Develop a simple Markov Model to consider the impact of a new flu vaccine. Run the numbers over the course of five years in a healthy elderly population. Assume that the population is either healthy, or with the flu, and that the flu lasts for one year in terms of its impact on mortality. Without the vaccine, the overall annual mortality rate (if healthy) is 1% and a 20% mortality rate with the flu. The chance of getting the flu with no vaccine is 25%. The chance of getting the flu with the vaccine is 5%. With the vaccine there is a 3% annual mortality rate if healthy and a 8% mortality rate with the flu. Consider a population of 1000 elderly and report the expected difference in average (per person) life years over a 4 year period. Also, report the expected difference in life years using the life table method of correcting for population changes (ie the better version of the half-cycle correctionnote you need 5 years of the model to run it over a 4 year period with the life table method). Explain why the numbers are different and which one is likely to be more accurate.