terminology endemic - habitual presence of a disease within a given area epidemic - occurrence of a...
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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
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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
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Modes of Transmission
• Direct - person to person– Airborne transmission– Droplet transmission– Fecal-oral transmission– Sexually transmission– Blood-borne transmission
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Modes of Transmission
• Indirect - through a common vehicle or vector– Exposure to a contaminant (single,
multiple or continuous exposure)– Vector-borne transmission
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Examples• Virus with aerosol transmission
– Measles, mumps, rubella
• Bacteria with food/water transmission– Cholera, salmonella
• Protozoan with vector-borne transmission– Malaria, giardia
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Basic Model Concepts
• Identify all stages of a given disease– Susceptible– Exposed– Infectious– Recovered / Removed– Vaccinated– Etc.
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Basic Model Concepts• Identify disease progression• Link stages according to
epidemiology of disease
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SIR
• SIR - Chicken Pox
S I R
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SIR
St1 St It StN
It1 It It StN
ItD
Rt1 Rt ItD
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Results of SIR model
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Sample R0
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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
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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
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What did you get?
• How many of each bead did you get?
• Did everyone get the same results?
• Why or why not?
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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
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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?
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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
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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
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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
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Founder Effect
• What were the results?• What does that imply for genetics
in isolated populations?
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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
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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?