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DIMACS Special Focus on Computational and Mathematical Epidemiology

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Title: DIMACS Special Focus on Computational and Mathematical Epidemiology


1
DIMACS Special Focus on Computational and
Mathematical Epidemiology
2
The Role of the Mathematical Sciences in
Epidemiology
  • Emergence of new infectious diseases
  • Lyme disease
  • HIV/AIDS
  • Hepatitis C
  • West Nile Virus
  • Evolution of antibiotic-resistant strains
  • tuberculosis
  • pneumonia
  • gonorrhea

3
  • Great concern about the deliberate introduction
    of diseases by bioterrorists
  • anthrax
  • smallpox
  • plague
  • Understanding infectious systems requires being
    able to reason about highly complex biological
    systems, with hundreds of demographic and
    epidemiological variables.
  • Intuition alone is insufficient to fully
    understand the dynamics of such systems.

4
  • Experimentation or field trials are often
    prohibitively expensive or unethical and do not
    always lead to fundamental understanding.
  • Therefore, mathematical modeling becomes an
    important experimental and analytical tool.

5
  • Mathematical models have become important tools
    in analyzing the spread and control of infectious
    diseases, especially when combined with powerful,
    modern computer methods for analyzing and/or
    simulating the models.

6
What Can Math Models Do For Us?
7
What Can Math Models Do For Us?
  • Sharpen our understanding of fundamental
    processes
  • Compare alternative policies and interventions
  • Help make decisions.
  • Prepare responses to bioterrorist attacks.
  • Provide a guide for training exercises and
    scenario development.
  • Guide risk assessment.
  • Predict future trends.

8
  • In order for math. and CS to become more
    effectively utilized, we need to
  • make better use of existing tools

9
  • In order for math. and CS to become more
    effectively utilized, we need to
  • develop new tools
  • establish working partnerships between
    mathematical scientists and biological
    scientists
  • introduce the two communities to each others
    problems, language, and tools
  • .

10
  • introduce outstanding junior researchers from
    both sides to the issues, problems, and
    challenges of mathematical and computational
    epidemiology

11
  • involve biological and mathematical scientists
    together to define the agenda and develop the
    tools of this field.
  • These are all fundamental goals of this special
    focus.

12
Methods of Math. and Comp. Epi.
  • Math. models of infectious diseases go back to
    Daniel Bernoullis mathematical analysis of
    smallpox in 1760.

13
  • Hundreds of math. models since have
  • highlighted concepts like core population in
    STDs

14
  • Made explicit concepts such as herd immunity for
    vaccination policies

15
  • Led to insights about drug resistance, rate of
    spread of infection, epidemic trends, effects of
    different kinds of treatments.

16
  • The size and overwhelming complexity of modern
    epidemiological problems calls for new
    approaches.
  • New methods are needed for dealing with
  • dynamics of multiple interacting strains of
    viruses through construction and simulation of
    dynamic models
  • spatial spread of disease through pattern
    analysis and simulation
  • early detection of emerging diseases or
    bioterrorist acts through rapidly-responding
    surveillance systems.

17
Statistical Methods
  • Long used in epidemiology.
  • Used to evaluate role of chance and confounding
    associations.
  • Used to ferret out sources of systematic error in
    observations.
  • Role of statistical methods is changing due to
    the increasingly huge data sets involved, calling
    for new approaches.

18
Dynamical Systems
19
Dynamical Systems
  • Used for modeling host-pathogen systems, phase
    transitions when a disease becomes epidemic, etc.
  • Use difference and differential equations.
  • Little systematic effort to apply todays
    powerful computational tools to these dynamical
    systems and few computer scientists are involved.
  • We hope to change this situation.

20
Probabilistic Methods
  • Important role of stochastic processes, random
    walk models, percolation theory, Markov chain
    Monte Carlo methods.

21
Probabilistic Methods Continued
  • Computational methods for simulating stochastic
    processes in complex spatial environments or on
    large networks have started to enable us to
    simulate more and more complex biological
    interactions.

22
Probabilistic Methods Continued
  • However, few mathematicians and computer
    scientists have been involved in efforts to bring
    the power of modern computational methods to bear.

23
Discrete Math. and Theoretical Computer Science
  • Many fields of science, in particular molecular
    biology, have made extensive use of DM broadly
    defined.

24
Discrete Math. and Theoretical Computer Science
Contd
  • Especially useful have been those tools that make
    use of the algorithms, models, and concepts of
    TCS.
  • These tools remain largely unused and unknown in
    epidemiology and even mathematical epidemiology.

25
DM and TCS Continued
  • These tools are made especially relevant to
    epidemiology because of
  • Geographic Information Systems

26
DM and TCS Continued
  • Availability of large and disparate computerized
    databases on subjects relating to disease and the
    relevance of modern methods of data mining.

27
DM and TCS Continued
  • The increasing importance of an evolutionary
    point of view in epidemiology and the relevance
    of DM/TCS methods of phylogenetic tree
    reconstruction.

28
How does a Special Focus Work?
  • Get researchers with different backgrounds and
    approaches together.
  • Stimulate new collaborations.
  • Set the agenda for future research.
  • Act as a catalyst for new developments at the
    interface among disciplines.
  • DIMACS has been doing this for a long time.

29
Components of a Special Focus
  • Working Groups
  • Tutorials
  • Workshops
  • Visitor Programs
  • Graduate Student Programs
  • Postdoc Programs
  • Dissemination

30
Working Groups
31
Working Groups Continued
  • Interdisciplinary, international groups of
    researchers.
  • Come together at DIMACS.
  • Informal presentations, lots of time for
    discussion.
  • Emphasis on collaboration.
  • Return as a full group or in subgroups to pursue
    problems/approaches identified in first meeting.
  • By invitation but contact the organizer.
  • Junior researchers welcomed. Nominate them.

32
Tutorials
33
Tutorials Continued
  • Integrate research and education.
  • Introduce mathematical scientists to relevant
    topics in epidemiology and biology
  • Introduce epidemiologists and biologists to
    relevant methods of math., CS, statistics,
    operations research.
  • Financial support available by application.

34
Workshops
35
Workshops Continued
  • More formal programs.
  • Widely publicized.
  • One-time programs.
  • Some educational component encourage
    participation by graduate students tutorials.
  • Interdisciplinary flavor.
  • Can spawn new working groups.
  • Financial support available in limited
    amountscontact the organizer.

36
Visitor Programs
37
Visitor Programs Continued
  • Interdisciplinary groups of researchers will
    return after working group meetings.
  • Workshop participants can come early or stay
    late.
  • Visits can be arranged independent of workshops
    or working group meetings. Contact DIMACS Visitor
    Coordinator.
  • Visits by junior researchers and students will be
    encouraged.
  • We want to make DIMACS a center for collaboration
    in mathematical and computational epidemiology
    for the next 5 years (and beyond).

38
Grad. Student/Postdoc Programs
39
Grad. Student/Postdoc Programs
  • Each working group, workshop, tutorial will
    support students/postdocs. Contact organizer.
  • Students/postdocs visiting for longer will have a
    host/mentor. Contact DIMACS visitor coordinator.
  • Local graduate students will get involved through
    participation in working groups and small
    research projects.
  • We hope to raise funds for postdoctoral fellows
    to participate by spending a year or more at
    DIMACS.

40
Dissemination
  • DIMACS technical report series.
  • Working group and workshop websites.
  • DIMACS book series.

41
Working Groups
  • WGs on Large Data Sets
  • Adverse Event/Disease Reporting, Surveillance
    Analysis.
  • Data Mining and Epidemiology.
  • WGs on Analogies between Computers and Humans
  • Analogies between Computer Viruses/Immune Systems
    and Human Viruses/Immune Systems
  • Distributed Computing, Social Networks, and
    Disease Spread Processes

42
WGs on Methods/Tools of TCS
  • Phylogenetic Trees and Rapidly Evolving Diseases
  • Order-Theoretic Aspects of Epidemiology
  • WGs on Computational Methods for Analyzing Large
    Models for Spread/Control of Disease
  • Spatio-temporal and Network Modeling of Diseases
  • Methodologies for Comparing Vaccination
    Strategies

43
WGs on Mathematical Sciences Methodologies
  • Mathematical Models and Defense Against
    Bioterrorism
  • Predictive Methodologies for Infectious Diseases
  • Statistical, Mathematical, and Modeling Issues in
    the Analysis of Marine Diseases
  • WG on Noninfectious Diseases
  • Computational Biology of Tumor Progression

44
Workshops on Modeling of Infectious Diseases
  • The Pathogenesis of Infectious Diseases
  • Models/Methodological Problems of Botanical
    Epidemiology
  • WS on Modeling of Non-Infectious Diseases
  • Disease Clusters

45
Workshops on Evolution and Epidemiology
  • Genetics and Evolution of Pathogens
  • The Epidemiology and Evolution of Influenza
  • The Evolution and Control of Drug Resistance
  • Models of Co-Evolution of Hosts and Pathogens

46
Workshops on Methodological Issues
  • Capture-recapture Models in Epidemiology
  • Spatial Epidemiology and Geographic Information
    Systems
  • Ecologic Inference
  • Combinatorial Group Testing
  • Other Topics
  • Suggestions are encouraged.

47
Tutorials
  • Dynamic Models of Epidemiological Problems
  • The Foundations of Molecular Genetics for
    Non-Biologists
  • Introduction to Epidemiological Studies
  • DM and TCS for Epidemiologists and Biologists
  • Promising Statistical Methods for Epidemiology
    for Epidemiologists and Biologists

48
Challenges for Discrete Math and Theoretical
Computer Science
49
What are DM and TCS?
  • DM deals with
  • arrangements
  • designs
  • codes
  • patterns
  • schedules
  • assignments

50
TCS deals with the theory of computer algorithms.
  • During the first 30-40 years of the computer age,
    TCS, aided by powerful mathematical methods,
    especially DM, probability, and logic, had a
    direct impact on technology, by developing
    models, data structures, algorithms, and lower
    bounds that are now at the core of computing.

51
DM and TCS have found extensive use in many areas
of science and public policy, for example in
Molecular Biology. These tools, which seem
especially relevant to problems of epidemiology,
are not well known to those working on public
health problems.
52
So How are DM/TCS Relevant to the Fight Against
Disease?
53
Detection/Surveillance
  • Streaming Data Analysis
  • When you only have one shot at the data
  • Widely used to detect trends and sound alarms in
    applications in telecommunications and finance
  • ATT uses this to detect fraudulent use of credit
    cards or impending billing defaults
  • Columbia has developed methods for detecting
    fraudulent behavior in financial systems
  • Uses algorithms based in TCS
  • Needs modification to apply to disease detection

54
  • Research Issues
  • Modify methods of data collection, transmission,
    processing, and visualization
  • Explore use of decision trees, vector-space
    methods, Bayesian and neural nets
  • How are the results of monitoring systems best
    reported and visualized?
  • To what extent can they incur fast and safe
    automated responses?
  • How are relevant queries best expressed, giving
    the user sufficient power while implicitly
    restraining him/her from incurring unwanted
    computational overhead?

55
Cluster Analysis
  • Used to extract patterns from complex data
  • Application of traditional clustering algorithms
    hindered by extreme heterogeneity of the data
  • Newer clustering methods based on TCS for
    clustering heterogeneous data need to be modified
    for infectious disease and bioterrorist
    applications.

56
Visualization
  • Large data sets are sometimes best understood by
    visualizing them.

57
Visualization
  • Sheer data sizes require new visualization
    regimes, which require suitable external memory
    data structures to reorganize tabular data to
    facilitate access, usage, and analysis.
  • Visualization algorithms become harder when data
    arises from various sources and each source
    contains only partial information.

58
Data Cleaning
  • Disease detection problem Very dirty data

59
Data Cleaning
  • Very dirty data due to
  • manual entry
  • lack of uniform standards for content and formats
  • data duplication
  • measurement errors
  • TCS-based methods of data cleaning
  • duplicate removal
  • merge purge
  • automated detection

60
Dealing with Natural Language Reports
  • Devise effective methods for translating natural
    language input into formats suitable for
    analysis.
  • Develop computationally efficient methods to
    provide automated responses consisting of
    follow-up questions.
  • Develop semi-automatic systems to generate
    queries based on dynamically changing data.

61
Social Networks
  • Diseases are often spread through social contact.
  • Contact information is often key in controlling
    an epidemic, man-made or otherwise.
  • There is a long history of the use of DM tools in
    the study of social networks Social networks as
    graphs.

62
Spread of Disease through a Network
  • Dynamically changing networks discrete times.
  • Nodes (individuals) are infected or non-infected
    (simplest model).
  • An individual becomes infected at time t1 if
    sufficiently many of its neighbors are infected
    at time t. (Threshold model)
  • Analogy saturation models in economics.
  • Analogy spread of opinions through social
    networks.

63
Complications and Variants
  • Infection only with a certain probability.
  • Individuals have degrees of immunity and
    infection takes place only if sufficiently many
    neighbors are infected and degree of immunity is
    sufficiently low.
  • Add recovered category.
  • Add levels of infection.
  • Markov models.
  • Dynamic models on graphs related to neural nets.

64
Research Issues
  • What sets of vertices have the property that
    their infection guarantees the spread of the
    disease to x of the vertices?
  • What vertices need to be vaccinated to make
    sure a disease does not spread to more than x of
    the vertices?
  • How do the answers depend upon network structure?
  • How do they depend upon choice of threshold?

65
These Types of Questions Have Been Studied in
Other Contexts Using DM/TCS
  • Distributed Computing

66
  • Distributed Computing
  • Eliminating damage by failed processors -- when a
    fault occurs, let a processor change state if a
    majority of neighbors are in a different state or
    if number is above threshold.
  • Distributed database management.
  • Quorum systems.
  • Fault-local mending.

67
Spread of Opinion
68
Spread of Opinion
  • Of relevance to bioterrorism.
  • Dynamic models of how opinions spread through
    social networks.
  • Your opinion changes at time t1 if the number of
    neighboring vertices with the opposite opinion at
    time t exceeds threshold.
  • Widely studied.
  • Relevant variants confidence in your opinion (
    immunity) probabilistic change of opinion.

69
Evolution
70
Evolution
  • Models of evolution might shed light on new
    strains of infectious agents used by
    bioterrorists.
  • New methods of phylogenetic tree reconstruction
    owe a significant amount to modern methods of
    DM/TCS.
  • Phylogenetic analysis might help in
    identification of the source of an infectious
    agent.

71
Some Relevant Tools of DM/TCS
  • Information-theoretic bounds on tree
    reconstruction methods.
  • Optimal tree refinement methods.
  • Disk-covering methods.
  • Maximum parsimony heuristics.
  • Nearest-neighbor-joining methods.
  • Hybrid methods.
  • Methods for finding consensus phylogenies.

72
New Challenges for DM/TCS
  • Tailoring phylogenetic methods to describe the
    idiosyncracies of viral evolution -- going beyond
    a binary tree with a small number of
    contemporaneous species appearing as leaves.
  • Dealing with trees of thousands of vertices, many
    of high degree.
  • Making use of data about species at internal
    vertices (e.g., when data comes from serial
    sampling of patients).
  • Network representations of evolutionary history -
    if recombination has taken place.

73
New Challenges for DM/TCS Continued
  • Modeling viral evolution by a collection of trees
    -- to recognize the quasispecies nature of
    viruses.
  • Devising fast methods to average the quantities
    of interest over all likely trees.

74
Decision Making/Policy Analysis
75
Decision Making/Policy Analysis
  • DM/TCS have a close historical connection with
    mathematical modeling for decision making and
    policy making.
  • Mathematical models can help us
  • understand fundamental processes
  • compare alternative policies and interventions
  • provide a guide for scenario development
  • guide risk assessment
  • aid forensic analysis
  • predict future trends

76
Consensus
  • DM/TCS fundamental to theory of group decision
    making/consensus
  • Based on fundamental ideas in theory of voting
    and social choice
  • Key problem combine expert judgments (e.g.,
    rankings of alternatives) to make policy

77
Consensus Continued
  • Prior application to biology (Bioconsensus)
  • Find common pattern in library of molecular
    sequences
  • Find consensus phylogeny given alternative
    phylogenies
  • Developing algorithmic view in consensus theory
    fast algorithms for finding the consensus policy
  • Special challenge re bioterrorism/epidemiology
    instead of many decision makers and few
    candidates, could be few decision makers and
    many candidates (lots of different parameters to
    modify)

78
Decision Science
  • Formalizing utilities and costs/benefits.
  • Formalizing uncertainty and risk.
  • DM/TCS aid in formalizing optimization problems
    and solving them maximizing utility, minimizing
    pain,
  • Bringing in DM-based theory of meaningful
    statements and meaningful statistics.
  • Some of these ideas virtually unknown in public
    health applications.
  • Challenges are primarily to apply existing tools
    to new applications.

79
Game Theory
80
Game Theory
  • History of use in military decision making
  • Relevant to conflicts bioterrorism
  • DM/TCS especially relevant to multi-person games
  • Of use in allocating scarce resources to
    different players or different components of a
    comprehensive policy.
  • New algorithmic point of view in game theory
    finding efficient procedures for computing the
    winner or the appropriate resource allocation.

81
Some Additional Relevant DM/TCS Topics
  • Order-Theoretic Concepts
  • Relevance of partial orders and lattices.
  • The exposure set (set of all subjects whose
    exposure levels exceed some threshold) is a
    common construction in dimension theory of
    partial orders.
  • Point lattices may be useful for visualizing the
    relationships of contigency tables to effect
    measures and cut-off choices.

82
Combinatorial Group Testing
  • Natural or human-induced epidemics might require
    us to test samples from large populations at
    once.
  • Combinatorial group testing arose from need for
    mathematical methods to test millions of WWII
    draftees for syphilis.
  • Identify all positive cases in large population
    by
  • dividing items into subsets
  • testing if subset has at least one positive item
  • iterating by dividing into smaller groups.

83
Challenges Outside of DM/TCS
Were expecting your input!
84
See You at DIMACS
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