The bi-linear incidence term S I for the number of new infected individuals
per unit time corresponds to homogeneous mixing of the infected and
susceptible classes. The total population size should remain constant, and
this easily follows from the SIR system: that the sum of the left hand sides
of the three equations is the derivative of the total population size and the
sum of the right hand sides is zero. We denote the total population size by
N. Since R(t) = N