Integration with input distributions and potential for fitting

[adamkucharski]

There a couple of use cases that are common in early stages of an epidemic, which could be useful (and slightly more advanced) applications for epidemics:

1. Simulating epidemic curves based on input priors. For example, early COVID scenarios (see Fig S2 and S3) used a meta-analysis of R0, then simulated a number of trajectories drawing from this distribution. Could similarly have a set-up that can simulate from a distribution vector of parameters rather than a single one (kind of like scenarios does, but with tighter integration, e.g. taking input distributions from epiparameter).

2. Fitting early growth data then simulating forward scenarios. In early stages of epidemic, can usually only identify a couple of parameters from growth curve (i.e. R0 and initial number of infections). So if epidemics model outputs case numbers over time, could use a simple fitting package like quickfit to estimate these values, and hence plausible future trajectories, without requiring a full MCMC-type approach. Basically R0 value will move the fitted early curve up and down, and I(0) moves it left-right.

I realise that some (all?) of this functionality may be better placed within another package, like scenarios. But may influence some of the design choices in epidemics, e.g. speed of simulations; structure of simulation outputs, and hence ease of incorporation into a likelihood.

[adamkucharski]

This should be feasible for advanced users once issues #222 and #223 are complete.