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Question 4
Consider a SIR model that we studied in the lectures.
(1) Write the equation that describes transitions to and from infected state. Describe which parameters determine the transitions and how. Describe in detail how lockdowns, vaccines, and masks affect transitions to the infected state, specifying which parameter(s) and state variable(s) these affect.
(2) Let the infection rate alpha equal 0.3 and let R zero equal to 3. Suppose on day 30 of the pandemic, a vaccine becomes available. Suppose 30% of those who haven't ever been infected get vaccinated on day 30. Suppose the vaccine instantly gives 100% immunity. What is the highest percentage of the population that is infected on any given day before the vaccine is available (up to day 29)? What is the highest percentage of the population that is infected on any given day when the vaccine is available (starting from day 30)? Explain how you derived the answer.
(3) Discuss the importance of the Lucas critique and the Peltzman effect when using a SIR model to predict the pandemic.