When are population dynamics models useful?
Population dynamics occupies a whole subset of mathematical biology. Perhaps the most pragmatic uses for modelling population dynamics come from the fields of epidemiology for modelling disease infection and transmission through a population (one such article), or ecology modelling things like forestation, fishing dynamics, predator-prey relationships (an example). Then there are more abstract uses, when you cannot measure a population to test a hypothesis because the labour is too intensive, or it's too costly, or no such surveillance mechanism exists. Theoretical models of population dynamics are built to gain an understanding of what the system as a whole may do under certain conditions. In this sense, population models are more of a theoretical exercise or a thought experiment.