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A Spatial-Temporal Model for Identifying
Dynamic Patterns of Epidemic Diffusion
Tzai-Hung Wen [email protected]
Associate Professor
Department of Geography, National Taiwan University
Contents
1. Introduction
2. Data and Methods
3. Simulation Experiment
4. Case Study: A dengue epidemic
5. Conclusions
Introduction
Spatial Epidemiology
focus on the study of the spatial distribution of
health outcomes
concerned with the description and examination
of disease and its geographic variations.
(Snow, 1854)
Detecting Space-time Clustering
Space-Time Scan Statistics
(Kulldorff, 2001)
Spatial cluster
Space-time cluster
Diffusion Patterns of Epidemics
Transmission routes and diffusion patterns
Expansion
Contagious
Hierarchical
Relocation
(Meade and Emch, 2010)
Methodological Challenges in Space-time
Clustering Analysis
Identifying areas with spatial-time clustering
Dynamics of clustering remain unknown
Methodological Challenges in Space-time
Clustering Analysis
Identifying
areas with spatial-time
clustering
Sub-clusters：Groups
from the same
infection
Dynamicssources
of clustering remain unknown
Properties of Clustering Dynamics
Contagious diffusion
Space-time process
Concept of life cycle
(Takaffoli et al., 2011)
Life Cycle: t2 to t4
t1
Occurrence
Growth
Split
t2
t3
t4
Disappear
t5
Research Objectives
1. Develop a space-time model for identifying
epidemic sub-clusters and detecting their
dynamic behaviors
2. Differentiate spatial epidemic risk patterns
based on the dynamic behaviors of sub-clusters
Data and Methods
Understanding Spatial Behaviors of Humans
In average, people stay in their residential homes
around 8-10 hours each day
(Herder & Siehndel, 2011, Gonzalez et al., 2008,
Isaacman et al., 2012)
Home
Working
Places
Understanding Spatial Behaviors of Humans
(cont’d)
Routine travel patterns
(Herder & Siehndel, 2011, Gonzalez et al., 2008,
Isaacman et al., 2012, Rattan et al., 2012)
Summary: Spatial Behaviors of Humans
Routine travel patterns
Contacts follow distance-decayed property
(Herder & Siehndel, 2011, Gonzalez et al., 2008,
Isaacman et al., 2012)
Home
Working
Places
Disease Transmission Risk
Ranges of human mobility
(D: Radius of transmission)
e.g: 0.8 kilometers (Rattan et al., 2012)
Transmission Cycle (T1 and T2):
Period between next-case and first-case onset
e.g.：from 7th day to 17th day after onset of index case
Onset of first case
T0 = 0
Possible onset of
the second case
T1 = 7
T2 = 17
day
Example: Estimating Transmission Cycle
Transmission cycle
Data
Persons with illness
Residential homes
Onset date / week
Framework of the Analytical Method
1. Defining Space-time Relationships
Infection pair
Clustering pair
2. Detecting sub-clusters
and temporal dynamics
Probability of
getting infected
Common Origin
Probability
3. Identifying dynamic
behaviors of sub-clusters
1. Defining Space-time Relationships
Define clustering pair and infection pair
• Space distance < D
• Space distance < D
• Time distance < T1
• T1 < Time distance < T2
Clustering pair
Infection pair
1. Defining Space-time Relationships (cont’d)
Define clustering pair and infection pair
• Space distance < D
• Space distance < D
• Time distance < T1
• T1 < Time distance < T2
Space
distance
D
Clustering pair
Infection pair
0
Clustering
pair
Infection
pair
T1
T2
Time
distance
Infection Pair
•
•
Temporal
weight
Probability of getting infected
Risk of Infection (RI)
= Temporal weight (WT) x Spatial weight (WS)
Transmission
Cycle
Spatial
Weight
Rage of infection
Distance
Time
T0
T1
T2
D
Infection Risk = spatial weight x temporal weight
Example: Calculating Infection
RiskDistance：0.4 km
Space
Range of Infection (D): 0.8 km
Transmission Cycle
(T1 and T2): 8 - 12 day
Time Distance：10 days
RI = WT x Ws
= 1.0 x 0.44
= 0.44
Time
Weight
1
Spatial
Weight
Clustering pair
Infection pair
8
10
12
日
0.44
0.4
0.8
公里
Probability of getting infected
0.75
0.21
0.31
0.09
0.59
0.44
RI
PI =
Σ RI
0.39
0.39
0.44
0.41
0.38
Clustering pair
Infection pair
Example: Probability of getting infected
0.75
0.21
0.31
0.09
0.59
0.44
0.39
0.39
0.44
RI
PI =
Σ RI
0.41
0.38
PI =
PI =
0.31
0.31 + 0.44
0.44
0.31 + 0.44
= 41%
= 59%
Clustering pair
Infection pair
Probability of getting infected
78%
22%
41%
13%
87%
59%
RI
PI =
Σ RI
100%
49%
100%
51%
100%
Clustering pair
Infection pair
Clustering Pair
Common Origin Probability:
78%
22%
41%
Probability of one pair from
the same infection source
13%
87%
59%
100%
49%
100%
51%
100%
Clustering pair
Infection pair
Common Origin Probability (C.O.P)
78%
22%
41%
13%
87%
59%
100%
49%
100%
51%
100%
C.O.P = 59% * 100%
= 59%
C.O.P = 78% * 87%
+ 22% * 13%
= 71%
Clustering pair
Infection pair
Common Origin Probability (C.O.P)
71%
9%
5%
59%
0%
49%
51%
Clustering pair
Infection pair
Framework of the Analytical Method
1. Defining Space-time Relationships
Infection pair
Clustering pair
2. Detecting sub-clusters
and temporal dynamics
Probability of
getting infected
Common Origin
Probability
3. Identifying dynamic
behaviors of sub-clusters
Detecting sub-clusters
Using Bootstrap method to determine the
threshold of Common Origin Probability
Sample 1
59%, 5%, 51%, 71%, 5%, 51%, 49%
Average：41.47%
Sample 2
51%, 9%, 9%, 71%, 71%, 59%, 49%
Average ：45.57%
Sample 3
5%, 0%, 49%, 71%, 51%, 59%, 49%
Average ：40.57%
Clustering pair
Infection pair
Detecting sub-clusters (cont’d)
Using Bootstrap method to determine the
threshold of Common Origin Probability
Sample 1
Sample 2
Sample 3
average：41.47%
average ：45.57%
average ：40.57%
Average of samples：42.53
Standard deviation：2.18
Threshold of COP = 46.80% (95% CI)
Clustering pair
Infection pair
Detecting sub-clusters (cont’d)
Using Bootstrap method to determine the
threshold of Common Origin Probability
Sample 1
Sample 2
Sample 3
71%
9%
5%
average：41.47%
average ：45.57%
average ：40.57%
Average of samples：42.53
Standard deviation：2.18
59%
0%
49%
Threshold of COP = 46.80% (95% CI)
51%
Clustering pair
Infection pair
Temporal dynamics of sub-clusters
Using Infection Pairs to
establish temporal
progression of sub-clusters
Clustering pair
Infection pair
Temporal dynamics of sub-clusters (cont’d)
Using Infection Pairs to
establish temporal
progression of sub-clusters
Merge
Clustering pair
Infection pair
Dynamic Behaviors of Sub-clusters
Occurrence / Disappearance：Life Cycle
Growth / Shrink：Change of Severity
Split：Source of Infection
Merge：Vulnerable Areas shrink
growth
Procedure of the algorithm
Procedure of the algorithm (cont’d)
Simulation Experiment
Simulating an epidemic in Taipei City
Scenario (initial state)：
4 initial cases
4 transmission chains
Transmission Route:
Contagious
Different color means different
transmission chains
Results: Tracking the dynamics of the sub3 transmission chains
4 initial cases
clusters
Results: Tracking the dynamics of the subclusters
Dynamics of sub-clusters in time and space
Case Study:
A Dengue Epidemic in Kaohsiung
Dengue Fever: a mosquito-borne disease
Transmission route: human-mosquito-human
people stay in their residential homes around 8-10
hours each day
6 pm
6 am
(Stoddard et al., 2009)
Dengue Fever: a mosquito-borne disease
Flight range of mosquitoes: 400-800 meters
(Taiwan Centers of Disease Control, 2003)
Transmission cycle
Dengue Epidemic in Kaohsiung, 2009-2010
Kaohsiung
Study Period:
2009/7/27 - 2010/3/30
Total Cases: 770
Parameters:
Range of Infection (D):
0.8 km
Transmission Cycle
(T1 and T2): 10 - 25 day
Results: identifying 4 major transmission chains
Results: identifying 4 major transmission chains
Diffusion process
Dynamics of sub-clusters
Results: Tracking the dynamics of the subclusters of the dengue epidemic
Life Cycle
Green Chain：
Index case: 1
2009/9/28 - 2010/1/09
Sub-cluster: 12 cases
Blue Chain
Index case : 2
2009/9/22 - 2009/12/21
Sub-cluster: 18 cases
Red Chain：
Index case : 1
2009/12/28 - 2010/1/4
Sub-cluster: 14 cases
Yellow Chain：
Index case: 3
2009/10/15 - 2010/1/2
Sub-cluster: 15 cases
7
8
9
10
11
12
1
2
3
4
Results: Identifying dynamic behaviors of the
sub-clusters of the dengue epidemic
Growth: increase in severity
Shrink: decrease in severity
Split: source of infection
Merge: vulnerable areas
Results: Differentiating spatial risk patterns
Results: Differentiating spatial risk patterns and
environmental characteristics
Comparisons with SaTSCan Results
Conclusions
Conclusions
Disease clustering is not a “static” phenomena, but a
complex dynamic process in time and space.
The study proposed a space-time model for tracking the
dynamics sub-clusters, identifying their dynamic behaviors
and differentiating spatial risk patterns of an epidemic.
Spatial risk patterns may be caused by different factors and
environmental characteristics, which implies that different
intervention strategies may be implemented in different
locations.
Thank you for your listening
Tzai-Hung Wen [email protected]
Associate Professor
Department of Geography, National Taiwan University