10.7 Modeling the Spread of a Disease

Main Points:
Differential equations can be used to describe disease outbreaks and are helpful in finding the necessary vaccination to stop the spread of a disease. The SIR model is used to model this. S stands for the number of people capable of becoming sick. I represents the the number of infected people, and R represents the number of recovered or people who are unable to get sick. The number of people susceptible decreases, so the slope that represents this (dS/dt) = -aSI. The rate of infected increases at the same rate as the rate of susceptible category minus those who have recovered OR DIED. This slope can be represented as (dI/dt)= aSI - bI. The recovered group OR DEAD GROUP has the rate of increase of (dR/dt)= bI. a represents how infectious a disease is, so if you know the initial conditions, you can roughly calculate this constant. b represents the rate at which the infected are removed from the infected population. If you consider vaccination, the vaccinated represent people removed from the infected population. The threshold is the point when the number of infecteds starts to decrease. If enough people are vaccinated that the disease can only infect as many as are represented by the threshold, then it will decrease rapidly just like the graph shows.

Challenges
I honestly think the book explains how to graph this very poorly, I do understand it, but I feel it is a challenging thing to look at this section in the text book and figure out through their jargon how the heck to graph it.

Reflections
This is really really useful stuff. Learning how and when to stop an epidemic or at least an outbreak with calculus is pretty amazing.