Year 12 & 13 Inspire

STEM Daily Activity: Thursday

Posted by St John's College Access on

Throughout this week, we will be running daily competitions: every morning at 10am, we will upload that day’s activity, and anyone who sends in their answer before 9am the following day will be entered into a prize draw, with prizes awarded next week. Solutions to the puzzles will also be uploaded by 10am the following day so you can check your work.

Thursday: 6 August

SIR model and the reproductive number R0

In the disease modelling lecture we discussed the basic reproductive number R0 in the context of an epidemic and derived its formula as:

"SIR model and the reproductive number R0" equation
  1. How can we reduce the value of R0?
  2. If we take R0 = 3 as was originally estimated for the initial spread of COVID-19, and assume that the entire population is initially susceptible, what values could r and a take?
  3. Using the values you calculated in Q2, plot the appropriate graphs at mathigon.org/pandemic and use them to answer the following questions:
    1. What is the maximum % of the population that is infected at any one time?
    2. What happens to the graphs if you increase the value of the transmission rate r? What happens if you decrease the value of r?
    3. What happens to the graphs if you increase the value of the recovery rate a? What happens if you decrease the value of a?
    4. What happens to the graphs when you increase the ‘incubation time’ (bottom slider) to a value above zero? What do you think this represents?

How to enter

  • Complete the question above, showing the work you did to arrive at your answer
  • Fill out the Competition Cover Sheet (if the document is not working for you, you can also provide the information requested in the cover sheet in the body of your email)
  • Email your entry and your cover sheet to us at inspire@sjc.ox.ac.uk

Terms & Conditions

  1. All students enrolled on the Year 12 Inspire Programme are eligible to enter this competition.
  2. You must complete the Competition Cover Sheet and submit it along with your entry to inspire@sjc.ox.ac.uk before the closing date. If we do not receive a completed cover sheet with your entry, we will NOT be able to consider the entry.
  3. The competition closes at 9am Friday 7 August.
  4. The work you submit must be entirely your own, and should not exceed 300 words in length.
  5. Competition winners will be contacted via email next week. One entry will be selected at random to win a £10 Amazon voucher and to be published on Inspire Digital.

Wednesday’s solution

Exponential versus polynomial growth

View Wednesday’s solution above