In Chap. 1 , we studied Lotka’s stable population theory along with the associated renewal equation. In Chaps. 1 and 2 , we saw Malthus’ kind of one population model using a differential equation. In this chapter, we will begin by exploring the Lotka–Volterra system of a two-population model and understanding the stability of such a system. We will provide a general overview of a two-population system of differential equations, followed by a standard three-population model known as the susceptible-infection-recovered (SIR) model proposed by Kermack and McKendrick. We will conduct a stability analysis for the three-population SIR model. Later in the chapter (Sect. 4.4), we will introduce newer definitions of population stability in the context of population momentum, and define metrics related to population replacement, and summarize the associated theories.