Why Bio-Math?

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Why Bio-Math? Why Now?
Avian flu
RNA
Fred Roberts, Rutgers University
2
Why Bio-Math? Why Now?
In 2002, I was invited to join the Secretary of
Health and Human Services Smallpox Modeling
Group. How did a mathematician come to do that?
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Mathematical Models of Disease Spread

• Mathematical models of infectious diseases go
  back to Daniel Bernoullis mathematical analysis
  of smallpox in 1760.

4
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.
5

• 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.

6

• 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.

7

• Great concern about the deliberate introduction
  of diseases by bioterrorists has led to new
  challenges for mathematical modelers.
• 
  

anthrax
8

• Great concern about possibly devastating new
  diseases like avian influenza has also led to new
  challenges for mathematical modelers.
• 
  

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• Hundreds of math. models since Bernoullis models
  of smallpox have
• highlighted concepts like core population in
  sexually transmitted diseases

10

• 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.

12

• The size and overwhelming complexity of modern
  epidemiological problems -- and in particular the
  defense against bioterrorism -- calls for new
  approaches and tools.

13

• The size and overwhelming complexity of modern
  epidemiological problems -- and in particular the
  defense against bioterrorism -- calls for new
  approaches and tools.
• As a result, in 2002, DIMACS launched a special
  focus on mathematical and computational
  epidemiology that has paired mathematicians,
  computer scientists, and statisticians with
  epidemiologists, biologists, public health
  professionals, physicians, etc.

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Why Bio-Math? Why Now?

• I have long been interested in applications of
• mathematics.
• I was even interested in mathematical problems
• in biology very early in my career.
• As a graduate student in the 1960s, I worked on
• a problem posed by Nobel prize winning geneticist
• Seymour Benzer.

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Benzers Problem

• The problem was How can you understand the
• fine structure inside the gene without being
  able
• to see inside?

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Benzers Problem

• The problem was How can you understand the
• fine structure inside the gene without being
  able
• to see inside?
• Classically, geneticists had treated the
  chromosome
• as a linear arrangement of genes.
• Benzer asked in 1959 Was the same thing true
• for the fine structure inside the gene?

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Benzers Problem

• The problem was How can you understand the
• fine structure inside the gene without being
  able
• to see inside?
• The Question was the gene fundamentally linear?

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Benzers Problem

• Or was the gene fundamentally circular?

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Benzers Problem

• Or was the gene fundamentally like a figure-8?

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Benzers Problem

• At the time, we could not observe the fine
  structure
• directly.
• Benzer studied mutations.
• He assumed mutations involved connected
• substructures of the gene.
• By gathering mutation data, he was able to
  surmise
• whether or not two mutations overlapped.

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Benzers Problem
S1 S2 S3 S4 S5 S6
S1 1 1 0 0 0 0
S2 1 1 1 1 0 0
S3 0 1 1 1 0 0
S4 0 1 1 1 1 0
S5 0 0 0 1 1 1
S6 0 0 0 0 1 1
i,j entry is 1 if mutations Si and Sj overlap, 0
otherwise.
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Benzers Problem
S1 S2 S3 S4 S5 S6
S1 1 1 0 0 0 0
S2 1 1 1 1 0 0
S3 0 1 1 1 0 0
S4 0 1 1 1 1 0
S5 0 0 0 1 1 1
S6 0 0 0 0 1 1
S4
S6
S2
S3
S1
S5
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Benzers Problem

• If we represent the tabular (matrix) information
• as a graph, we say that the graph is an interval
  graph
• if it is consistent with a linear arrangement.
• Interval graphs have been very important in
  genetics.
• Long after Benzers problem was solved using
  other
• methods, interval graphs played a crucial role in
  
• physical mapping of DNA and more generally in the
• mapping of the human genome.

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Why Bio-Math? Why Now?

• So how did I get from Benzers problem to
• modeling smallpox for the Secretary of Health
• and Human Services?
• It has become increasingly clear that biology has
• become an information science.

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DNA and RNA
Deoxyribonucleic acid, DNA, is the basic building
block of inheritance and carrier of genetic
information. DNA can be thought of as a chain
consisting of bases. Each base is one of four
possible chemicals Thymine (T), Cytosine (C),
Adenine (A), Guanine (G)
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DNA and RNA
Some DNA chains GGATCCTGG, TTCGCAAAAAGAATC Real
DNA chains are long Algae (P. salina) 6.6x105
bases long Slime mold (D.
discoideum) 5.4x107 bases long
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DNA and RNA
Insect (D. melanogaster fruit fly) 1.4x108
bases long Bird (G. domesticus)
1.2x109 bases long
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DNA and RNA
Human (H. sapiens) 3.3x109 bases
long The sequence of bases in DNA encodes
certain genetic information. In particular, it
determines long chains of amino acids known as
proteins.
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DNA and RNA
RNA is a messenger molecule whose links are
defined from DNA. An RNA chain has at each link
one of four bases. The possible bases are the
same as those in DNA except that the base Uracil
(U) replaces the base Thymine (T).
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Counting
Fundamental methods of combinatorics (the
mathematics of counting) are important in
mathematical biology.
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DNA and RNA
How many possible DNA chains are there in
humans?
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The Product Rule
How many sequences of 0s and 1s are there of
length 2? There are 2 ways to choose the first
digit and no matter how we choose the first
digit, there are two ways to choose the second
digit. Thus, there are 2x2 22 4 ways to
choose the sequence. 00, 01, 10, 11 How many
sequences are there of length 3? By similar
reasoning 2x2x2 23.
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The Product Rule
Product Rule If something can happen in n1 ways
and no matter how the first thing happens, a
second thing can happen in n2 ways, then the two
things together can happen in n1 x n2 ways. More
generally, if something can happen in n1 ways and
no matter how the first thing happens, a second
thing can happen in n2 ways, and no matter how
the first two things happen a third thing can
happen in n3 ways, then all the things together
can happen in n1 x n2 x n3 ways.
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DNA and RNA
How many possible DNA chains are there in
humans? How many DNA chains are there with two
bases? Answer (Product Rule) 4x4 42
16. There are 4 choices for the first base and,
for each such choice, 4 choices for the second
base. How many with 3 bases? How many with n
bases?
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DNA and RNA
How many with 3 bases? 43 64 How many with n
bases? 4n How many human DNA chains are
possible? 4(3.3x109) This is greater than
10(1.98x109) (1 followed by 198 million
zeroes!)
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DNA and RNA
How many human DNA chains are possible? 4(3.3x1
09) This is greater than 10(1.98x109) (1
followed by 198 million zeroes!) A simple
counting argument helps us to understand the
remarkable diversity of life.
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Diversity of Life
A simple counting argument helps us to understand
the remarkable diversity of life. Mathematical
modeling will help us protect the remarkable
diversity of life on our planet.
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Diversity of Life
Mathematical ecology and population biology has a
long history. Modern mathematical methods allow
us to deal with huge ecosystems and understand
massive amounts of ecological data.
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DNA and RNA
More sophisticated methods of counting help us
to understand biological information processing
in important ways.
40
2003 NSF NIH asked me to organize a Workshop
Information Processing in the Biological
Organism(A Systems Biology Approach)
41

• Key Thesis of the Workshop
• The potential for dramatic new biological
  knowledge arises from investigating the complex
  interactions of many different levels of
  biological information.

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Levels of Biological Information

• DNA
• mRNA
• Protein
• Protein interactions and biomodules
• Protein and gene networks
• Cells
• Organs
• Individuals
• Populations
• Ecologies

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The workshop investigated information processing
in biological organisms from a systems point of
view.
44

• The list of parts is a necessary but not
  sufficient condition for understanding biological
  function.

Understanding how the parts work is also
important. But it is not enough. We need to know
how they work together. This is the systems
approach.
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The Workshop Was Organized Around Four Themes

• Genetics to gene-product information flows.
• Signal fusion within the cell.
• Cell-to-cell communication.
• Information flow at the system level, including
• environmental interactions.

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Example 1 Information processing between
bacteria helps this squid in the dark.
Bonnie Bassler Princeton Univ.
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Bacteria process the information about the local
density of other bacteria. They use this to
produce luminescence.The process involved can be
modeled by a mathematical model involving quorum
sensing. Similar quorum sensing has been
observed in over 70 species
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Example 2 The P53-MDM2 Feedback Loop and DNA
Damage Repair
Kohn, Mol Biol Cell, 1999
Uri Alon, Weizmann Institute Galit Lahav, Harvard
University
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Network motifs are conceptual units that are
dynamic and larger than single components such as
genes or proteins. Such motifs have helped to
understand the nonlinear dynamics of the process
by which the P53 - MDM2 feedback loop contributes
to the regulation of DNA damage repair.
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The p53 Network
MDM2
p53
One cell death Protection of the whole organism
Is the damage repairable?
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Example 3 Mathematical Modeling of Multiscale
phenomena arising in excitation/contraction
coupling in the ventricle
RaimondWinslow, Johns Hopkins
Canine Heart
52

• The models study the stochastic behavior of
  calcium release channels.
• Model components range in size from 10 nanometers
  to 10 centimeters.
• The work has application to the connection
  between heart failure and sudden cardiac death.

Ca2 Release Channels (RyR)
lt-10 nm-gt
L-Type Ca2 Channel
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The Mathematics of InfectiousDisease is
Different from theMathematics of Diseases Like
Heart Disease
AIDS
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Models of the Spread and Control of Disease
through Social Networks
AIDS

• Diseases are spread through social networks.
• Contact tracing is an important part of any
  strategy to combat outbreaks of infectious
  diseases, whether naturally occurring or
  resulting from bioterrorist attacks.

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A Model Moving From State to State
Social Network Graph Vertices People Edges
contact Let si(t) give the state of vertex i
at time t. Simplified Model Two states
susceptible, infected (SI Model) Times
are discrete t 0, 1, 2,
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A Model Moving From State to State
More complex models SI, SEI, SEIR, etc. S
susceptible, E exposed, I infected, R
recovered (or removed)
measles
SARS
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More About States
Once you are infected, can you be cured? If you
are cured, do you become immune or can you
re-enter the infected state? We can build a
directed graph reflecting the possible ways to
move from state to state in the model.
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The State Diagram for a Smallpox Model
The following diagram is from a Kaplan-Craft-Wein
(2002) model for comparing alternative responses
to a smallpox attack.
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BioTerrorism

• Great concern about the deliberate introduction
  of diseases by bioterrorists has led to new
  challenges for mathematical scientists.
• This is a major reason for our interest in
  smallpox which has been eradicated in the
  natural world.
• 
  

smallpox
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Homeland Security What Can Mathematics Do?
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Homeland Security What Can Mathematics Do?
My interest in disease got directed to
bioterrorism after the World Trade Center attacks
and following anthrax attacks.
anthrax
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Homeland Security What Can Mathematics Do?
I gave a talk to Congressmen and their staffers
on Capitol Hill in September 2004.
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Bioterrorist Event Detection

• Modern data-gathering methods bring with them new
  challenges for mathematicians.
• They allow us to get early warning of the
  outbreak of an infectious disease whether
  naturally-occurring or caused by a bioterrorist.
• Biosurveilliance. (More on this tonight.)
• Method called syndromic surveillance

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New Data Types for Public Health Surveillance

• Managed care patient encounter data
• Pre-diagnostic/chief complaint (ED data)
• Over-the-counter sales transactions
• Drug store
• Grocery store
• 911-emergency calls
• Ambulance dispatch data
• Absenteeism data
• ED discharge summaries
• Prescription/pharmaceuticals
• Adverse event reports

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Syndromic Surveillance NYC Dept. of Health Data
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Many New Mathematical Methods and Approaches
under Development

• Spatial-temporal scan statistics
• Statistical process control (SPC)
• Bayesian applications
• Market-basket association analysis
• Text mining
• Rule-based surveillance
• Change-point techniques

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Syndromic Surveillance

• Has gotten me and DIMACS involved in a
  partnership with CDC Centers for Disease Control
  and Prevention
• CDC has just launched a new program on
  mathematical modeling of disease.

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The Bioterrorism Sensor Location Problem
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• Early warning is critical
• This is a crucial factor underlying governments
  plans to place networks of sensors/detectors to
  warn of a bioterrorist attack

The BASIS System
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Two Fundamental Problems

• Sensor Location Problem (SLP)
• Choose an appropriate mix of sensors
• decide where to locate them for best protection
  and early warning

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Two Fundamental Problems

• Pattern Interpretation Problem (PIP) When
  sensors set off an alarm, help public health
  decision makers decide
• Has an attack taken place?
• What additional monitoring is needed?
• What was its extent and location?
• What is an appropriate response?

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• The work on bioterrorism and epidemiology led to
  the designation of DIMACS as a U.S. Department of
  Homeland Security Center of Excellence in 2006.

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New Challenges for Modelers of Infectious
Diseases of Africa
DIMACS Programs in Africa Sept. 2006, June 2007
AIDS orphans
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• Endemic and emerging diseases of Africa provide
  new and complex challenges for mathematical
  modeling.

HIV/AIDS
Malaria
Tuberculosis
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• Endemic and emerging diseases of Africa provide
  new and complex challenges for mathematical
  modeling.
• Because of modern transportation systems, no one
  in the world is safe from diseases originating
  elsewhere.

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• Major new health threats such as avian influenza
  present especially complex challenges to modelers
  in the context of developing countries.

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• Two DIMACS workshops and a student short course
  were 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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• Two DIMACS workshops and a student short course
  in Africa

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Themes of our Meetings

• In recent years, mathematical 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
FMD
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• 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
• measles, rubella, polio

AIDS
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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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Themes of our Meetings

• 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 Meetings

• 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 drug-resistant
  strains
• Interaction with other infections TB, malaria
  co-infection a major theme in mathematical
  epidemiology

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Themes of our Meetings

• 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)
• Led to new DIMACS initiative
• on climate and health

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Themes of our Meetings

• 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 Meetings

• Mathematical Modeling of Diseases that Inflict a
  Significant Burden on Africa
• Diseases of Plants
• Major threat to the food supply.
• In U.S.. DHS has established two
• research centers at universities
• that deal with protection of the
• food supply.

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Themes of our Meetings

• 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 Meetings

• Optimization of Scarce Public Health Resources
• How to handle shortages of drugs and vaccines,
  physical facilities, and trained personnel.
• Not just an issue in Africa
• 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 Meetings

• 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-relate
  d models
• DIMACS Vaccination Modeling Group

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New DIMACS African Initiative

• Workshops and Advanced Study Institutes
• Modeling Workshop South Africa 2009
• Economic Epidemiology Uganda 2009
• Conservation Biology Kenya 2010
• Mathematics of ecological reserves
• Genetics and Disease Control Madagascar 2010
• Are genetically altered crops safe?
• Malaria control by genetically modifying
  mosquitoes?

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Bio-Math Connect Institute

• BMC was born from these kinds of themes.
• Bio-Math has become a major topic at the
  undergraduate level and at the graduate and
  postgraduate level.
• Why not in the schools?

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Bio-Math Connect Institute

• Thesis Exposing biology students to the
  importance of mathematical methods in biology
  will help them appreciate biology more.
• Thesis Exposing mathematics students to their
  usefulness in modern biological problems will
  help them appreciate mathematics more.

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Bio-Math Connect Institute

• Thesis Exposing students to the bio-math
  interface will open up new horizons for them and
  expose them to new career opportunities and new
  opportunities for further education.
• Thesis Exposing students to the bio-math
  interface will motivate them as students.

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We need your help to explore these ideas.