Epidemiological modeling of infectious disease has a long and rich history and has received recent broad attention due to the tragic SARS-CoV-2 pandemic. Predicting the spread, severity, and duration of a contagion requires understanding the complex interplay between the biology of the vector and the host mobility. We examine the role of population dynamics in determining the infectiousness of a disease, focusing on the simple but robust SIR compartmental epidemiological model and a random walk description of population mobility. In particular, we show both that the tails of the individual-reproduction-number distribution, more than its mean value, determine the epidemic outcome and that a well-mixed population (an underlying assumption of compartmental epidemiological models) is difficult to achieve from an initial source of infection unless the population is confined. We point the way to a probabilistic approach that may be able to account for spatial and temporal inhomogeneities in large domains.
