Replicate TIV analysis as worked example

[aezarebski]

Description

Application of the TIV model to real data seems like a good example for the hybrid modelling approach. Baccam et al (2006) provides an analysis we could replicate to validate our approach.

Replicating the results of Baccam et al (2006) would demonstrate our method can be applied to real problems (and how to pair it with an simulation based inference method). Importantly, this should be more palatable to people opposed to Petri nets.

In scope is a close replication of the existing analysis recast as a CTMC model. A slight extension to consider the probability of early stochastic extinction is definitely in-scope. Improving the statistical method and the observation model is definitely out-of-scope.

Suggested solution

1. Create a new branch and work in a new directory particle-filter-example-tiv.
2. Extract the data from the figures in the existing analysis.
3. Replicate the "target cell-limited model" with ODEs to ensure everything is working as expected.
4. Create a CTMC version of the model and as a stretch attempt to replicate the analysis using tau-leaping.
5. Replicate the analysis using the hybrid model based on the CTMC derive above.
6. Stretch goal is to use the hybrid model to estimate the probability of stochastic die-out early on in an infection.

[aezarebski]

i've started work on this in the pypfilt-tiv branch