Interaction Based Computer Modeling for Comprehensive Incident Characterization to Support Pandemic Preparedness

Transcription

1 Interaction Based Computer Modeling for Comprehensive Incident Characterization to Support Pandemic Preparedness Madhav V. Marathe Virginia Bio-Informatics Institute & Dept. of Computer Science Virginia Tech NDSSL-TR Web Site:

2 These slides are a version of the invited lecture given on April 22nd as a part of Workshop on Spatial Data Mining held as a part of the Annual SIAM Data Mining Conference, April Organizers: Professors Naren Ramakrishnan, Virginia Tech & Chris Bailey-Kellogg, Dartmouth University Venue & Date: Washington DC April 22nd 2006.

3 Acknowledgements Virginia Tech: Members, Network Dynamics & Simulation Science Laboratory, VBI Karla Atkins, Christopher L. Barrett, Richard Beckman, Keith Bisset, JiangZhou Chen, Stephen Eubank, V.S. Anil Kumar, Achla Marathe, Henning Mortveit, Paula Stretz, External Collaborators: Aravind Srinivasan (U. Maryland), Nan Wang (Morgan Stanley), Zoltan Toroczkai (NotreDame), Doug Roberts (RTI) Work funded in part by National Institute of General Medical Sciences, National Institutes of Health, Pilot Projects for Models of Infectious Disease Agent Study (MIDAS) contract U01-GM

4 Avian Influenza Avian influenza -- infection caused by avian (bird) influenza (flu) viruses Spreads thru saliva, nasal secretions, and feces, Categorized based on surface proteins hemagglutinin [HA] and neuraminidase [NA] Person to person has been limited and has not continued beyond one person. Antigenic shift vs drift Little historical information on evolution of virus in animals In circulation: H1N1 (1918) & H3N2 (1968) (has displaced H2N2 (1957)) Library/influenza_site/influenza_virus.jpg

5 Intervention Strategies for Human Influenza Vaccine Vaccine based on circulating avian flu [oops, shift] Vaccine based on pandemic strain [takes 4-6 months] Antivirals Amantadines(resistance develops rapidly ) Neuraminidase inhibitors: oseltamivir (TamiFlu) and zanamivir (raw material?) Prophylaxis (only while doses received) Social distancing Isolation and quarantine of cases Reduced contacts for others

6 Classical ODE Model: Coupled Rate Equation with Complete Mixing Partition the population into compartments Susceptible Infected Removed S Assume mass action (uniform mixing) R I β γ Kermack, W. O. and McKendrick, A. G. Proc. Roy. Soc. Lond. A 115, , Also see May, Hethcote, Heesterbeek, Murray,.

7 Are ODE Models Up to the Task? ODEs lack agency and heterogeneity of contact structure True complexity stems from interactions among many discrete actors Each kind of interaction must be explicitly modeled Refinement is difficult ODE models say very little about transients Use constants such as R 0 as if they are universal constants E.g. what is the R 0 for smallpox? Human behavioral issues Inhomogeneous compliance Changes in the face of crisis Are not naturally suited for formulating and testing policies that can be implemented E.g. reduce contact rates by 30% --- is an ambiguous statement

8 An Alternative Approach -- Network Based Representation t=0 t=1 Initially node 1 is infected. Each node runs SIR model At each step an infected node infects its uninfected neighbors with probability p and this is done independently A node is infected if one or more of its neighbor successfully infects it Node remains infected for 2 steps and then recovers

9 Models Shape Thinking Compartmental models suggest Reduce contact rates at work by 50% Three different ways to reduce rates resulting in very different networks

10 Effect of decreasing fidelity in social networks (above) on disease dynamics (below)

11 Taking this one step further -- A Bottom up Highly Resolved Simulation Create a proto-population(s) Humans, animal reservoirs, Refine it by adding necessary attributes Disease model Demographics Behavioral response to outbreak Critical workers Interactions with other infrastructures Simulate to develop correlations among attributes Test intervention scenarios

12 Simfrastructure: Modeling Interdependent Infrastructures A collection of interoperable simulations of societal infrastructures each mimics the time-dependent interactions of every individual in a regional area with the built environment (critical infrastructures) based on: where they are, why they are there, what they are doing, how they got there, and who they went with

13 Phase 1: Creating a dynamic social contact networks Creating a synthetic microscopic urban environment Locating every individual in a city every second at the scale of block group Individuals have statistically correct demographic characteristics Built infrastructure synthesized to provide the context

14 Data Fusion from Multiple Sources

15 Example Synthetic Household (ca.1990) Age Income $27k $16k $0 Status worker worker student Automobile

16 Example Located Synthetic Population

17 Example Route Plans SHOP first person in household WORK LUNCH WORK SHOP HOME second person in household DOCTOR HOME

18 Routing and Microsimulation Microsimulation of vehicles Route Density by time

19 Synthetic Social Contact Networks Vertex attributes: age household size gender income People (8 million) Locations (1 million) Vertex attributes: (x,y,z) land use Edge attributes: activity type: shop, work, school (start time 1, end time 1) (start time 2, end time 2)

20 Various Projections of People-Location Temporal Social Visitation Network Temporal Projections G P G PL G S P G L G S L People Projections Static Projections Location Projections

21 Phase 2: Modeling Disease Dynamics

22 Within and Among Host Disease Model: Coupled Probabilistic Timed Transition System On each time step, each person s state of health can change susceptible -> infectious in t time steps with probability depending on health and duration of contacts in a social network infectious -> removed or recovered and thus susceptible after t time step (dependency is stochastic and on demographics) Removed -> terminal state (could become Susceptible again) S R I

23 Location: present 2 infected 1 infectious

24 Effect of Network Structure on Performance* * Nature May 2004

25 Pandemic Preparedness: Issues

26 Functional Requirements for a Useful Incidence Management System Specifying a Situation Multiple complex systems interact via effects on subsytems How to represent critical workers? cascading failures? specific incidents? Assist reasoning about the situation Specifying an Intervention What does it mean to close schools in a pandemic? Inhomogeneous society => models adapted to local circumstances Structural validity versus Predictability Stopped watch vs slow watch Deduce sign, relative magnitude, and interaction of controls effects

27 Considerations in designing effective containment methods Choosing the Battlefield Treat non-human populations Interrupt cross-species transmission or re-assortment May require treating most of the population (backyard poultry) + swine Drive new human variants extinct before they are well adapted Control isolated outbreaks as they occur Mitigate a full-blown pandemic (30-40% attack rate ~simultaneously) Cost Functions Human suffering averted (referenced to baseline?) Number of doses of drug required and maximum application rate Time gained (delay of exponential growth) Robustness to mis-specification and resource limitation Economic impact: immediate and long term

28 Closing schools When? Representing & Implementing an Intervention What happens to the people at school? Who else is affected? those most likely to spread disease may stay home with sick child. correlation is inherent in the model, not specified by the modeler Evacuating an area How will it be staged? What means of transportation? With whom will people coordinate movements? Where will congestion appear?

29 Data Mining Challenges to Support Pandemic Preparedness

30 Classical Questions in New Settings Classical Questions Classification Finding Nuggets, correlations Simple hierarchical aggregation Spatial Queries Data Sets Social Contact Networks are new, large and evolving Large number of attributes Data is being refined continually New kinds of data sets being integrated: e.g. data from monitoring stations Application Specific Questions Classification: Classifying who is vulnerable and critical Aggregation: Finding regions with high level of infectivity Correlations: Households with children going to a stadium feel sick

31 Basic Structural Properties of Portland Social Network Degree distribution of the (temporal) people-ppl. graph Degree distributions of the bipartite graph Clustering Coefficient

32 Spatial & Temporal Degree Distribution of People and Activities

33 Example of Cultural Measurements: Degree Distribution in Labeled Networks Partition based on age (Portland) New, fundamental characterization of a realistic social contact network Partition the population based on some properties (age, income, etc.) For each part, determine fraction of neighbors in every other part The measure can only be produced by Simfrastructure-like simulations

34 Temporal Degrees by Activity Location Types* * DIMACS Issue on Epidemiology

35 Structural Robustness of Complex Networks -- Naïve ways to prevent disease-spread Vaccinating (quarantining) high-degree people Shattering the social network by: Closing down high-degree locations Router Level Network serving Portland

36 Alternative - Placing Sensors* A B C Locations Choose locations to place sensors w/ min. cost Equivalent to min. dominating set problem Minimum locations covering (almost) all people Hard to approximate within ratio Θ(log n) { {B, C} is a minimum dominating set} is People ACM SIAM SODA 2004

37 Solution: Early detection and targeted vaccination/quarantining -- Efficient algorithms for Sensor Placement* High degree buildings do not share too many individuals Most people go to atleast one high-degree location Measured by uniformly sampling people Sampled people lead us to high-degree locations. Not too many High-degree locations Real CL Our RG Implication: Simple provable method for sensor placement Place Sensors at high degree nodes Fast-1 Traditional Fast % 41.23% < 15 sec % 54.47% < 15 sec % 55.78% < 15 sec. Traditional > 4 hr. > 5 hr. > 7 hr. * Eubank et al. Nature 04, SODA 04

38 An Illustrative Example: Vulnerability versus Criticality Vulnerability Probability of becoming infected Useful measure for weighting vertex statistics Depends on where disease starts and spreading dynamics Criticality Expected # infections stopped by removing vertex/edges Involve time, initial conditions, topology & dynamics at time 1, both reduce to function of degree and transmission probabilities Easy to compute Easily extended to sets of vertices / edges General problem is computationally hard, need approximations Interventions reduce vulnerability, critical edge/vertices are potential points of interventions Node 1 is most vulnerable and 7 most critical

39 Some Open Questions in Spatial Databases and Data mining Fast Computations of Network Properties, E.g. Provable approximation algorithms for computing expansion, betweeness, community structure Properties of time varying graphs, e.g. stochastic mining Methods for Storage and Regeneration E.g. Can we store the dendogram efficiently so that certain macroscopic parameters can be computed efficiently Use model driven methods for predicting how disease will spread

40 Challenges: A Biased Perspective

41 Data Mining and Simulations Simulation based systems have two interwoven steps synthesizing and integrating known data (akin to join operations) Creating new relations and data as a result of interactions between individuals and infrastructures (achieved via simulations) E.g. Tom got infected since he visited a location L and came in spatial proximity of Jack who was sick Simulations are a procedural form of representation of large data sets (as opposed to data bases that are extensive form) Monitor-Simulate-Mine-Loop Mine simulation generated data to actively guide simulations Data Mining is thus a part of the simulation based model

42 Example and Illustrative questions Social Distancing by reducing contacts Use Data Mining methods to decide which contacts to reduce E.g. can I reduce 30% of everyone s contacts uniformly, or reduce the overall contact rate by 30% by quarantining some individuals Run Simulations to see the outcome Based on simulations, execute the policy Observe the outcome and modify the policy Incremental Nuggets Instead of finding the most critical set of individuals, we find a partial set and then incrementally extend the solution Variant of Online/Streaming model where information is revealed incrementally and actions taken modify the future Co-evolution of Epidemic Policy, Simulation and Mining

43 Public Health Informatics System to Support Pandemic Preparedness

44 Where are we heading

45 Next Generation Simfrastructure: Web and Grid Enabled

46 U.S. Proto-Population Who: People 256 million individuals with composable attributes Household structure and some demographics from U.S. Census What: Activities Activity sequences based on data from national travel survey Includes travel between cities/countries Where: Locations Disaggregate locations and infrastructure information Locations assigned to activity sequences Why: Examples Spread of pandemic disease Dynamic demand on infrastructures Situation assessment for emergency response

47 Conclusions and Summary Described an Interaction based modeling tool to support pandemic preparedness and response (Simfrastructure) Resolved at the level of individuals and locations Individualized Model, allows to represent heterogeneous populations Realistic social contact network captures heterogeneous social interaction Models for within host and between host transmission Aids development and analysis of policies that can be implemented Suggests new directions for future research in data mining Fast algorithms to analyze and store massive data sets Data Mining is a part of the model

48 Related References 1. C. Barrett, S. Eubank, V. Anil Kumar, M. Marathe. Understanding Large Scale Social and Infrastructure Networks: A Simulation Based Approach, in SIAM news, March Appears as part of Math Awareness Month on The Mathematics of Networks. 2. C. Barrett, J.P. Smith and S. Eubank. Modern Epidemiology Modeling, in Scientific American, March C. L. Barrett, R. J. Beckman, K. P. Berkbigler, K. R. Bisset, B. W. Bush, K. Campbell, S. Eubank, K. M. Henson, J. M. Hurford, D. A. Kubicek, M. V. Marathe, P. R. Romero, J. P. Smith, L. L. Smith, P. L. Speckman, P. E. Stretz, G. L. Thayer, E. V. Eeckhout, and M. D. Williams. TRANSIMS: Transportation Analysis Simulation System. Technical Report LA-UR , Los Alamos National Laboratory Unclassified Report, S. Eubank, H. Guclu, V.S. Anil Kumar, M. Marathe, A. Srinivasan, Z. Toroczkai and N. Wang, Modeling Disease Outbreaks in Realistic Urban Social Networks, Nature, 429, pp , May S. Eubank, V.S. Anil Kumar, M. Marathe, A. Srinivasan and N. Wang, Structural and Algorithmic Aspects of Large Social Networks, Proc. 15th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp , S. Eubank, V.S. Anil Kumar, M. Marathe, A. Srinivasan and N. Wang, Structure of Social Contact Networks and their Impact on Epidemics. to appear in AMS-DIMACS Special Volume on Epidemiology, 2006.

49 Additional References 1. I. Longini, A. Nizam, S. Xu, K. Ungchusak, W. Hanshaoworakal, D. Cummings, E. Hollaran, Science, 2005, pp I. Longini, E. Hollaran, A. Nizam and Y. Yang, American J. Epidemiology, 2004, pp T. German, K. Kadau, I. Longini, C. Macken, Mitigation Strategies for Pandemic Influenza in the United States, PNAS, 2006, 105(15), pp N Ferguson, D. Cumming, S. Cauchemez, C. Fraser, S. Riley, A. Meeyai, S. Lamsrrithaworn, D. Burke, Nature, 2005, pp R. Anderson and R. May, Infectious Disease of Humans, Oxford University Press, UK, E.H. Kaplan, D.L. Craft, and L.M. Wein. Proc. Natl. Acad. Sci. USA, 99: , L. Meyers, M. E. J. Newman, M. Martin, and S. Schrag. Emerging Infectious Diseases, pages , M. E. J. Newman. SIAM Review 45, (2003). 9. R. Albert and A. Barabasi, Rev. Mod. Phys. 74, (2002).