What to do
The tasks below are described in a way that assumes that everything is in units of DAYS (rate parameters, therefore, have units of inverse days). If any quantity is not given in those units, you need to convert it first (e.g. if it says a week, you need to convert it to 7 days).
Task 1:
- Set the model parameters such that it corresponds to the following setting:
- Susceptible S0 = 500, and initially untreated infected host Iu0 = 1. No other infected hosts It0 = 0 and Ir0 = 0.
- Set simulation duration, tmax, to approximately half a year.
- Assume that untreated individuals transmit at bU = 0.001, treated at bT = 0.0005, and resistant at bR = 0.0008.
- Assume that the duration in days of the infectious period is gU = 1/5 for untreated, gT = 1/4 for treated, and gR = 1/5 for resistant.
- Set the number of simulations to 20.
- With parameters set to correspond to the scenario just described, run the simulation.
- You should see some simulations with outbreaks and some without. For those with outbreaks, you should have around 10-100 susceptible left at the end.
Task 2:
- With everything as before, set the initial number of untreated infected hosts to 10.
- Run simulations. You should pretty much always get outbreaks. Record the average number of susceptibles left.
Task 3:
- With the same settings as Task 2 turn on treatment ( f > 0 ). Run the simulation with fraction receiving treatment, f, at 0, 0.25, 0.5, 0.75 and 1.
- Observe what happens to the susceptibles, S, at the end of the outbreak as you change treatment. Draw conclusions about the usefulness of treatment.
Task 4:
- Now allow resistance to be generated during treatment ( cT > 0 ).
- Set cT = 0.2 for the fraction of resistant generation from treatment.
- Set treatment level to 0. Contemplate what you expect to see. Run simulations to check.
- Now turn on treatment. Run the simulation with f at 0.25, 0.5, 0.75 and 1.
Task 5:
- Repeat task 3 with the number of simulations set to 50. For each of the 5 treatment levels ( f ) record the average number of susceptibles ( S ) left at the end.
- Set the rate of transmission to bR = 0.001 for resistant hosts, bU = 0.001 for untreated hosts, and turn resistance generation on cT = 0.3.
- Repeat running 50 simulations at a time (you can repeat a few times to get a better idea of random variation). For each of the 5 treatment levels ( f ) record the average number of susceptibles ( S ) left at the end.
- In your head or on a piece of paper, sketch out the relationship between treatment level ( f ) and the number of susceptibles ( S ) left at the end in the absence and presence of resistance evolution, cT. What do you conclude from that?
Task 6:
Keep exploring. For instance, try the following:
- Turn on resistance generation by treated, cT, and untreated, cU.
- Explore how population size, S0, the fraction of resistance generation ( cT or cU ) and fitness of the different strains ( bT or bU or bR ) affect outcomes.