Before revision:  We derive an integral equation for the distribution of the waiting time for an individual to get infected. In a special case the integral equation is equivalent to the Bernoulli differential equation and implies the classic SIR model under an appropriate scaling  .
After revision:  We derive an integral equation for the distribution of the time before infection can be expressed in terms of the solution of an integral equation, special cases of which are equivalent to the Bernoulli differential equation and implies the classic SIR model under an appropriate scaling .