In this practical we will run a stochastic version of the SIR model and compare it to the deterministic model from practical series 2.
Having created our stochastic version of the SIS model in the previous practical we are now ready to extend this framework to the SIR model.
Using the code from the previous demo d0304_run_SIS and
timestep_stochastic_SIS() (from Practical 3-4), create a
new demo d0305_run_SIR and a new function,
timestep_stochastic_SIR() that will simulate the stochastic
SIR model.
To produce timestep_stochastic_SIR() requires a small
change to the update step to move the newly recovered individuals into
the recovered class rather than back into the susceptible class.
Remember also to include the recovereds in the population size
calculation.
To overlay the corresponding plot from the deterministic model you
will also need to use run_simulation() on the
timestep_deterministic_SIR() function from Practical 2-4,
and then plot using new.graph = FALSE.
This should be relatively straightforward. To produce
d0305_run_SIR you need to add a “recovereds” population to
the data frame, remembering to specify initial values for this new
population.
Run the code with a transmission rate of 0.2, a recovery rate of 0.1, 2 initial infecteds and 0 initial recovereds from a population size of 100. Demonstrate the variability in the results of the stochastic model and overlay the deterministic results from Practical 2-5.
Run the code for different initial conditions (number of infecteds and recovereds), and population size. Why do the plots of the stochastic simulation end before those of the deterministic simulation? What happens as you increase the population size? Illustrate these effects in your demo.
Now try increasing the transmission rate to increase the value of \(R_0\). Given a default value for the recovery rate of 0.1 what would the transmission rate need to be to simulate an outbreak with an \(R_0\) of 15?
As with previous exercises, you need to check that everything works correctly – that the package installs, and the demos and help files work and you can generate reports from the demos – and then we want you to get a couple of other people in your subgroup to check your code and make sure it works for them, and we want you to check other people’s code too. We describe how to do this for packages in GitHub in Practical 3-1 (also under Check it works) if you’re uncertain.
Remember, interacting like this through GitHub to help each other will count as most of your engagement marks for the course.