Single Variable Equations for the SIR Model

 

  One can also derive single variable equations for the SIR Model. We start with a short review of the model.

We can eliminate I from the equation for the rate of change for S as follows.

Note that the first two terms are a logistic function so we might refer to all the terms as a modified logistic function. Note that if S0 is larger than S the logarithm is negative and the last term is positive reducing the infection rate.  The single variable equation for I is more complicated.