2. Example: Infection with a Macroparasite (As time allows, homework?) Suppose a person can be infected with up to 2 macroparasites (worms). Usually, these infections happen one at a time, but there is a small likelihood that a person could get infected with both worms at the same time. Treatment can reduce parasite load by 1 , by 2 , or (if ineffective) can result in no reduction. Model the infection within one host in weekly increments making the following assumptions. - The maximum number of worms within the host at any given time is 2 . - There is a 20% chance the host is infected by one additional worm in one week. - There is a 10% chance the host is infected by 2 additional worms in one week (from zero). - There is a 40% chance treatment removes exactly 1 worm. - There is a 10% chance treatment removes 2 worms. Try the following: (a) Draw a diagram describing these possibilities. The Markov states should be a host infected by 0,1 , or 2 worms. Remember to include the likelihood that a host retains the same number of worms in a week. (b) Write the Markov model in matrix form. What does the vector represent? (c) Suppose there are initially 46 uninfected people and no one is infected. How many people are infected with 2 worms one week later? (d) Find the steady state numbers assuming 46 people total. How many people are infected with 2 worms after a long time? Hint: In 2d, the augmented matrix will row reduce to 10001011/57/50000