[stem-ebola] Operon Labs Ebola Models Versions C3 Released

[alex@xxxxxxxxxxxxxx]

New Fixed 'C3' STEM Ebola Models are up for West Africa and USA.

First, thanks to Dr. Christian Althaus for his insights, which were 
necessary to get these parameters working properly.  There may be a few 
minor bugs in these new models, but they are much better than before.

The main results was that the STEM Ebola C3 model shows the West African 
incidence peaks in late-March 2015 (with I+R+D in millions) assuming no 
changes in parameters like R0, and no effective control interventions.  
In reality, however, the Confidence Interval here is so wide you could 
drive a truck through it.

Too many unknowns to predict that far out, but I suppose this could be a 
worst-case scenario assuming R0 doesn't increase..

Christian: I ended up using pretty much all your recommendations, 
including deriving Gamma from the published serial interval. Your 
formulas for derivation of the infectious mortality rate also worked 
great.  Thank you.

The latest Operon 'C3' Ebola Outbreak Model SEIR parameters are as 
follows (derived from the NEJM/WHO data):

1/σ (Incubation Period) : 9.4 days (Single-day Exposures, All Countries, 
Observed)
1/γ (Infectivity Period): 8.2 days (Derived from Observed Serial 
Interval (All Countries) - Incubation Period) (17.6 Days - 9.4 Days)=8.2 
days
σ (Incubation Rate, STEM)  : 1 / 9.4 days = 0.1063830
γ (Infectivity Rate)  : 1 / 8.2 days = 0.12195120
f (Case Fatality Rate): 0.708 (NEJM/WHO)
γ_STEM:	Recovery Rate (STEM): (1-f)*γ = 0.292*γ = 0.03560976
δ_STEM	Mortality Rate (STEM):	f*γ = 0.708γ = 0.0863414496
R0 (Reproduction Num#) : 1.84 ( Weighted Avg, All Countries)
βstem(Transmission Rate) = R0 * γ
βstem(Transmission Rate) = 1.84 * 0.12195120
βstem(Transmission Rate): = 0.224390208

Td_model (Model Doubling Time) = ~16.3 days (Simple calc.. from two 
points in output..Td=(t2-t1)*(log 2 / log(q2/q1))
Td_actual (Actual Doubling Time) = 15.74 days (Weighted Average, 
Liberia+SL+Guinea)
Serial Interval (Model Serial Interval) = Not Calculated
Serial Interval (Actual Serial Interval) = 17.6 days (NEJM/WHO. Used to 
derive the infectious period)

The models for the USA and West Africa can be downloaded here:

http://wiki.eclipse.org/Ebola_Models#Operon_Labs_Ebola_Models

Feedback is appreciated -- in case I missed anything.  Feel free to use 
these as a base to build other models.

Thanks,
Alex