Assume a population of n people. At the beginning of each day, each individual is either infected or is capable of contracting the flu (susceptible). Suppose that each pair, (i,j), where i cannot equal j, come into contact with each other independently during the daytime with probability p. Whenever an infected individual comes into contact with a susceptible individual, they infect them. Additionally, assume that overnight, any individual who has been infected for at least 24 hours will recover with probability 0

a) Suppose that there are m infected individuals at daybreak. What is the distribution of the number of new infections by day end?

b) Draw a Markov chain with as few states as possible to model the spread of the flu or N=2, and identify all the recurrent states.