Section 10.7

Main Points: Differential equations can predict an outbreak of a disease epidemic as well as the level of vaccination necessary to stop the disease. The standard model used for this is the S-I-R model. S stands for number of susceptibles, or the people who are not yet sick but can become ill. I stands for the number of infecteds, or those that are currently sick. R represents the number of recovered people, or people who cannot be reinfected or continue to infect others. The number of susceptibles decreases with time as more people become infected. The sum of S, I, and R is unchanged, however, the numbers pertaining to each group can change within that certain number. Trajectories and graphs are also used in this type of problem to show how a disease is spreading. Where the rate of change of infecteds vs. susceptibles equals 0 (dI/dS = 0), a threshold population occurs. If the number of susceptibles is larger than the threshold population, an epidemic is present.

Challenges: I was a little confused wiht the constants used, and I don't really understand how the threshold population equals the proportion b/a.

Reflections: This section was pretty interesting because I always hear on the news about epidemics, but was never sure how people at the CDC and NIH decided that something was an epidemic. Now that I pretty much understand the S-I-R method, I can see how the scientists come to these conclusions.