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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.