1.3. Consider a population comprising a fixed number N of individuals.

Suppose that at time t = 0 there is exactly one infected individual and N - 1 susceptible individuals in the population. Once infected, an individual remains in that state forever. In any short time interval of length h, any given infected person will transmit the disease to any given susceptible person with probability ah + o(h). (The parameter a is the individual infection rate.) Let X(t) denote the number of infected individuals in the population at time t ? 0. Then X(t) is a pure birth process on the states 0, 1, . . . , N. Specify the birth parameters.