I have been trying to figure this problem out for a few days now and don't seem to know where to start.
Consider a population made of a fixed number (N) of people. At time t=0 there is only one infected individual and N-1 susceptible people in the population. When you get infected, you remain in the infected state forever. In any short time interval that is h long, any given infected person will transmit the disease to any susceptible person with a probability of alpha * h + o(h) where o(h) is an error term and alpha is the individual infection rate. Let X(t) denote the number of infected individuals in the population at time t >= 0. So X(t) is a pure birth process on states 0, 1, ... N.
What are the birth parameters?