(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.