Stochastic version of SEIR-V model

[roberthinch]

Add a stochastic version of the SEIR-V model which will allow to model stochastic extinction and vaccine trials. The supported features should and be the same as the current deterministic SEIR-V model (ie. model_default()).

A possible simple solution is discrete time stochastic compartment model within a structured population.

[adamkucharski]

Thanks for the suggestion – perhaps the easiest way would be to tweak the odin implemention of model_default so we can compile straight to dust as an option for a stochastic simulation. Tagging @alxsrobert as he's been thinking more about current implementation.

[roberthinch]

Okay, I'll wait for the odin version of model_default to come out and then it can be extended to have a stochastic version. The main part of the work is to convert the interventions and population into the form usable by odin, which will be the same for both deterministic and stochastic versions.

One thing to think about with the stochastic version is the return data structure. I've got a scratch odin version which evaluates 1000 replicates of the school closure example in 0.7s, however, once converting to data.table output it takes about 2.5s in total (the table has 7 million rows). The base R version in the PR takes about 3s (returning in data.table), so quite similar. However, if we returned results by arrays, or summary statistics in a data.table, I expect it will not take much more longer than the 0.7s.

[adamkucharski]

We've discussed a bit more, and would require swapping out the deriv() implementation we currently have with odin to an update() formulation in the odin DSL, so it can be compiled to dust. Although do-able, this would add a dependency that we want to hold off on until structure of odin2 and monty are clearer (hopefully will be at workshop next week!).

Perhaps as a starting point in meantime, this implementation by @LloydChapman might be useful: https://github.com/LloydChapman/seir/blob/main/inst/odin/seirhdagevax.R