Tahmina Akhter, Applied Math, University of Waterloo
Stochastic and deterministic models of the pharmacokinetics of drugs
Pharmacokinetics (PK) is the study of the rate of change of drug concentration in the body by means of mathematical models. Traditionally, these models are compartment type (or lumped parameter) models, with the consequence that the drug concentration C(t) is just a function of time and the mathematical model consists of a system of coupled ordinary differential equations (ODE’s). These are simply rate equations in which the coefficients (the rates) are unknown and must be determined from experimental data. The PK rates capture, in general, a multiplicity of phenomena which are often neglected in the deterministic approach. But if we consider the so called macroscopic constants along with a random noise term either additive or multiplicative, then we will be able to evaluate important PK parameters more accurately. Now we have to deal with Random Differential Equations (RDE) and I will be discussing some of the problems and challenges which will be the focus of my PhD research.