AM3615A – 2021 – Assignment #4 – individual
Answer all the questions below. Upload the final version of your assignment to Gradescope on OWL, by 11:55pm
on Sunday, November 21. Remember that we negotiated this long due-date when we collaboratively refined
the course outline, to give everyone as much flexibility as possible. However you’ll be using the skills learned in
this assignment before that point, so it might be helpful to do it earlier, if that works in your schedule.
1. Find a dataset of COVID-19 infections each day for a country of your choice. Have fun and choose somewhere
interesting! This assignment will work best if you choose a time period when COVID-19 did not infect a
large fraction of the total population of the country, but there are enough infections that the data are not
too noisy.
2. Manipulate your data if necessary such that the data represent, as closely as possible, the total number of
infectious individuals at a given time (e.g. not just the number of new infections each day, and not the
total number of infections to date). Give a one-sentence explanation of why the data you are using are a
reasonable approximation to the number of current active cases.
3. As before, indentify a time period during which the data appear to show exponential growth, over a time
period of a month or two. If possible, aim for at least 20 data points of growing case numbers, even if the
growth is not exactly exponential.
In this assignment, we’ll consider the very simple model:
dI
dt
= βSI γI , with I(0) = I0 . (1)
Here I(t) is the number of infectious individuals at time t, and β is the infection rate per unit time. Note
that γ is the overall rate at which infectious individuals leave the infectious compartment (are no longer
infectious). The initial condition, I0 is unknown; treat it as an unknown parameter. Since you will be
considering a relatively short time period, assume that the number of susceptibles, S, is a constant.
4. A naive observer would say this model has 4 parameters (β, γ, S and I0). How many independent parameters
does this model actually depend on You don’t need to renormalize, but you should factor the equation and
then “clump” to reduce parameters before data fitting!
5. Fit the data (during the time period you identified) to the model given by Equation 1. Report your best-fit
parameter value(s). You can do this using any of the techniques we’ve learned in class. Be sure to shift the
time units so that the beginning of your fitted time interval is at time zero.
6. Give an equation for R0 for this model, based on Equation 1.
7. Find a literature estimate for the numerical value of R0 for COVID-19 (not necessarily for your country).
Use this, along with the results of your data fitting, to provide two equations in terms of β, S, and γ. Take
S to be the population of the country, and then use these two equations in two unknowns to solve for the
value of γ.
8. Interpret your result. What does γ represent in this model (hint: it’s not just recovery), and what does 1/γ
represent List some factors during the course of an epidemic that would influence γ. I am really curious
about how different your estimates from different countries and time periods will be.
