## MATH / PUBH-EPI 5421 Course Projects

Logistics: These are intended to be group projects, roughly 2-4 students per group (more is possible, but check with me). The following are due May 3: 1) One written report per group. This should be organized in a similar fashion to scientific paper (i.e. introduction, concise statement of what precisely you are trying to accomplish, methods, your findings and their implications, references). Please make it readable -- your writing is part of your grade. Rough guideline 10-15 pages. 2) Oral presentation, including participation by all group members. 20 minutes for presentation, plus questions. 3) Feedback on other group presentations. This includes active participation in the Q&A session, together with providing some written feedback on a short form following the presentations.

Suggested topics: Below are some possible course project topics, broadly defined. I am very open to other topics -- if you have something in mind, please discuss with me and we can see if it is suitable.

• Basic model of Zika virus. Develop a simple model of Zika virus that captures key elements of the disease. Parameterize your model from the literature, and also from publicly available data on case counts. Use your model to estimate the basic reproduction number, outbreak size, and predicted prevalence levels of Zika.

• Zika-dengue competition model. The Aedes mosquitoes that serve as vectors for both dengue and Zika do not seem to support co-infection with both Zika and dengue. How will the introduction of dengue into dengue-endemic areas affect dengue dynamics? Can the two diseases coexist long term? Use a mathematical model to try to address these questions.

• Mixing patterns and disease spread on campus. Develop a multi-group model for infectious disease spread on campus. One possible motivating disease would be mumps, as OSU experienced a mumps outbreak in 2014. To parameterize your model, you will need to make some choice as to how mixing occurs in your model. One possibility would be to empirically estimate contact patterns between different segments of the OSU population by interviewing students about their contacts, or asking them to keep a contact diary. Possible subsets of the OSU population could be students in different dorms, majors, or fraternities / sororities. Even a modest-sized empirical dataset would be very interesting.

• Clustering and dynamics on networks. Most networks of practical interest have a high degree of structure, for example due to a high clustering coefficient, or the presence of communities within the network. Explore how these features affect disease spread on the network.

• Facebook. Take a portion of the Facebook graph, as posted publicly on the Stanford Large Network Dataset Collection (SNAP). Consider some sort of infection process on the Facebook graph. For example, this might be whether a post is "liked" by others. Propose a plausible model of how this infection process occurs. For example, in the preceding example there may be cooperativity in transmission, in the sense that the more likes a post has the more individuals are likely to see the post. Simulate the spread on the network.