Effective population size in infectious disease models

The effective population size Ne was introduced by geneticist Sewall Wright to describe idealized populations. Ne has been a research interest because of its mathematical theory and population management utility. Inspired by such potential, we (re)-introduce the notion of the effective population size N∗ in mathematical epidemiology. Our aim is to see if a simple model with the population size as a variable N∗ can capture disease dynamics in various data types. We introduce a simple SIR model and derive methods of estimating N∗. We apply our methods to both simulated and real outbreak data. We compare N∗ to N and look at how corresponding solution curves match data. We identify preferable methods and settings where these methods are applicable. We state possible implementations of N∗ in public health management as well as extensions and limitations of our methodology.