Analyzing the Romaine Lettuce E. Coli Outbreak using Epidemic Models
Recently the Centers for Disease Control and Prevention warned Americans to stop eating and throw out all romaine lettuce due to an outbreak of E. Coli. This warning was issued after 32 people in 11 states were sickened by the lettuce. At the time, they were not able to determine where the infected lettuce was coming from so they applied the warning to all romaine lettuce. This was considered a fairly dramatic move due to the scope and the fact that Thanksgiving was only a few days away. This was done to help prevent the spread of the outbreak since there was no other way to control it.
We can model the E. Coli outbreak using the epidemic models discussed in class. The main changed we will have to make to the models is that there are actually two different types of nodes in the graph for the epidemic model. There a node type for people and a node type for lettuce and other foods. The reason for the two types of nodes is that the transmission probabilities between person/person, lettuce/lettuce, and lettuce/person are all quite different. For person to person transmission, the probability of transmitting E. Coli would be fairly low since usually transmission can only occur due to improper hygiene. For lettuce to lettuce transmission, there would be a slightly higher probability because the bacteria could easily move between them when there is contact during processing or shipping. For lettuce to person transmission, there would be a very high probability since actually ingesting the bacteria puts you at a high risk for infection.
The actual graph structure would also be a bit different than normal since lettuce and person nodes would have a different number of connections for each of the different types of nodes. Actually estimating the number of connections for each node type would be difficult but we can get relative numbers. Each lettuce node would have a decent number of connections to other lettuce nodes due to all the places where it could come in contact with lettuce during transportation and preparation. On the other hand, each lettuce node would only have a few connections to person nodes since in general only a few people will actually eat from the same head of lettuce. Person to person connection would probably be similar to the lettuce to lettuce connections if we only consider people that come in direct contact with each other.
Now that we have reasoned about the transmission probabilities and graph structure, we can analyze the spread of the epidemic. We can the SIR model discussed in the book. The lettuce nodes will be considered resistant once they are eaten or disposed of. So the epidemic starts will the initially infected lettuce and then spreads to other lettuce. This then eventually spreads to people. After a period of time no more lettuce will be infected due to preventive measures taken. Then the bacteria will just be spreading between people (assuming no person to lettuce transmission). This will then eventually die off due to the fact that people become resistant and then relatively low probability of the bacteria spreading between people.