Modeling Techniques for Complex Biological Systems: Sensitivity, Identifiability,

Filtering and Optimal Control

by

Hien T. Tran

Department of Mathematics

Center for Research in Scientific Computation

North Carolina State University

Raleigh, North Carolina 27695

U.S.A.

Abstract:

Ordinary differential equations (ODE) are a powerful tool for studying complex biological systems. In general, these equations often contain a large number of unknown parameters whose values are difficult to determine even with state-of-the-art laboratory equipments. In this case, it is necessary to determine unknown parameters in ODE models from available experimental data. Typically only a subset of the parameters can be estimated due to restrictions imposed by the model structure and limited experimental data. In this talk, sensitivity and identifiability analyses will be presented as the first step in determining unknown parameters in nonlinear ODE models. An example from modeling HIV infection will be used to illustrate how to apply these sensitivity and identifiability analyses in practice. Finally, receding horizon control (RHC), which is a nonlinear feedback control

methodology, will be presented as a promising approach for deriving optimal therapies for viral infections. However, implementation of RHC technique in clinical settings will require the design and construction of nonlinear state estimator or observer. We will examine a nonlinear Kalman filtering based state estimator that used viral load and T-cell count measurements to construct the feedback control law.