There are N individuals in a population, some of whom have a certain infection that spreads as...

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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 non-infected individual, then with probability p the non-infected individual becomes infected. Once infected, an individual remains infected throughout. Let X(t) denote the number of infected members of the population at time t . (a) Is {X (t), t 0} a continuous-time Markov chain? (b) Specify its type. (c) Starting with a single infected individual, what is the expected time until all members are infected? Sep 15 2014 06:32 AM

 

Solution ID:609096 | This paper was updated on 26-Nov-2015

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