There are N individuals in a population, some of whom have a certain infection that spreads as follows. Contacts between two members of this population occur in accordance with a Poisson process having rate . When a contact occurs, it is equally likely to involve any of the pairs of individuals in the population. If a contact involves an infected and a noninfected individual, then with probability p the noninfected individual becomes infected. Once infected, an individual remains infected throughout. Let X(t) denote the number of infected members of the population at time r..

(a) Is [X(r), 0] a continuous-time Markov chain?

(b) Specify the type of stochastic process.

(c) Starting with a single infected individual, what is the expected time until all members are infected?