A Spatial-Temporal Model for Identifying Dynamic Patterns of Epidemic Diffusion Tzai-Hung Wen 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 clusterSpace-time cluster

Diffusion Patterns of Epidemics Transmission routes and diffusion patterns ExpansionContagiousHierarchicalRelocation (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 Sub-clusters ： Groups from the same infection sources Identifying areas with spatial-time clustering Dynamics of clustering remain unknown

Properties of Clustering Dynamics Contagious diffusion Space-time process Concept of life cycle t1t1t1t1 Occurrence t2t2t2t2 t4t4t4t4 t3t3t3t3 t5t5t5t5 GrowthSplit Disappear Life Cycle: t2 to t4 (Takaffoli et al., 2011)

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 HomeHome Working Places (Herder & Siehndel, 2011, Gonzalez et al., 2008, Isaacman et al., 2012)

Understanding Spatial Behaviors of Humans (cont’d) (Herder & Siehndel, 2011, Gonzalez et al., 2008, Isaacman et al., 2012, Rattan et al., 2012) Routine travel patterns

HomeHome Working Places Summary: Spatial Behaviors of Humans Routine travel patterns Contacts follow distance-decayed property (Herder & Siehndel, 2011, Gonzalez et al., 2008, Isaacman et al., 2012)

Disease Transmission Risk Ranges of human mobility 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 T 0 = 0T 1 = 7T 2 = 17 Onset of first case Possible onset of the second case day D: Radius of transmission) (D: Radius of transmission)

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 Clustering pair 1. Defining Space-time Relationships Infection pair Clustering pair Clustering pair 2. Detecting sub-clusters and temporal dynamics 3. Identifying dynamic behaviors of sub-clusters Probability of getting infected Common Origin Probability

Space distance < D Time distance < T1 Space distance < D T1 < Time distance < T2 Space distance < D Time distance < T1 Space distance < D T1 < Time distance < T2 1. Defining Space-time Relationships Define clustering pair and infection pair Clustering pair Infection pair

1. Defining Space-time Relationships (cont’d) 0 TimedistanceSpacedistanceClusteringpairInfectionpair D T1T1 T2T2 Space distance < D Time distance < T1 Space distance < D T1 < Time distance < T2 Space distance < D Time distance < T1 Space distance < D T1 < Time distance < T2 Define clustering pair and infection pair Clustering pair Infection pair

Infection Pair Probability of getting infected Probability of getting infected Risk of Infection (R I ) = Temporal weight (W T ) x Spatial weight (W S ) Risk of Infection (R I ) = Temporal weight (W T ) x Spatial weight (W S ) T0T0 T1T1 T2T2 Distance D Temporal weight SpatialWeight Transmission Cycle Time Rage of infection

Infection Risk = spatial weight x temporal weight

Example: Calculating Infection Risk Space Distance ： 0.4 km Time Distance ： 10 days Range of Infection (D): 0.8 km Transmission Cycle (T1 and T2): day 812 日 Time Weight 10 1 公里 0.8 Spatial Weight R I = W T x W s = 1.0 x 0.44 = 1.0 x 0.44 = 0.44 Clustering pair Infection pair

Probability of getting infected PI =PI =PI =PI = RIRIRIRI R I Σ R I Clustering pair Infection pair

PI =PI =PI =PI = = 41% = 59% PI =PI =PI =PI = PI =PI =PI =PI = RIRIRIRI R I Σ R I Example: Probability of getting infected Clustering pair Infection pair

100% 59% 41% 13% 22% 78% 87% 100% 49% 51% 100% Probability of getting infected PI =PI =PI =PI = RIRIRIRI R I Σ R I Clustering pair Infection pair

Clustering Pair 100% 59% 41% 13% 22% 78% 87% Common Origin Probability: Probability of one pair from the same infection source 100% 49% 51% 100% Clustering pair Infection pair

Common Origin Probability (C.O.P) 100% 59% 41% 13% 22% 78% 87% C.O.P = 59% * 100% = 59% C.O.P = 78% * 87% + 22% * 13% = 71% 100% 49% 51% 100% Clustering pair Infection pair

59% 71% 49% 51% 0% 5% 9% Common Origin Probability (C.O.P) Clustering pair Infection pair

Framework of the Analytical Method 1. Defining Space-time Relationships Infection pair Clustering pair Clustering pair 1. Defining Space-time Relationships Infection pair Clustering pair Clustering pair 2. Detecting sub-clusters and temporal dynamics 3. Identifying dynamic behaviors of sub-clusters Probability of getting infected Common Origin Probability

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) average ： 41.47% Sample 1 Sample 2 average ： 45.57% Sample 3 average ： 40.57% Average of samples ： Average of samples ： Standard deviation ： 2.18 Standard deviation ： 2.18 Threshold of COP = 46.80% (95% CI) Clustering pair Infection pair Using Bootstrap method to determine the threshold of Common Origin Probability

Detecting sub-clusters (cont’d) 59% 71% 49% 51% 0% 5% 9% Clustering pair Infection pair average ： 41.47% Sample 1 Sample 2 average ： 45.57% Sample 3 average ： 40.57% Average of samples ： Average of samples ： Standard deviation ： 2.18 Standard deviation ： 2.18 Threshold of COP = 46.80% (95% CI) Using Bootstrap method to determine the threshold of Common Origin Probability

Temporal dynamics of sub-clusters Using Infection Pairs to establish temporal progression of sub-clusters Clustering pair Infection pair

Merge Temporal dynamics of sub-clusters (cont’d) Using Infection Pairs to establish temporal progression of sub-clusters 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 growth shrink

Procedure of the algorithm

Procedure of the algorithm (cont’d)

Simulation Experiment

Simulating an epidemic in Taipei City Different color means different transmission chains Scenario (initial state) ： 4 initial cases 4 initial cases 4 transmission chains 4 transmission chains Transmission Route: Contagious Contagious

4 initial cases Results: Tracking the dynamics of the sub- clusters 3 transmission chains

Results: Tracking the dynamics of the sub- clusters

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 (Stoddard et al., 2009) 6 am 6 pm

Flight range of mosquitoes: meters (Taiwan Centers of Disease Control, 2003) Dengue Fever: a mosquito-borne disease

Transmission cycle

Dengue Epidemic in Kaohsiung, Parameters: Range of Infection (D): 0.8 km Transmission Cycle (T1 and T2): day Kaohsiung Study Period: 2009/7/ /3/30 Total Cases: 770

Results: identifying 4 major transmission chains

Diffusion processDynamics of sub-clusters

Results: Tracking the dynamics of the sub- clusters of the dengue epidemic Life Cycle 2009/9/ /12/ /9/ /1/ /12/ /1/4 2009/10/ /1/ Blue Chain Index case : 2 Sub-cluster: 18 cases Green Chain ： Index case: 1 Sub-cluster: 12 cases Red Chain ： Index case : 1 Sub-cluster: 14 cases Yellow Chain ： Index case: 3 Sub-cluster: 15 cases

Split: source of infection Merge: vulnerable areas Growth: increase in severity Shrink: decrease in severity Results: Identifying dynamic behaviors of the sub-clusters of the dengue epidemic

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 Associate Professor Department of Geography, National Taiwan University