(A) Basic S-E-I-R compartmental model of infectious disease, in which outbreak dynamics are represented by the number of individuals in four compartments corresponding to susceptible, exposed, infectious, and removed (or recovered) individuals.

<div><p>The rate at which individuals move from susceptible to exposed is according to mass-action dynamics with proportionality constant <i>α</i>.</p> <p>Individuals move from exposed to infectious at rate <i>η</i> and from infectious to removed at rate <i>γ</i>.</p> <p>(B) By assuming that the number of susceptible individuals is approximately constant (an appropriate approximation for outbreaks in which prevalence is never a large fraction of the total population) we introduce the new variable β = α<i>S</i> and reduce the four-compartment S-E-I-R model to a two-compartment model, designated here by the state variables <i>X</i> and <i>Y</i>. </p>