Statistical distributions of compartmentalized populations governed by continuous time, discrete state semi-Markov processes

Abstract

Stochastic compartmental modeling theory is extended to represent nonhomogeneous Poisson immigration of an arbitrary discrete population into an open system subdivided into compartments in which residence times of individuals in each compartment are statistically independent, are identically distributed, and follow arbitrary piecewise continuous distributions. The model is fitted to time series of chloride concentrations using an L1 metric implemented by a linear goal program, covering lakes Huron, Erie, and Ontario. Advantages of the stochastic model are: (1) fitting a multivariate model to a multivariate data set using formal methods of statistical inference, and (2) allowance for multiple sources of random variability covering input, residence times, and distribution of individuals among compartments. Feasibility of numerical implementation of the model is demonstrated.