From Network Structure to Consequences & Control

Transcription

1 From Network Structure to Consequences & Control Shweta Bansal Isaac Newton Institute, Cambridge University Infectious Disease Dynamics Programme August 2013

2 Number of papers Network Epidemiology

3 Network Epidemiology Network models capture host population contact heterogeneity and structure Invasion dynamics [e.g. SARS] Social structure [e.g. STDs] [Image: Bearman et al] Multi-scale dynamics [e.g. livestock infections] [Image: Danon et al] Public health interventions [e.g. hospital infections] [Image: Meyers et al]

4 Outline How structure drives epidemiological dynamics? (Theoretical findings) Future Challenges How structure impacts epidemiological consequences and control policy? (Empirical findings) Future Challenges

5 How Structure Drives Epidemiological Consequences

6 Network Structure Disease Consequences ARE RANDOM GRAPHS USEFUL? Bansal et al, 2009 Molloy & Reed, 1995 Poisson degree dist. Scale-free degree dist. Lowly clustered Highly clustered Low modularity High modularity Sah et al.

7 Size of Epidemic Network Degree & Epidemic Outcomes Larger average degree increases epidemic size Average Degree (same degree distribution, same pathogen transmissibility) Newman (2002), Meyers et al (2005)

8 Epidemic Threshold Network Degree & Epidemic Outcomes Large variance in degree decreases epidemic threshold R 0 = T k2 k 1 Variance in Degree (same average degree) Scale-free networks (relevant for STDs) have small epidemic threshold Refs: Diekmann & Heesterbeck (2000); Newman (2002); Pastor-Sattoras & Vespignani (2002); Rocha et al, 2010/2011

9 Number of Infecteds Concurrency & Epidemic Outcomes Concurrency = current number of contacts Epidemics grow faster and spread farther with concurrency Concurrency Kretzschmar & Morris (1996); Morris & Kretzschmar (1997)

10 Network Transitivity & Epidemic Outcomes Transitivity = propensity of triangles Transitivity makes populations harder to invade, and leads to smaller and longer epidemics

11 Network Clustering & Epidemic Outcomes The effect of spatial clustering is strongest for small connectivity Keeling, 1999

12 Network Transitivity: What s realistic?

13 Rewiring & Epidemic Outcomes STATIC Network ρ: mixing parameter DYNAMIC Network Rewiring Volz & Meyers, 2009

14 Network Structure & Population Immunity Risk of future infection = 0 Risk of infecting = 0 Immune individual epidemic Original Contact Network Residual Contact Network Ferrari et al ;( 2006 ) Bansal & Meyers (2012)

15 Probability Network Structure & Population Immunity Residual network Original network epidemic Degree (# of contacts per susceptible individual) o k r Residual Degree Distribution : p ( k ; T ) 1 r p k u u k o 1 c k 0 k k o r r k k k o r Original degree distribution Prob. of being uninfected Prob. that k r neighbors uninfected Bansal & Meyers (2012)

16 Future Challenges Combined effects of structural features Which structural features matter? Ames et al, 2011

17 How structure can be exploited for epidemiological interventions

18 Theoretical Intuition for Control Design Transmission-reducing interventions (reduce T) Face masks Gloves Washing hands Pourbohloul et al. (2005)

19 Theoretical Intuition for Control Design Contact-reducing interventions (reduce # edges) Patient quarantining School closure Social distancing Pourbohloul et al. (2005)

20 Theoretical Intuition for Control Design Vaccination (remove nodes and edges) Original contact network Vaccinated contact network Random individual Random neighbor of a random individual Anderson & May (1991); Pastor-Satorras & Vespignani (2002) ; Cohen et al (2003)

21 Shirley & Rushton (2005); Bansal et al (2006); Otterstater et al (2007); Natale et al (2009); High Degree for Control Finding proxies for high degree Degree: Age Degree:Social Role Degree: Activity

22 Contact Tracing Contact tracing = real-time tracking of infected individuals and their exposed contacts Therapy (treatment + prophylaxis) Isolation/social distancing Provides targeted control by automatically identifying high-risk Especially useful for asymptomatic infections Efficiency scales with R 0 in most cases (Eames & Keeling, 2003; Kiss et al, 2005)

23 Network Connectedness Tasmanian devils make up one connected component Hamede et al (2009)

24 Bridging Groups & High-Risk High betweeness = high risk Truck Drivers Seasonal Migrant Workers Carswell et al (1989), Lurie et al (2003)

25 Community Structure for Regionalization

26 Core Group & Resistance Spread Core group = high degree + degree assortativity Without resistance With resistance Chan et al (2012)

27 Post-hoc Policy Analysis FMD and livestock standstill policy Robinson et al (2007)

28 Future Challenges Expand suite of network models to other disease transmission classes Mosquito-borne disease contact network?

29 Future Challenges What quality/quantity of network data are required for policy decisions? Holding Parish/Zip code County Region/State

30 Risk of Infection (Second Season) Frequency Risk of Infection (First Season) Future Challenges Adaptive Management epidemic susceptible immune Bansal et al (2010) Degree Degree

31 Immunity Future Challenges Evolutionary consequences of policy 0 0 Second epidemic possible Poisson Scale-free Second epidemic possible.5.5 Minimum transmissibility for reinvasion 1 1 Bansal et al (2012)

32 Future Challenges Quantifying and incorporating uncertainty in network and disease parameters Shed light on the relationship between network classes and disease classes Multiple infection processes: simultaneous spread of biological and social contagion (e.g. risky behaviors) Behavioral responses to public health policies and their impact on network structure Clustering of vaccine refusal Incorporating epidemiology, behavior, economics and operations science into one unified framework for policy makers

33 Acknowledgements Collaborators: Bryan Grenfell (Princeton) Lauren Ancel Meyers (UT Austin) Babak Pourbohloul (BC CDC) Nathaniel Hupert (CDC) Ryan Miller (USDA APHIS) Colleen Webb (Colarado State) Thomas Scott (UC Davis) Jonathan Read (University of Liverpool) Georgetown Group: Pratha Sah Elizabeth Lee Eamon O Dea Adam Graves Eric Mooring Sarah Kramer Funding: RAPIDD Program of the Science & Technology Directorate and the Fogarty International Center, National Institutes of Health. Department of Homeland Security National Science Foundation

34 From Network Structure to Consequence & Control Shweta Bansal