1. We can use a Markov chain to model the spread of a virus in a population. One of the simpler models, called an SIR model, classies individuals as Susceptible (S), Infected (I), or Resistant (R). Suppose that at each time step: 0 A susceptible person has a 50% chance of remaining susceptible and a 50% chance of becoming infected. 0 An infected person has a 60% chance of remaining infected, a 30% chance of becoming resistant, and a 10% chance of becoming susceptible. o A resistant person has an 80% chance of remaining resistant, a 10% chance of becoming infected, and a 10% chance of becoming susceptible. Then, the status of a single person over time is generated by a Markov chain. (8.) Draw a diagram of this Markov chain. (b) Write the transition probabities as a matrix. (c) Find a stationary distribution; that is, a probability distribution vector that does not change as time moves forward. (You can do this algebraically or by using matrix multiplication in Python.) (d) In the long term, what percentage of the population will be infected at any given time