Terminology

1
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

2
Causes of diseases

• Bacteria - single-celled, no nucleus
• Virus - sub-microscopic infectious agent that
  cant 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

3
Modes of Transmission

• Direct - person to person
• Airborne transmission
• Droplet transmission
• Fecal-oral transmission
• Sexually transmission
• Blood-borne transmission

4
Modes of Transmission

• Indirect - through a common vehicle or vector
• Exposure to a contaminant (single, multiple or
  continuous exposure)
• Vector-borne transmission

5
Examples

• Virus with aerosol transmission
• Measles, mumps, rubella
• Bacteria with food/water transmission
• Cholera, salmonella
• Protozoan with vector-borne transmission
• Malaria, giardia

6
Basic Model Concepts

• Identify all stages of a given disease
• Susceptible
• Exposed
• Infectious
• Recovered / Removed
• Vaccinated
• Etc.

7
Basic Model Concepts

• Identify disease progression
• Link stages according to epidemiology of disease

8
SIR

• SIR - Chicken Pox

9
SIR
10
Results of SIR model
11
Sample R0
12
Learn by doing

• Time for hands on games
• Rules for games
• Divide into groups of 4-6 students
• Share responsibility for tasks
• Dont spill the beads!!
• Ask any questions you have

13
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

14
What did you get?

• How many of each bead did you get?
• Did everyone get the same results?
• Why or why not?

15
Game 2 Disease Modeling Revisited

• 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, 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

16
Modifications

• Not always sick forever so could replace sick
  people with recovered people at some time
• Could vaccinate people so they cant get sick
• Other ideas?

17
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

18
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

19
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

20
Founder Effect

• What were the results?
• What does that imply for genetics in isolated
  populations?

21
Game 4 Predator-Prey

• Tasks Rabbit breeder, Lynx, scribe
• Rules
• 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 doesnt get 3 rabbits, it dies
• If no lynx, one immigrates. If no rabbits, 3
  immigrate
• Repeat

22
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?