MIAMI, FLORIDA - Epidemics such as COVID-19 or opiate addiction can push medical systems and public policy to their breaking points. Understanding potential threats to public health before they occur allows medical infrastructure, medical personnel, and public officials to plan effective responses to threats and thus limit the impact on public health and the economy as much as possible (Delivorias and Scholz, 2020).

Dozens of methods exist for simulating potential epidemics, but underlying all of these are a set of equations that govern how easily a disease or behavior is transmitted through a population and how quickly it dissipates (Brauer, 2006). Epidemics that transmit at higher rates than they dissipate are far more likely to spread (Ma, 2020).

The Kermack-McKendrick model is a basic one that links three equations relating to the number of susceptible people: First, who can catch the disease or behavior; second, the number of infected people who are transmitting the disease or behavior; and third, the number of recovered people no longer spreading the disease or susceptible to catching it (Brauer, 2005). This is not a straightforward process; sometimes, the recovered can become susceptible again, and other equations can be added to the model later to reflect a return to the original state of susceptibility (Brauer, 2006). Births and deaths can be added as other model parameters, and populations of individuals can be geographically separated with occasional mixing periods to simulate spread across geographies (Brauer, 2006).

Whatever equations the model includes are updated for each time period of interest, with individuals changing their infection status under the probabilities defined by the model.

The Kermack-McKindrick model is therefore often called the susceptible-infected-recovered (SIR) model. The SIR’s behavior hinges on two important parameters in the set of equation