Q4. We are asked to model the progression of an epidemic for a population of 5 million. Contact tracing at the beginning of an outbreak shows that each infected person is on average infectious for 7 days and causes on average 4.5 new infections. (a) Find the parameter ,8 for an SIR model when the time unit is one day. (b) How many infections can we expect before the epidemic peaks? (0) Give an approximate value of how many people will have avoided an infection by the end of the outbreak. (d) Early into the outbreak infected people start to self isolate. Their time of being infectious in the community reduces to 3 day on average. How will you change )3 in your model to account for this new situation? Give a reason for your choice of 3. (e) What is R0 when self isolation is observed? (f) How many people will be infected before the epidemic peaks? (g) How many people will have escaped an infection by the end of the epidemic when self isolation is observed