RESIDENCE TIME MOMENTS OF STOCHASTIC COMPARTMENTAL MODELS WITH AGE-DEPENDENT AND TIME-DEPENDENT RATES (MARKOV PROCESS, MATHEMATICAL BIOLOGY)

The residence time moments and cross moments are derived for the general stochastic compartment model with constant transition rates. These moments are obtained for the n-compartment, irreversible catenary system with transition rates that are general functions of time. The two-compartment, reversible system with time-dependent rates is also considered; however, a closed form solution for the moments is derived only for particular functions of time. The residence time moments and cross moments for stochastic compartmental systems with age-dependent transition rates are found by relating survivorship theory to the rates. Necessary characteristic functions for obtaining these moments are derived for the n-compartment, irreversible catenary system and the two-compartment, reversible system. The procedure for the general reversible system is outlined.