Homework problems

(feel free to copy and paste these over to another file and write your answers below each question)

1. A new parasite is discovered infecting bess beetles in Mexico. Design an experiment to test whether the parasite exhibits frequency or density dependent transmission. This parasite is also found in Italy. How would you test for evidence of enemy release relative to other drivers of this parasite’s emergence in Mexico?

2. Walk through the determination of $R_0$ for the SIR model, deriving $R_0$ as we did in class. Discuss $R_0$ with respect to it’s utility in public health as well as the inherent issues around it.

3. Two towns are connected by a rarely traveled road. One is large and the other small. The larger town has endemic measles and the smaller town has small recurrent epidemics of measles. Describe why this might be the case.

4. Based on the setup above: a recent push from city planners will connect these two cities by bus and improve road conditions in an effort to increase transportation. How might this influence (or not influence) measles cases in both towns?

5. We talked about superspreaders. Why are they difficult to incorporate into the traditional SIR modeling framework? How would you go about incorporating the role of superspreaders into the SIR model?

6. We also talked about supershedders. Differentiate a supershedder from a superspreader, including examples of how they differ as a function of parasite transmission mode.

7. A helminth parasite is transmitted within a host population through the environment. Design an experiment to test whether or not superinfection could be occurring.

8. We talked about parasite aggregation a fair bit, including the odd tendency for parasites that infect with larger mean burden to also have higher variation in infection burden. What would the slope of this relationship between mean and variation in burden tell us with respect to parasite aggregation?

9. Incorporate vaccination into the SIR model structure (hint: use equations, show the model, calculate R0, etc.)

10. A parasite has been discovered that infects the host through direct transmission, and hosts can clear the pathogen, but are immediately susceptible again to infection. Write out how this would modify the SIR model structure. Sketch out what you think the time series of infection would look like for such a parasite (x-axis is time, y-axis is infected people or fraction of population infected).