West Nile Virus: DYCAST spatialtemporal model

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West Nile Virus DYCAST spatial-temporal model
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Why spatial is special

• Modifiable area unit problem (MAUP)
• Results of statistical analysis are sensitive to
  the zoning system used to report aggregated data
• Results of statistical analysis are sensitive to
  the scale at which the analysis are performed
• Examine sensitivity of results to MAUP
• Boundary problem
• Study areas are bounded and results just outside
  the study are can affect results.
• Size and shape can affect results
• Migration
• Rhode Island (xs)
• Tennessee (xl)
• Ohio (jr)

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Why spatial is special (cont.)

• Spatial sampling
• Space can be used as a means of stratification
• Spatial autocorrelation
• Refers to the fact that values of phenomena close
  in space are related
• Problem Implication for sampling is that samples
  close in space may not be independent
• Spatial autocorrelation can be calculated and
  variances can be adjusted accordingly
• Prospects spatial autocorrelation can be used to
  estimate values at unknown locations based on
  surrounding know points (interpolation).

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Why spatial is special (cont.)

• Data management
• Editing
• Editing of spatial data is a long transaction
• User needs to check out a region for extended
  periods of time
• Other users need access
• Spatial databases are version managed to permit
  multiple long-transaction editing
• Access
• Indexes are spatially based
• Quad-tree recursive algorithm
• Addition of temporal dimension requires a second
  index. Optimization of spatial-temporal searching
  is still a topic under research

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Map to Geographic Information Systems (GIS)

• Maps as layers of geographic information
• Desire to automate map
• Evolution of GIS
• Create automated mapping systems
• Analyze geographic relationships
• Model real-world phenomena

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What is GIS?

• Component definition set of subsystems for the
  input, storage, transformation and retrieval of
  geographic data.
• Tool definition measuring and analyzing aspects
  of geographic phenomena and processes.
• Model definition a model of the real world.

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GIS Its about

• Modeling and analyzing relationships and
  processes that occur across space, time and
  different scales.
• New tools for modeling
• Geo-statistical procedures (Dead Crows)
• Object-based GIS (Tiger model)
• Seamless geographic databases (Big Apple)

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Global issues and motivation

• Hundreds Dead
• Thousands Infected and Sick. Sickness can last
  for months and result in long term neurological
  problems.
• Threatening the blood supply. One of the most
  common pathogens.
• Kills wildlife and threatens ecological balance.
• Remediation can cause problems.

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Diffusion of West Nile Virus in Birds, USA
Jan 1, 1999 to Dec 31, 1999
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Diffusion of West Nile Virus in Birds, USA
Jan 1, 2000 to Dec 31, 2000
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Diffusion of West Nile Virus in Birds, USA
Jan 1, 2001 to Dec 31, 2001
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Diffusion of West Nile Virus in Birds, USA
Jan 1, 2002 to Dec 31, 2002
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Diffusion of West Nile Virus in Birds, USA

• Jan 1, 2002 to Dec 31, 2002

Jan 1, 2003 to Dec 31, 2003
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Diffusion of West Nile Virus in Birds, USA
Jan 1, 2004 to Dec 31, 2004
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Diffusion of West Nile Virus in Birds, USA
Jan 1, 2005 to Dec 31, 2005
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Diffusion of West Nile Virus in Birds, USA
Jan 1, 2006 to Dec 31, 2006
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Diffusion of West Nile Virus in Birds, USA
Jan 1, 2007 to Sept. 25, 2007
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Confronting the problem at hand

• Newly introduced infectious agent arrives in New
  York City
• Observations
• Wildlife are killed especially birds
• Individuals become sick in close geographic
  proximity
• Seasonal effect

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Synthesizing a hypothesis literature review

• What do we know about this disease from other
  parts of the world?
• Outbreaks have been observed for decades in the
  Middle East, Africa and Europe
• Mosquitoes are the vectors
• These mosquitoes tend to be ornithophilic
• Birds play a primary role as the reservoir host
• Amplification cycle and spillover

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Synthesizing a hypothesis local observations and
experience

• Many birds die prior to human onset
• Most are resident Passerines particularly
  Corvids
• Patterns of birds deaths tend to be highly
  localized and dynamic
• Human infections tend to follow these patterns of
  bird deaths

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Spillover effect hypothesized by some researchers
Source The Centers for Disease Control and
Prevention http//www.cdc.gov/ncidod/dvbid/westn
ile/cycle.htm
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Birds

• Resident, wild passerine birds act as the
  principal amplifying hosts of West Nile virus.
• Data from Komar (2003)
• Crows suffer highest casualties. 82 dead in
  Illinois, by 2003.
• The nature of the bird as a reservoir for WNV
  transmission is still! under investigation.

Photo Source Ornithology and Mammalogy
Department, Cornell University
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Birds continued
Data Source Komar, N. unpublished. Used with
permission
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Mosquitoes

• Culex pipiens
• The most common pest mosquito in urban and
  suburban settings.
• An indicator of polluted water in the immediate
  vicinity.
• Recognized as the primary vector of St. Louis
  encephalitis (SLE).
• Is normally considered to be a bird feeder but
  some urban strains have a predilection for
  mammalian hosts and feed readily on humans.
  (American Hybrids?).
• Extrinsic incubation period of 4-12 days.
• Species identified in transmission in NYC
  include Culex pipiens, Culex restuans, Culex
  salinarius and Aedes vexans.

Photo source Iowa State University online image
gallery
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Hypotheses

• Primary Hypothesis Dead birds are an integral
  part of the process that results in human
  infection.
• Sub goals
• How do we quantify dead bird activity?
• How can we establish the relationship between
  dead birds and human infection?
• Is there a statistical procedure that mirrors the
  process governing this relationship?
• Are the statistical measures adequate?

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Quantifying WNV dead bird activity.

• Point Indicators of WNV
• Laboratory Confirmation in Birds-Mosquitoes
• Temporal lag between laboratory detection of
  positives and actual presence of virus in the
  wild.
• Does not allow for early identification of
  amplification cycle.
• Point data, no continuity in space.

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Quantifying WNV dead bird activity.

• Area estimates of WNV infection
• Density of Dead Crows and Blue Jays
• Arbitrary thresholds.
• Surveillance bias.
• Modifiable Areal Unit Problem (MAUP).
• Data regarding the ecology of the disease
  ignored.

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Quantifying WNV dead bird activity.DYCAST
Analysis (Dynamic Continuous Area Space Time
Analysis)

• Assumptions
• Good surveillance design and adequate public
  participation in reporting.
• Persons are infected at place of residence.
• Non-random space-time interaction of bird deaths
  attributed to WNV.
• WNV is continuous across space.

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Quantifying WNV dead bird activity.DYCAST
Analysis (contd.)

• Model Components
• Space-time correspondence of the death of birds
  as amplification measure.
• Knox method (statistical)
• Run Knox as an interpolation function to estimate
  a surface of WNV activity .
• Calibrate the model using ecological information
  and statistical analysis.
• Dynamic Use a moving window for the temporal
  domain.

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Quantifying WNV dead bird activity.Statistical
Approach.
MEASURES OF SPACE TIME INTERACTION THE KNOX TEST
(1963)
Where N the total number of pairs that can be
formed from n data points
Where T the test statistic tij the distance
between points i and j 0 if greater than the
critical distance, 1 otherwise sij the time
between points i and j 0 if greater than the
critical time, 1 otherwise
Where cell o11 is T, close in space and
time cell o21 are the pairs close in space only
(not in space and time) cell o12 are the pairs
close in time only (not in space and time) cell
O22 are pairs not close in space nor time
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Quantifying WNV dead bird activity.Significance
Testing
Poisson P(X T) 1 - Chi-Square P(X T)
where Oij O11, O12, O21, O22 of the Knox
matrix Monte Carlo Space-Time Label
switching. Monte Carlo Completely random seeding
in space and time.
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Monte Carlo Simulations Space-Time Swindles
Sweep the cylinder with a smaller cylinder of
closeness in search for close pairs.
Randomly swap the time labels keeping the
location fixed
1.5 m
Count the number of pairs that can be formed from
the points that fall in the smaller cylinder of
closeness.
3 days
0.25 m
21 days
Repeat 5000 times and rank the counts of close
pairs.
Problem In case of heavy clustering in either
dimension, the swapping of already close labels,
results in variance underestimation.
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Random Monte Carlo Simulations
Randomly seed the cylinder with X number of
points.
i.e. 10
1.5 m
Count the number of pairs that can be formed from
the points that fall in the smaller cylinder of
closeness. Also keep track of close-space,
close-time pairs.
21 days
Repeat 5000 times.
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Methodology

• Calibration Methodology
• Home address of humans testing positive
  considered the most definitive location of WNV
  existence.
• Calibration date assumed to be 7 days before
  symptoms onset for each case.
• Spatial and temporal domains of 1.5 miles and 21
  days were chosen based on ecological factors.
• Close space/time values were chosen from an
  ecologically relevant range (.25-.75 miles/3-7
  days).

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Calibration Results
2000 retrospective analysis in New York City
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Methodology

• Spatial Design-Prospective Surveillance
• Overlay Grid (0.5 x 0.5 miles ) across NYC and
  Chicago and run Knox test at centroid of grid
  cells (each as a potential human case) on a daily
  basis for the year 2001 season, using all birds
  except pigeons.

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Result evaluation

• Ran for NYC in 2001
• not sufficient number of human cases to quantify.
• Chicago 215 human cases.
• Rate of success.
• Kappa index of agreement.
• Chi-Squared test.

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Publication
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CHICAGO 2002

• Unconditional Monte Carlo

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Days before area was identified as at-risk
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Number of days area was lit.
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Kappa
Measures inter-rater agreement excluding chance
where   N is the total number of areas
considered,   and xii, xi, xi are the elements
of the following matrix  
  The sum of which amounts to N.
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Space-Time Application of kappa
Run for a selected combination of windows and
days prior
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Monte Carlo kappa table
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Interpreting the results

• The maximum kappa value is for a 2 day window for
  12 days prior
• With a 1 day reporting lag and lag for maximum
  viremia 1-2 days prior to death we have maximum
  viremia occurring on days 15 and 16 prior to
  onset of human illness.
• Given that extrinsic incubation period in
  mosquitoes averages 9 days and intrinsic
  incubation in humans averages 7 days, the above
  results are consistent with this pathology.

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Comparison of statistical analysis and
epidemiology
Figure 1 Illustration of temporal windows and
days prior to onset and model prediction most
likely time maximum viremia exist in environment
Figure 2. Time mosquito infection to onset date
of human infection.
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Interpreting the results

• Maximum kappa is followed by a gradual drop of
  30 by 7 days prior to infection.
• This can be explained by a reduction in avian
  hosts which may be causing mosquitoes to search
  for other sources of blood meals perhaps humans
• This coincides with the likely infection of
  humans by mosquitoes and may explain the so
  called spill over effect.
• Maximum kappa occurred for window size 2, 3 and 1
  respective
• Maximum viremia in birds occurs between 1-3 days

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Monte Carlo-Chi-Square comparison
Significant at lt 0.001 level.
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Broader implications of results

• Proved the role of dead-birds in human
  infections. Important for control.
• Supported hypothesis concerning the amplification
  cycle and spillover effect in WNV
• Identified a weakness of the Knox statistic and
  proposed a way of resolving it.
• First space-time implementation of the Kappa
  statistic.

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Publication
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DYCAST Implementation in California
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DYCAST Implementation in California
Implementation
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DYCAST Implementation in California
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DYCAST Implementation in California

• For 2006/07 the entire state of California
  (every ½ by ½ mile grid cell) is being run every
  day beginning May 1, 2006/07 and ending October 1
  of each year

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Alert to Mosquito control boards in California

• Dave,
• Here is an update on the DYCAST risk in
  Sacramento and Yolo counties, in case you may
  find it useful in advance of the aerial spraying
  scheduled for next week. The risk has continued
  to rise sharply in Sacramento County, with a new,
  large cluster appearing in the Citrus
  Heights/Foothill Farms/North Highlands area
  (Attachment A). As you can see from Attachment B,
  the level of DYCAST risk in Sacramento County is
  at the exact same level as it was on this date
  last year (199 lit tiles, 49.75 square miles).
  Sacramento County also has the highest level of
  risk (i.e., the largest combined square mileage
  of high risk areas) of any county in California
  at this time (Attachment C).
• A         current DYCAST risk map
• B         comparative DYCAST risk profiles from
  2006-2007
• C         comparative DYCAST risk profiles (top
  6 high risk counties), 2007
• D         animation of the DYCAST high risk
  areas from June 16 to July 26, 2007
• DYCAST high risk areas in 2007
•                         Sacramento               
  Yolo
• date                tiles   sq.
  mi.              tiles   sq. mi.
• 6/17/2007          2          0.5       
              0          0         
• 7/1/2007            24         6         
              2          0.5
• 7/2/2007            34         8.5       
              3          0.75
• 7/3/2007            35         8.75     
              4          1
• 7/4/2007            31         7.75     
              4          1
• 7/5/2007            44         11        
              5          1.25
• 7/6/2007            33         8.25     
              4          1
• 7/7/2007            40         10        
              6          1.5
• 7/8/2007            42         10.5     
              6          1.5
• 7/9/2007            60         15        
              6          1.5

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24-Bit Encoding Schemes (Master Templates)
Deriving Cellular Automata Rules for Areas at
Risk of West Nile Virus Infection
G. Green, PhD student, CARSI, Hunter College
City University of New York S. Ahearn, CARSI,
Hunter College CUNY R. Carney, California
Department of Health Services and A. McConchie,
CARSI, Hunter College - CUNY
ArcEngine Model with Daily Sacramento Area
DYCAST Output Raster
Selection of master template and sub-templates
via mutual information and genetic algorithm
based on accuracy of CA output
2005 Sacramento Season
Sacramento CA Accuracy
Data California Department of Health Services