["model"] Fit all free parameters against longer hospital time series

### Summary

Among the inputs to the model, parameters can be broken up by which ones should be firm details of the population and hospital, or reliable local calculations, and which ones are unknowns that observations should fit

Firm
- Regional population
- Market share
- ICU and Ventilator usage, as a fraction of hospitalized cases
- Lengths of stay

Unknown
- % Infections requiring hospitalization
- Spread parameter (as initial beta, doubling time, whatever)
- latency from infection to hospital presentation (#340 for implementation of this variable)
- Effect of social distancing measures (as contact reduction rate, or adjusted beta, whatever)

Given a week or two worth of actual hospital admissions, it should be possible to automatically estimate values for all of these parameters.

### Additional details

One potential confounding factor would be if the standard for hospitalization changes over time, to reflect increasing healthcare system burden and narrowed focus on the most critical cases.

Of the unknowns, latency should be the most general across regions and populations, but may still vary with distribution of demographics, comorbidities, etc, so it seems worth treating it as local.

### Suggested fix

Take as many days of hospital admission data as available as input, and automatically determine all possible parameters.