Allow parameter time dependence

[pratikunterwegs]

This PR is fixes #92, by allowing users to pass a list of functions to epidemic models that specify how model rate parameters vary over time. This is implemented in both R-only and Rcpp. The R-only version mirrors the Rcpp version and hence does not use {deSolve} events.

A good place to get started with reviewing is the vignette on time dependence.

See also #76.

[pratikunterwegs]

Example after running the code (not a reprex):

epidemic_default_cpp(
  population = uk_population,
  infection = pandemic,
  vaccination = vax_regime,
  time_dependence = list(
    beta = mod_beta
  ),
  time_end = 365, increment = 1
)

[pratikunterwegs]

Merging this PR today.

[adamkucharski]

Thanks for putting together, this looks very useful – no major comments for this version from a quick review of the vignette.

One thing that would be useful consider for next version is how to convert temporal data (e.g. vaccine coverage over time) into a continuous function for easy incorporation into {epidemics}/ODE model – as this conversion is often one of the more time-consuming pre-processing tasks when dealing with temporal interventions. {odin} has some useful interpolation functions we may want to lean on if relevant (as it's on CRAN): https://mrc-ide.github.io/odin/articles/odin.html

[pratikunterwegs]

Thanks for taking a look, very helpful.

Passing data such as vaccine coverage and interpolating it is actually pretty relevant for the ebola model which currently doesn't have a vaccinated compartment, so passing vaccine coverage changes will be useful. Just off the top of my head I think this can already be done in an ad hoc way within the function passed to time_dependence, using approx() to interpolate data that are used in the function f(t, x, data = data).

I'll convert the suggestion into an issue and perhaps we can address it on the development day, happy to have input.