5. There are individuals in a population, some of whom have a certain infection that spreads...
Question:
5. There are Í 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 A. When a contact occurs, it is equally likely to involve any of the i l pairs of individuals in the population. If a contact involves an infected and a noninfected individual, then with probability ñ 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 /.
(a) Is W O , t > 0) a continuous-time Markov chain?
(b) Specify the type of stochastic process it is.
(c) Starting with a single infected individual, what is the expected time until all members are infected?
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