Transcript Mathematical Epidemiology

Terminology
• Endemic - habitual presence of a
disease within a given area
• Epidemic - occurrence of a disease in
a region in excess of normal
• Pandemic - worldwide epidemic
Causes of diseases
• Bacteria - single-celled, no nucleus
• Virus - sub-microscopic infectious agent
that can’t survive outside a host cell
• Environmental - non-biological agent such
as a toxic substance
• Genetic - hereditary disease from genetic
defects
• Prion - Abnormal proteins
• Protist - diverse group of eukaryotic
microorganisms
• Fungi and more
Modes of Transmission
• Direct - person to person
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Airborne transmission
Droplet transmission
Fecal-oral transmission
Sexually transmission
Blood-borne transmission
Modes of Transmission
• Indirect - through a common vehicle
or vector
– Exposure to a contaminant (single,
multiple or continuous exposure)
– Vector-borne transmission
Examples
• Virus with aerosol transmission
– Measles, mumps, rubella
• Bacteria with food/water transmission
– Cholera, salmonella
• Protozoan with vector-borne transmission
– Malaria, giardia
Basic Model Concepts
• Identify all stages of a given disease
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Susceptible
Exposed
Infectious
Recovered / Removed
Vaccinated
Etc.
Basic Model Concepts
• Identify disease progression
• Link stages according to epidemiology
of disease
SIR
• SIR - Chicken Pox
S
I
R
SIR

St 
St 1  St      It  

N 

St  It 
It 1  It      It    

N  D
It
Rt 1  Rt 
D
Results of SIR model
Sample R0
Learn by doing
• Time for hands on games
• Rules for games
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Divide into groups of 4-6 students
Share responsibility for tasks
Don’t spill the beads!!
Ask any questions you have
Game #1 – Disease
Modeling
• Tasks: Cup holder, scribe, clear bead manager,
blue bead manager, bead selector
• Rules:
– Start with 20 clear beads and 1 blue bead
– Bead selector pulls out 2 beads (no peeking!!)
– If 2 clear or 2 blue – put both back, if 1 clear and 1 blue –
put 2 blues back
– Repeat until time is up
– Scribe counts final numbers
What did you get?
• How many of each bead did you get?
• Did everyone get the same results?
• Why or why not?
Game #2 – Disease
Modeling Revisited
• Tasks: Cup holder, scribe, clear bead
manager, blue bead manager, bead selector
• Rules:
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Start with 20 clear beads and 1 blue bead
Bead selector pulls out 2 beads (no peeking!!)
If 2 clear or 2 blue – put both back
If 1 clear and 1 blue, flip a coin. If heads, put 2
blues back, if tails, put 1 clear and 1 blue back
– Repeat until time is up
– Scribe counts final numbers
Modifications
• Not always sick forever so could
replace sick people with recovered
people at some time
• Could vaccinate people so they can’t
get sick
• Other ideas?
What about ecology?
• Ecology has benefited from math for
a longer time
• Many ecology concepts are natural
models such as predator-prey and
competition
• Again, looking at populations and flow
rates between them
More games!!
• Again often start from a simple hands
on experiment links the math and
biology more closely
• Often send students out to
– measure length and width of leaves
– measure length of middle finger to
height
– Anything that teaches relationships
Game #3 Founder Effect
• Tasks: Cup holder, scribe, clear bead manager,
blue bead manager, bead selector
• Rules:
– Start with one blue bead and one clear bead
– Bead selector pulls out 1 bead (no peeking!!)
– If pull a blue bead, put two blues back into cup. If pull a
clear bead, put two clear beads back into cup.
– Repeat until time is up
– Scribe counts final numbers
Founder Effect
• What were the results?
• What does that imply for genetics in
isolated populations?
Game #4 Predator-Prey
• Tasks: Rabbit breeder, Lynx, scribe
• Rules:
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Start with 3 rabbits spread across the meadow
Toss the lynx square once to catch rabbits
3 rabbits = lynx survives and reproduces
All rabbits breed so double the number of
rabbits and disperse across the meadow
– If lynx doesn’t get 3 rabbits, it dies
– If no lynx, one immigrates. If no rabbits, 3
immigrate
– Repeat
Predator-Prey
• Plot the numbers you got for lynx and
rabbits in each generation
• Can you predict how many there would
be in the next generations?