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

Results of SIR model

Sample R 0

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?