ECON 467 Final Project Ivan Korolev∗ Due Date: by the end of day on May 11, 2020 Reminder: Collaboration in allowed. However, you are required to work out details by yourself. Identical assignments are not allowed and will be penalized. Late answers cannot be accepted. In this project, you will learn how to simulate the SEIRD epidemic model and estimate its parameters from the data. It will consist of several parts. In order to simulate SIR-type models in R, you need to install an appropriate package. I use deSolve, and to install it on my Mac I had to follow these steps: (a) Download GNU Fortran for Mac here: https://cran.r-project.org/bin/macosx/ tools/ (b) Download Xcode here: https: //apps.apple.com/us/app/xcode/id497799835?mt=12 After that, I was able to install deSolve with the usual install.packages command. You can use other packages, such as EpiDynamics or shinySIR, if you prefer. Install your preferred package. Let me know if you have any issues. Total: 100 points 1. (20 points) In this part you will code the SEIRD (Susceptible, Exposed, Infectious, Recovered, Dead) model in R. Your model should include the following parameters: γ – the inverse of the time to recovery. You can use γ = 1/10. σ – the inverse of the length of infectious period. You can us σ = 1/4. α – the case fatality ratio. r0 – the basic reproduction number. The initial values are I(0) = 0, E(0) = 1, D(0) = 0, R(0) = 0, S(0) = N − I(0) − E(0) − R(0) − D(0). N is the population size. You can code your model ∗Department of Economics, Binghamton University. E-mail: [email protected]. 1 in population shares or in numbers. You can take the population numbers from https://population.un.org/wpp/Download/Standard/Population/ and https:// www.census.gov/data/tables/time-series/demo/popest/2010s-state-total.html, from Wikipedia, or from other sources. Write a code that takes α and r0 as inputs and simulates the SEIRD model. The output should include 5 time series: S(t), E(t), I(t), R(t), D(t). Simulate your model for r0 = 5 and α = 0.005 for T = 360 periods. Plot the results. 2. (20 points) Download the data on the number of deaths from COVID-19 for one country, one state of the US, and one county. The country level data is available at https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_ data/csse_covid_19_time_series. The state and county level data is available at https://github.com/nytimes/covid-19-data. Using your code above that simulates the SEIRD model, write a function that fits the model to the data by minimizing the RSS. You can do it as follows: write a function that computes the RSS (sum of squared differences between the number of deaths in the model D(t, r0, α) and in the data D(t)) for the fixed values of r0 and α and for time series data on deaths. Then find the parameters that minimize the RSS. 3. (20 points) Estimate the model for your selected country, state, and county. Report the estimated parameters. Plot the model fit, i.e. fitted values and actual deaths against time. Simulate the model into the future. Note: you may want to restrict your sample to the observations before social distancing took place, as it might have affected the value of r0. 4. (20 points) Change the initial values, e.g. to I(0) = 0, E(0) = 3 or to some other values, and re-estimate your model. Plot the results and compare them with those in the previous part. 5. (20 points) Now try simulating your model into the future with changing R0. For instance, if you have estimated your model using the first T0 observations, you could set the resulting values S(T0), E(T0), I(T0), R(T0), D(T0) as initial values of the new model and simulate it with different parameter values. You could try to simulate your model with r0 = 0.5rˆ0 and r0 = 0.25rˆ0, where rˆ0 is your estimate of r0 from the previous parts. Plot the simulated path of the model. Compare it with those in the previous parts. How does a decrease in r0 affect your results? 2
