What to do
A general note: Some of the tasks below (and in future apps) are fairly open ended. In general, I don’t want you to just do the tasks like a check-list. Instead, I want you to explore these simulations. Play with them, query them, go through iterations of thinking what you expect, observing it, and if discrepancies occur, figure out why. Essentially, I want you to “do science/research”.
Task 1:
- Set the model parameters such that it corresponds to the following setting:
- A population size of 1000, 1 initially infected, presymptomatic host, simulation duration 200 days.
- Assume that only symptomatic individuals transmit, at rate \(b_I = 0.001\).
- Assume that the duration of the presymptomatic, asymptomatic and symptomatic periods are all 5 days long. (Hint: The parameters gP, gA and gI are the inverse of these periods.)
- Assume that there are no asymptomatic infections and nobody dies due to disease.
- With parameters set to correspond to the scenario just described, run the simulation.
- Record the number and fraction of susceptible/infected/recovered remaining at the end of the outbreak.
- Check the results with the assumptions for the model and make sure they agree (you shouldn’t get any deaths, no asymptomatics, etc.)
- From the graph, contemplate how you would estimate the day at which the outbreak peaks. What’s the problem? How would you solve it?
- Run the simulation again, with the same values you just had. Does anything change? Why (not)?
Task 2:
- Assume now that half of the infected are asymptomatic. Don’t change any other assumption.
- What do you expect to get for the number/fraction of S/I/R at the end of the outbreak and the time at which the outbreak peaks?
- Run another simulation, record the same values as above.
- Compare your expectations with the results. How do they agree/disagree? Does it make sense? Anything surprising happening?
Task 3:
- Now assume that the asymptomatics transmit at the same rate as the symptomatics. Leave everything as in #2.
- How do you expect the results to change? (Try to make as precise/quantitative a prediction as you can)
- Run another simulation, record the same values as above.
- Compare your expectations with the results. How do they agree/disagree? Does it make sense? Anything surprising happening?
Task 4:
- Next, let’s assume that half the symptomatic infected die. Leave everything as in #3.
- How do you expect the results to change?
- Run another simulation, record the same values as above.
- Compare your expectations with the results. How do they agree/disagree? Does it make sense? Anything surprising happening?
Task 5:
- Further explore how changes in the infectiousness of the different groups (bP, bA, bI) and the average time a person spends in each of those states (gP, gA, gI) affects the infection dynamics.
- Every time, think about what you expect to get, then run the simulation, compare your expectations with the results. Then make sense of it.
Task 6:
- Further explore how changes in the fraction becoming asymptomatic and fraction dying does (or does not) affect the infection dynamics.
- Every time, think about what you expect to get, then run the simulation, compare your expectations with the results. Then make sense of it.
Task 7:
- Keep exploring.
- Think about real-world IDs and interventions. What groups would those interventions target, how would that affect the outcome?