Math Biology Integration University of AlaskaUniversity of
Florida Denise KindRebekka Darner Kristin OBrienDavid Julian Diana
WolfGabriela Waschewsky Facilitators: Brian WhiteBrad Brown
Audience: Large Introductory Biology Lecture Course
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Learning Goal: Understand what a mathematical model is and how
it is useful in biology Learning Objectives: Construct a model
Brainstorm parameters Construct an equation Use model to make
predictions Revise a model Design experiment Apply understanding to
new biological examples
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Zombies Attack!
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June 25, 2010 Jesse Campbell, became a zombie and flew from
Fairbanks, AK To Madison, WI Zombies are common in Alaska
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Zombieism Zombies are undead Zombie bites cause
zombification
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What parameters might influence the spread of zombieism?
Brainstorm as a class
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Parameters # zombies # people each zombie bites per day
Assumptions Every zombie bite results in zombification If bitten
today, a zombie tomorrow Zombies dont die or recover Unlimited
human population
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How can we express a model of zombie attack in words? Brains..
Brains What is the number of zombies each day? How does it
change?
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The total number of zombies present tomorrow will equal A.the
number of people who were bitten today. B.the number of zombies
present today, plus the number of people they bite today. C.twice
the number of zombies present today. D.the number of zombies
present today squared. E.the number of zombies present today, plus
the number of zombies present today squared.
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Write an equation B. The total number of zombies present
tomorrow will equal the number of zombies present today, plus the
number of people they bite today. Parameters: Z t = # zombies today
Z t+1 = # zombies tomorrow B = # people each zombie bites per
day
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Homework: Use your equation to graph the number of zombies over
the first week of the zombie attack There is 1 zombie on day 1 Each
zombie bites 2 people per day You may work in groups
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Remainder of Unit Groups share graphs and discuss Revise model
to include finite population Population growth, enzyme kinetics
Second homework Devise experiment to test model How H1N1 and HIV
might differ revisit brainstorm suggestions Discuss homework
Summative assessment Apply understanding of models Evaluate a novel
model
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A Which matches the graph you generated? Time (day) B D #
zombies C
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A Time (day) B D # zombies C The military has quarantined the
campus. Considering the population size is now finite, which of the
following best represents the revised model?
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Revise Equation
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Homework Design an experiment to test your model How would you
expect this model to differ for the transmission of more common
infectious diseases, like H1N1 flu and HIV
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Final Assessment A species of alligator reproduces once a year.
Each female produces 20-50 eggs. Of those eggs, typically about 15
hatch. 6 are still alive at the end of the first year. Which of the
following equations best represents the number of alligators that
would be present in a given year? (F = # females, M = # males, A =
# alligators, t = year) A.A t = F t-1 + M t-1 + 6(F t-1 ) B.A t = F
t-1 + M t-1 + 6(M t-1 + F t-1 ) C.A t = F t-1 + M t-1 + 15(F t-1 )
D.A t = F t-1 + M t-1 + 15(M t-1 + F t-1 )
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Short Answer: Name two additional parameters you would add to
the above model to more accurately model the number of alligators
present in a given year. In 1-2 sentences, briefly justify your
choices.