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Terminology

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

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Terminology

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  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 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

  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. S I R 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 • Don’t 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 can’t 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 doesn’t 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?

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