2 For the vaccine modeling fans On the course github, in the Exams folder, find Article.pdf, a recently penned New York Times article about

the Pfizer and Moderna vaccines. Read the brief article and then answer the following questions.

4. (5 points) In class, we studied one model for perfect vaccine efficacy and three models for imperfect vaccine efficacy (the all-or-nothing model, the leaky model, and the three-factor model). Based on the article, rank the models from (1) most appropriate to (4) least appropriate for modeling of the Pfizer/Moderna vaccines. Explain your reasoning in 2-3 sentences.

5. (10 points) Our models in class did not differentiate between those with one dose and those with two doses. Write down the flow diagram for a SIR model of disease transmission with two additional stages of vaccination called V1 and V2. Assume that (a) susceptible people receive the first dose of vaccine at a per-capita rate , (b) people with one dose receive the second dose at a per-capita rate /2, (c) both stages V1 and V2 follow a leaky model with vaccine efficacies V E1 and V E2, respectively. Label your diagram with typical SIR constants, and additional vaccine-related values as appropriate.

6. (10 points) Write a system of differential equations corresponding to this system.

7. (5 points) Find the equilibrium or equilibria in this system. Explain it/them in words.

8. (5 points) Is this a good model for COVID-19 dynamics with vaccination in the US? Point out a flaw with this model and relate it to something you read in the article. Suggest a possible way (just in words) to ameliorate this modeling flaw.

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