Analysis and parameter identification of stochastic compartmental models

Recently major advances have been made in the analysis and estimation of parameters of stochastic compartmental models. The theory of illness-death processes as given by Chiang (1) provides a basis for the analysis of this important class of stochastic models. Motivated by the need for stochastic pharmocokinetic models, we have derived results which enable us to identify the parameters of m compartment models using time series data from one to r compartments. Following Matis and Hartley (2) we have derived explicit expressions for the elements of the covariance matrix for the case of observations from r compartments. We then incorporate the covariance matrix in a generalized least squares estimation of the parameters from time-series data. The parameters identification procedure, which uses a modified Gauss-Newton technique to minimize the generalized sum of squares, yields estimates of the values of the flow rates between compartments and standard deviations for these parameters.