Spread of AIDS

Part 4: Summary: Using Your Model Function

1. Describe in general terms what you have learned about the growth pattern in the early stages of the AIDS epidemic. Can you describe some biological, sociological, or epidemiological factors that might explain this growth pattern if you had enough information about them?
2. Use your model function to estimate
   
   
   • the number of AIDS cases at the start of 1989;

   • the number of AIDS cases at the end of 1992;

   • the month in which the number of AIDS cases passed 10,000.
     
     

   How confident are you of each of these estimates? Can you think of any reasons why one or more of them might not be reasonably accurate?

3. CDC reported in 1999 that the number of reported AIDS cases through June 30 of that year was 711,344. Does that essentially agree with what your model function would have predicted, or is there a large discrepancy? If there is a large discrepancy, what factors do you think might account for the model not fitting very well in 1999? [Source: MMWR Recommendations and Reports, Dec. 10, 1999, Vol. 48, No. RR-13.]
4. What do the relative residuals tell us about whether residuals in a model are "small" or "large"?
5. Some of the characteristics of a good fit are that the relative residuals should not be wildly different in size, their signs should not be "predictable," and there should not be any obvious pattern in them. Did your relative residuals satisfy these criteria? If not, what do these criteria tell you about how you might achieve a better fit?