What to do
A general note: Some of the tasks below are fairly open-ended. You shouldn’t go through the tasks like a check-list. Instead, explore these simulations, play with them, query them. As you do, loop through iterations of formulating your expectations for a specific scenario/task, running the model and observing results, and if results don’t agree with your expectations, figure out why. Essentially, “do science/research”.
The tasks below are described in a way that assumes that everything is in units of MONTHS (rate parameters, therefore, have units of inverse months). If any quantity is not given in those units, you need to convert it first (e.g. if it says a year, you need to convert it to 12 months).
Task 1:
- Set the model parameters such that it corresponds to the following setting:
- A population size of 1000 for both hosts and vectors, 1 initially infected host, no infected vector, simulation duration approximately 10 years.
- Set host -> vector transmission rate, b2=0.001. Keep b1 = 0.
- Assume that the duration of the infectious period in hosts is half a month (about 2 weeks) long.
- Turn off births and deaths and waning immunity for now.
- Run the simulation, observe what you get.
- Now set b1 = b2, rerun. Then set b1 = 2 b2, run again.
- Record the number and fraction of susceptible/infected/recovered remaining at the end of the outbreak.
Task 2:
- Now start with no infected hosts and 1 infected vector. What do you expect to see? Run the simulation to check your expectation.
- Play around with a different initial number of infected hosts and vectors and different transmission rates.
- Anything surprising happening? Do you understand why you see what you see?
Task 3:
- Turn off any infection process by setting the number of initial infected hosts and vectors to 0.
- Let’s assume our vectors are mosquitos, and that they live for about 1 month. Set the death rate accordingly.
- Set the birth rate such that the vector population settles at 2000.
Task 4:
- Turn infection process back on by having an infected host. Everything else as above.
- Contemplate the dynamics you see.
- You have births and deaths now, and usually with those, you can get multiple outbreaks. Why not here?
Task 5:
- Assume host immunity wanes after an average of 4 months.
- What do you expect to see? Run simulations to check your expectations.
Task 6:
- Keep exploring.
- Try to figure out how the different parameters influence the dynamics, specifically the (lack of) sustained cycles.