Source: Mathematical Biology, J.D. Murray, Springer - Verlag, 1989.
Case Facts:
The week after Spring Break all 500 students and teachers at Contagious High School in Contagious, Maryland went home sick with influenza (the flu). It has been discovered that three students came back after Spring Break, each had a different infections flu. The rates at which each of the flus can infect another person (Infection Rate) and the rates at which a person with the flu gets better (Recovery Rate) are commonly known for each of these strains. You have been asked to determine which of these originally infected students was the source of the flu that was so virulent it affected nearly everyone in the school.
Modeling Task:
Build a computer model of this epidemic, looking to answer these two questions:
To build this model, you should use the 1927 Kermack - McKendrick model known as the SIR algorithm. This algorithm looks at the change in three pouplations: suscepitbles (S), infecteds (I), and recovereds (R). It assumes that once you recover, you don't get sick again. What is the relationship between S, I and R? Build your model based on this relationship.
The algorithm (equations) of importance are:
Get Sick= Susccpitble * Infecteds * Infection Probability
Get Better= Infecteds * Recovery Rate
This algorithm assumes a constant population, that is, no immigration or emigration of potential players. This also assumes, naturally, that no one dies of the illness! In this model 1/a is the average infectious period.
You also need to know the infection Probability and Recovery Rate for each type of flu:
| Student Name | Flu Strian | Infection Rate | Recovery Rate |
| Booby Getwels | Ick Flu | .002 | .5 |
| Amess Besick | Plu Flu | .001 | .5 |
| Majorly Ruddy | Gacky Flu | .08 | .2 |
Once you have built your model, show the three populations on your graph.
Extenison
What would happen if some of the students had been vaccinated prior to the beginning of the epidemic? Let's assume that 50% of the suscepitble students are vaccinated each day -- some of them getting the shot while the epidemic is happening in order not to get sick (this assumes, fasley, that instant immunity is relized once you've received the shot.) Experiment with the 50% vaccination rate to determine how it changes the intensity and duration of the epidemic.
USING THE MODEL:
[Technical note: you should graph suceptibles, infecteds, and recovereds on your graph. Scale each of these variables to a logical range, such as from a minimum of 0 people to a maximum of 500 people.]
Which student was responsible for shutting down the school?