A Nonlinear Model of Population Dynamics Containing an Arbitrary Number of Continuous Structure Variables

A nonlinear model is presented for the dynamics of a population in which each individual is characterized by its chronological age and by an arbitrary finite number of additional structure variables. The nonlinearities are introduced by assuming that the birth and loss processes, as well as the maturation rates of individuals, are controlled by a functional of the population density. The model is a generalization of the classical Sharpe-Lotka-McKendrick model of age-structured population growth, the nonlinear age-structured model of Gurtin and MacCamy, and the age-size-structured cell population model of Bell and Anderson. Based on a reformulation of the model in terms of a coupled system of equations, the existence for all positive time of unique solutions to the model is proved using a contraction mapping argument. The existence of equilibrium solutions is discussed, and sufficient conditions are proved for the local asymptotic stability of equilibria using results from the theory of strongly continuous...