A population model with pseudo exponential survival

Abstract

This paper considers a model for population dynamics with age structure. Following Dufresne (2006) and Beghriche et all (2022) the probability of survival is assumed to be a linear combination of exponentials, and a product of a polynomial and an exponential. The number of births in unit time is characterized through a system of ordinary differential equations. This is solved explicitly in special cases, which leads to closed form expressions for the population size. The later allows an assymptotic analysis with three cases; the population goes extinct, explodes, or converges to a finite number depending of the interplay between model parameters. From a practical standpoint our modelling approach leads to a better fit of population data when compared to the exponential survival, and it also allows for more shapes of population as a function of time.