## What to do

The tasks below are described in a way that assumes 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:

- 1000 susceptible hosts and 1 infected host of type 1.
- 200 susceptible hosts and 1 infected host of type 2.
- Simulation duration approximately 5 years.
- Assume that transmission from host 1 to host 1 is b11 = 0.002, from host 2 to host 2 is b22 = 0.01. No transmission from one host type to the other b12 = 0 and b21 = 0.
- Assume that the duration of the infectious period is 1 month long for both types ( g1 and g2 ).
- No waning immunity.
- Run the simulation and ensure you get outbreaks in both populations with 20% susceptibles left at the end.

### Task 2:

- Set b11 = 0.001. Rest as before.
- Run the simulation. You should get the same outbreak as before among type 2 hosts, no real outbreak among type 1 hosts.
- If you have worked through the reproductive number app already, contemplate what R was for both types/populations in task 1, what it is now in task 2, and how that influences what you see in the simulation.

### Task 3:

- Now set the transmission rate from host 2 to host 1 b21 = 0.001. Everything as before.
- Run the simulation. You should see an outbreak in both populations. This is an example of a core group driving the dynamics. Contemplate what the core group does.

### Task 4:

- Keep all settings as before, but set initial number of infected type 1 hosts to 0.
- Contemplate what you expect to see, run the simulation, see if your expectations are confirmed.

### Task 5:

- Now set the initial number of infected type 1 hosts back to 1, and infected type 2 hosts to 0.
- Contemplate what you expect to see, run the simulation, see if your expectations are confirmed.

### Task 6:

- Set I10 = 1 and I20 = 1.
- Set the transmission rates from host 1 to host 1 and host 2 to host 2 to 0.
- Set the transmission rate from host 2 to host 1 to b21 = 0.01, from host 1 to host 2 to b12 = 0.002. Those are the same values used in task 1 for transmission among the same hosts.
- Contemplate what you expect to see, run the simulation, see if your expectations are confirmed.

Transmission only between hosts of different type could for instance represent a sexually transmitted disease in a heterosexual population, with the 2 types of hosts being females and males.

### Task 7:

- Now set the transmission rate b12 = 0.01, and b21 = 0.002. Everything else as before.
- Again, think about your expectations, run simulation and check.

### Task 8:

- Repeat the previous task, with only an infected of type 1 initially present.
- Contemplate what you expect to see, run the simulation, see if your expectations are confirmed.

### Task 9:

- Repeat the previous task, with only an infected of type 2 initially present.
- Contemplate what you expect to see, run the simulation, see if your expectations are confirmed.

### Task 10:

- Set everything back as in task 1, but with waning immunity with an average duration of immunity of 5 months for each population (i.e. rates w1 and w2 need to be the inverse of 5 months.).
- Run simulation, confirm that both populations reach a steady endemic state.

### Task 11:

- Set transmission rate b21 = 0.005, everything else as before.
- Run the simulation and see what changes.

### Task 12:

- Set transmission rate b12 = 0.005, and b21 = 0, everything else as before.
- Run the simulation and see what changes.

### Task 13:

- With the settings you just had, turn off waning immunity for type 1, run the simulation and see what you get.

### Task 14:

- Turn waning immunity for type 1 back on and turn off for type 2, run the simulation and see what you get.

### Task 15:

- Keep exploring. Think of a real ID where accounting for 2 types of hosts is important, see if you can use the simulation to approximate and explore that ID.