Permanence of Structured Population Models Governed by ODEs and the Basic Reproduction Number

Abstract

This paper considers the dynamics of a general nonlinear structured population model governed by ordinary differential equations. We are especially concerned with the survival possibility of structured populations. Our results show that, under a certain mild condition, the instability of the population free equilibrium point implies that the structured population survives in the sense of permanence. Furthermore, the relationship between the basic reproduction number and the instability of the population free equilibrium point provides simple criteria for population survival. The results are applied to both stage-structured and spatially structured models.