Google Meningitis Modeling Tom Hopson October , 2010

A role for weather forecasts Meningitis epidemics are observed to occur in the dust season and end with the onset of the rains –Can we predict the onset of the rains with enough spatial resolution ad enough lead time so that decision makers can prioritize allocation of vaccines to those districts likely to remain dry. 2

More on relevant weather variables … Consensus?: irritation of the pharynx that allows the bacteria (which may already be there) to enter the body. Dryness? Diffusion equation (number density): => Diffusion ~ number density, or perhaps more accurately, ~ Tn A In terms of what we can forecast (measure), look at ideal gas law: or Look at terms ~ e and terms ~ (e / T K ) (air at body temperature) => e ~ e sat (T) RH

Possible simple model (MRSA) – Susceptible-Colonized-Infected reservoirs (over?-) simplifications: assume can develop a meningitis model that applies for all assume homogenous mixing over whole district same model applied to all available districts S t, C t, I t represent numbers of people in each district β coefficients depend on many factors Thanks to Vanja Dukic

Possible simple model (cont) - for closure, treat I t ( (d) terms) as sum of previous 2 weeks of cases (after 2 weeks, no longer infected) => I t = I t-1 + I t-2 weekly time increment, so model everything as weekly averages (met variables) Simplifying to: only observations are I t (actually positive change in I t ), and Population P => model last equation only => treat S t and C t as roughly fixed ratios of total population across all countries (proportionally-small variation in S and C) (a)(b)(c)(d) (a) (b) (c)

Possible simple model (cont) - Or in terms of cases per 100,000 …

2 other Possible simple models … => Population per Area dependence n A + m B → C + D {} => Per Population dependence or

Grouping all possible model terms together … Or in terms of real-time measurables (i.e. no I terms) …

Logistic Regression for probability of occurrence ( “any case” or “epidemic 15/10 5 )

Weather Variable fit … RHVPAIRTVP/TTOTWINDNEWIND current const lag1 const lag2 const current P lag1 P lag2 P current P/A lag1 P/A lag2 P/A current Pr/r lag1 Pr/r lag2 Pr/r current Pr/r/Ar lag1 Pr/r/Ar lag2 Pr/r/Ar100010

Overall Weather Variable fit … current const lag1 const lag2 const current P lag1 P lag2 P current P/A lag1 P/A lag2 P/A current Pr/r lag1 Pr/r lag2 Pr/r current Pr/r/Ar lag1 Pr/r/Ar lag2 Pr/r/Ar Next steps … 1) use cross-validation 2) compare with equation utilizing incidence reports

… followed by Quantile Regression (QR) for severity (cases) … E.g. Our application Fitting T quantiles using QR conditioned on: 1)Ranked forecast ens 2)ensemble mean 3)ensemble median 4) ensemble stdev 5) Persistence

Using ‘Quantile Regression’ to better calibrate ensembles Without Quantile Regression: Observations outside range of ensembles With Quantile Regression: Ensembles bracket observations From Tom Hopson

THORPEX-TIGGE “Grand Ensemble Experiment” Archive Centre Current Data Provider NCAR NCEP CMC UKMO ECMWF MeteoFrance JMA KMA CMA BoM CPTEC IDD/LDM HTTP FTP Unidata IDD/LDM Internet Data Distribution / Local Data Manager Commodity internet application to send and receive data NCDC

Archive Status and Monitoring, Variability between providers

Forecasting: Thorpex-Tigge “grand ensemble” -

Forecast “calibration” or “post- processing” Probability calibration Flow rate [m 3 /s] Probability Post-processing has corrected: the “on average” bias as well as under-representation of the 2nd moment of the empirical forecast PDF (i.e. corrected its “dispersion” or “spread”) “spread” or “dispersion” “bias” obs Forecast PDF Forecast PDF Flow rate [m 3 /s] Our approach: under-utilized “quantile regression” approach probability distribution function “means what it says” daily variation in the ensemble dispersion directly relate to changes in forecast skill => informative ensemble skill-spread relationship

Calibration Procedure For each quantile: 1)Perform a “climatological” fit to the data 2)Starting with full regressor set, iteratively select best subset using “step-wise cross-validation” –Fitting done using QR –Selection done by: a)Minimizing QR cost function b)Satisfying the binomial distribution 2nd pass: segregate forecasts into differing ranges of ensemble dispersion, and refit models => ensure ensemble has skill-spread information Probability Temperature [K]  obs Forecast PDF T [K] Time Forecastsobserved Regressors for each quantile: 1) ranked forecast ensemble member 2) ens mean 4) ens stdev 5) persistence

Questions about weather/health relationship How does the disease work? –Consensus?: irritation of the pharynx that allows the bacteria (which may already be there) to enter the body Consistent with dust, cooking smoke, and pneumococcal as risk factors. Problem of communal eating across belt – exchange of saliva