Dynamic populations with uniform natural increase across states

Abstract

Multistate populations with changing rates of interstate transfer are an example of compartment models and depict the experience of persons in distinct but intercommunicating states. Such models can be used in analyses of many demographic phenomena, including migration, labor force participation, and health status. This paper extends present knowledge of the relationships prevailing in such dynamic models by developing procedures that yield closed form expressions relating transfer rates to the state-specific population trajectories that they generate. The focus is on a subset of multistate models that do not recognize age and that have restricted variability in rates of transfer and natural increase. Dynamics in the two state, no-growth case, where the two time-varying transfer rates always sum to a constant value, are analyzed in depth. In specified models with any number of intercommunicating states, sine and cosine fluctuations in the transfer rates are shown to yield sine and cosine fluctuations in the numbers of persons in each state.