COMPARTMENTAL MODELING AND 2ND-MOMENT ANALYSIS OF STATE-SPACE SYSTEMS

Compartmental models involve nonnegative state variables that exchange mass, energy, or other quantities in accordance with conservation law s. Such models are widespread in biology and economics. In this paper a connection is made between arbitrary (not necessarily nonnegative) s tate space systems and compartmental models. Specifically, for an arbi trary state space model with additive white noise, the nonnegative-def inite second-moment matrix is characterized by a Lyapunov differential equation. Kronecker and Hadamard (Schur) matrix algebra is then used to derive an equation that characterizes the dynamics of the diagonal elements of the second-moment matrix. Since these diagonal elements ar e nonnegative, they can be viewed, in certain cases, as the state vari ables of a compartmental model. This paper examines weak coupling cond itions under which the steady-state values of the diagonal elements ac tually satisfy a steady-state compartmental model.