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– 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– 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

St1 St It StN

It1 It It StN

ItD

Rt1 Rt ItD

Results of SIR model

Sample R0

Learn by doing

• Time for hands on games• Rules for games

– 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:– 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:

– 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?