A model of growth with first-order birth and death rates

This paper describes the derivation, behavior, and application of a model of growth based on elementary kinetic considerations. The model is based on an abbreviated version of the cell cycle in which first-order kinetics govern both production in a growing fraction and loss from the resting fraction of a cell population. Transition between the resting and growing fraction is assumed. The model is derived in the form of a first-order ordinary differential equation with a simple general form, but no closed form solution. Model behavior is examined analytically at equilibrium, in a limiting case, and qualitatively by numerical integration. Because of the simplicity of the underlying assumptions, the model parameters have direct biological interpretations and simple units. Examples of model fitting to data are given, including a direct comparison to the Gompertz growth law.