the integrals of mass of compound in each compartment with time after application, ( b ) time to a maximum level of insecticide in compartment 2, and ( c ) distribution and loss of compound from the system with time, are derived. Methods for estimating the three parameters of the model ( k p , k e and λ) are presented. Further properties of the model with possible toxicological significance have been identified; in particular, the total integral for material in compartment 2 depends only on the elimination rate constant and the applied dose.