1. Make a record of the maximum number of infectives and the day on which this occurs. Then change the initial fraction of infectives to 0.01 and record the changes in these two quantities. Go back to an initial fraction of 0.001 and observe how long it takes for the population of infectives to increase by a factor of 10, so as to reach 0.01. Use the results to draw conclusions about how a different initial number of infectives changes the course of an epidemic. 2. COVID-19 has a basic reproductive number of approximately 5. Set RO to 5 (with initial infective fraction at 0.001) and describe the changes in the epidemic progress. Pay attention to the key output quantities and also the speed with which the epidemic develops and resolves. (Note: Even with the same basic reproductive number the SIR model with a 5-day disease duration is not a good match for COVID-19.) 3. The duration of COVID-19 infectivity is approximately 10 days rather than 5. Change this parameter and describe the effect this has on the progress of the epidemic. It is helpful to think of the end of the epidemic as roughly the point when the number of infectives is down to what it was initially. (Note: We still are not modeling COVID-19 because the SIR model fails to account for a long incubation period and asymptomatic transmission.) 4. The Incan Empire had a population of over one million when it was conquered by 168 Spanish Conquistadores in 1525. The Spanish had gunpowder weapons and horses, but these advantages would not have been sufficient to defeat the huge Incan army."(It took about 2 minutes to reload a single-shot arquebus.) They also benefitted by joining forces with peoples subjugated by the Incas, but that would not have happened on its own. In Guns, Germs, and Steel, author Jared Diamond argues that the key factor in the Incan defeat was the European diseases the Spanish brought with them. To test this theory, set the basic reproductive number at 5 and the duration at 20, values that roughly match smallpox. Describe the effect introduction of smallpox into Incan civilization would have had, even without considering the death toll of the disease. 5. The most contagious human disease is thought to be measles, with a basic reproductive number of approximately 15. It has an infective period of about 8 days. Describe the progress of a measles outbreak caused by 1 initial infective in a population of 10000 that had not previously been exposed. This event would have happened numerous times in human history. 6. Do a more thorough study of the effect of the basic reproductive number on the total number of people who get a disease having an infectious period averaging 5 days. A. Set the duration to 5 days. Label two columns "RO" and "total I". Enter the numbers 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 3.0, 3.5, 4.0, 4.5, and 5.0 in the RO column. Fill in the total I column one value at a time using the corresponding value of RO. Use the percentage of people who are no longer susceptible at the end of the simulation as a measure of the total number infected. B. Get a graph of the results. The easiest way to do this is to select the two-column table of numbers, click Insert, and choose a scatter plot with a smooth curve. This combination of key strokes will be correctly interpreted by Excel, so you won't have to change the data series. C. Describe and explain the results