New Challenges for Modelers
of Infectious Diseases of Africa
Fred Roberts, DIMACS
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Mathematical modeling of the spread of infectious
disease has a long history.
Bernoulli’s 1760 modeling of smallpox.
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Endemic and emerging diseases of Africa provide
new and complex challenges for mathematical
modeling.
HIV/AIDS
Malaria
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Tuberculosis
Major new health threats such as avian influenza
present especially complex challenges to modelers
in the context of developing countries.
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This workshop is aimed at:
•Studying challenges for mathematical models
arising from the diseases of Africa
•Understanding special challenges from diseases in
resource-poor countries.
•Bringing together U.S. and African researchers
and students to collaborate in solving these
problems.
•Laying the groundwork for future collaborations
to address problems of public health and disease in
Africa.
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What are the challenges for mathematical scientists
in the defense against disease?
This question led DIMACS, the Center for Discrete
Mathematics and Theoretical Computer Science,
based at Rutgers University, to launch a “special
focus” on this topic in Spring 2002.
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DIMACS Special Focus on
Computational and
Mathematical Epidemiology
Special Focus:
• Workshops
• Tutorials
• Research working groups
• Visitor Exchanges
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DIMACS Special Focus on
Computational and Mathematical
Epidemiology
One workshop was instrumental
in leading to the present one:
“Evolutionary Aspects of Vaccine Use”
DIMACS, June 2005
Organizers: Troy Day, Alison Galvani, Abba
Gumel, Claudio Struchiner
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DIMACS Special Focus on
Computational and Mathematical
Epidemiology
The special problems of vaccination
strategies in Africa that arose in
this workshop were one of the primary
motivations for Abba Gumel to propose
that DIMACS sponsor a workshop on
mathematical modeling of infectious
diseases of Africa.
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Snowbird Conference
•“Modeling the Dynamics of Human Diseases:
Emerging Paradigms and Challenges”
•July 2005, Snowbird, Utah
•Organizers: Carlos Castillo-Chavez, Dominic
Clemence, Abba Gumel, Travette Jackson,
Ronald Mickens
•One notable feature of conference: Recognition
of central role of developing nations in emergence
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of novel pathogens.
Snowbird Conference
•One notable feature of conference: Recognition
of central role of developing nations in emergence
of novel pathogens.
•This led meeting participant Simon Levin to
suggest that we pursue ways to more directly
engage US and African researchers and students.
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The Role of Mathematical Modeling
Hundreds of math. models since Bernoulli’s work
on smallpox have:
•highlighted concepts like core population in
STD’s;
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•Made explicit concepts such as herd immunity
for vaccination policies;
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•Led to insights about drug resistance, rate of
spread of infection, epidemic trends, effects of
different kinds of treatments.
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•In recent years, modeling has had an increasing
influence on the theory and practice of disease
management and control.
•Modeling has played an important role in
shaping public health policy decisions in a
number of countries.
– Gonorrhea, HIV/AIDS, BSE, FMD, measles,
rubella, pertussis (UK, US, Netherlands, Canada)
measles
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FMD
•Modeling has provided insights leading to
“optimal” treatment strategies
– Immuno-pathogenesis of HIV/AIDS and use of
highly active anti-retroviral therapy
•Modeling has played a role in
shaping vaccine design and
determining threshold coverage
levels for vaccine-preventable diseases:
AIDS
– measles, rubella, polio
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During SARS outbreaks in 2003, modelers and
public health officials worked hand-in-hand to
devise effective control strategies in a number of
countries.
Earlier, similar importance of efforts to control
FMD.
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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.
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•To maximize benefit from mathematical models,
need to:
– specialize them
– test assumptions in specific contexts and
populations
– gather local data to help define key
parameters
•That is one of the motivations for this workshop
and the plans we have for follow ups.
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•If scientists from Africa and outside Africa
collaborate:
– Vitally-needed access to data can be provided
– Data can be interpreted with the help of individuals
knowledgeable about local conditions
– Better and more realistic models can be developed.
•It is important for non-African researchers to:
– Understand effects of government policies in Africa
– Learn of modeling efforts in Africa
– Find key contacts knowledgeable about both endemic
diseases and deadly emerging diseases
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Themes of our Meeting
Current State of Infectious Diseases in
Africa
•Current state of different
diseases.
•Epidemiological data.
•Recent control initiatives:
failures and successes
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Themes of our Meeting
Mathematical Modeling of Diseases that
Inflict a Significant Burden on Africa
•HIV/AIDS
•TB
•Malaria
•Diseases of Animals
AIDS orphans, Zambia
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Themes of our Meeting
Mathematical Modeling of Diseases that
Inflict a Significant Burden on Africa
•HIV/AIDS
– Modeling/evaluation of
preventive and therapeutic strategies
– Allocation of anti-retroviral drugs
– Evolution and transmission of drugresistant strains
– Interaction with other infections: TB,
malaria
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Themes of our Meeting
Mathematical Modeling of Diseases that
Inflict a Significant Burden on Africa
•Malaria
– New methods of control (e.g.,
insecticide-treated cattle)
– Climate and disease (e.g.,
global warming and effect on
mosquito populations)
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Themes of our Meeting
Mathematical Modeling of Diseases that
Inflict a Significant Burden on Africa
•Diseases of Animals
– Bovine tuberculosis (in domestic and wild
populations)
– Avian influenza
– Trypanosomiasis
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Themes of our Meeting
Modeling Issues from Threat of Emerging
Diseases in Resource-poor Countries
•Special issues arising from:
– Slow communication
– Short supplies of vaccines
and prophylactics
– Difficulty of imposing
quarantines
– Special emphasis on problems
arising from avian or pandemic influenza
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Themes of our Meeting
Optimization of Scarce Public Health
Resources
•How to handle shortages of drugs and vaccines,
physical facilities, and trained personnel.
•Mathematical methods to:
– Allocate medicines to optimize impact
– Assign trained personnel to
most critical jobs
– Design efficient transportation
plans.
– Design efficient dispensing plans.
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Themes of our Meeting
Vaccination Strategies
•Explore protocols for vaccination
• for major diseases in Africa
•Discuss potential for vaccines for HIV, malaria
•Use of computer simulations to allow
comparison of vaccination strategies when field
trials are prohibitively expensive
•Identify major modeling challenges unique to
Africa: e.g., age-structured, health-status-related
models
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Themes of our Meeting
Next Steps
•Identify future research challenges for African
and non-African scientists in collaboration
•Identify training programs for African and nonAfrican students
•Identify future initiatives
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Methods of Mathematical
Epidemiology
•Many mathematical tools used in
epidemiological modeling.
•Not so widely known: Usefulness of newer
tools of discrete mathematics and algorithmic
methods of theoretical computer science.
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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.
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Dynamical Systems
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Dynamical Systems
•Used for modeling host-pathogen systems, phase
transitions when a disease becomes epidemic, etc.
•Use difference and differential equations.
•Need for new methods to apply today’s powerful
computational tools to these dynamical systems.
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Probabilistic Methods
•Important role of stochastic processes, random
walk models, percolation theory, Markov chain
Monte Carlo methods.
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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.
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Discrete Math. and Theoretical
Computer Science
• Many fields of science, in particular molecular
biology, have made extensive use of DM broadly
defined.
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Discrete Math. and Theoretical
Computer Science Cont’d
•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
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epidemiology.
DM and TCS Continued
•These tools are made especially relevant to
epidemiology because of:
–Geographic Information Systems
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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.
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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.
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Challenges for Discrete Math
and Theoretical Computer
Science
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What are DM and TCS?
DM deals with:
•arrangements
•designs
•codes
•patterns
•schedules
•assignments
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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.
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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
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those working on public health problems.
So How are DM/TCS Relevant to the
Fight Against Disease?
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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
•AT&T 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
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•DIMACS/CDC Adverse Events Detection Group
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
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computational overhead?
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 applications.
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Visualization
•Large data sets are sometimes best understood by
visualizing them.
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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.
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Data Cleaning
•Disease detection problem: Very “dirty” data:
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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
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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 followup questions.
•Develop semi-automatic systems to generate
queries based on dynamically changing data.
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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.
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Research Issues
•Dynamically changing networks
•Making use of other information about networks:
semantic graphs
•Handling large-scale networks
•Approximations of parameters (such as infectivity,
susceptibility, latent period) that are not well
specified
•Making use of analogous lines of research such as
spread of opinions through social networks.
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Evolution
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Evolution
•Models of evolution might shed light on new
strains of infectious agents.
•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.
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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.
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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 59
if recombination has taken place.
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.
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Decision Making/Policy Analysis
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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
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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
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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 epidemiology: instead of
many “decision makers” and few “candidates,”
could be few decision makers and many candidates
(lots of different parameters to modify)
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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
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new applications.
Game Theory
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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.
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Operations Research
•History of use in wide variety of practical
applications.
•Issues of fair allocation of limited resources.
•Transportation schedules
•Inventory planning
•Assignment of workers to jobs/locations
•Finding locations for clinics, hospitals, medicine
dispensing stations
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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.
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Dialogues on Mathematical
Epidemiology:
Infectious Diseases of Africa
•Let us use this meeting to:
– Survey new methods and
discuss new approaches.
– Open up new lines of
communication.
– Lay the groundwork for
future collaborations
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THANK YOU
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