Laboratory Experiences in Mathematical Biology

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  Zombie Game App

  Gabe Nelson

  The Zombie Game is a simplified representation of how a disease spreads through a population. In this representation, there are two "teams": the Zombies and the Humans. The Zombies win when there are zero Humans remaining, and the Humans win when there are zero Zombies remaining. Note that by default, Zombies cannot die, so the Humans will always lose.

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  Marshmallow Lab

  Melissa Pulley, Leoncio Rodriguez Quinones, Brynja Kohler, and Luis F. Gordillo

  This lab contains a short sequence of lessons aiming to improve students’ understanding of Holling’s type II functional response equation. The lessons incorporate experience with an artificial predator-prey system, first employed by C.S. Holling in his classic “disc experiment”, which is also reproduced via individual-based computer simulations, giving students the opportunity to gather different sets of data to model and interpret. The independent components in the lesson plan (mathematical, experimental, and computational) engage students in various modeling activities to meet multiple learning objectives.

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  Coffee Thermocline Lab

  Andrea Bruder and Brynja Kohler

  A layered system of coffee and milk serves as a physical model for temperature gradients in lakes or the atmosphere, where temperature depends on both a temporal and spatial variable. Students create, observe, and collect temperature data of their own, graph the data, and develop mathematical models to fit the data.

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  Brine Shrimp Lab

  Brynja Kohler, Rebecca Swank, Jim Haefner, and Jim Powell

  Young brine shrimp movements within a petri dish are tracked by students. Students are challenged to determine and verify whether the brine shrimp move in a random walk. From this exercise students gain greater understanding of PDE models, diffusion and parameter estimation.

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  Stream Lab

  Miro Kummel, Andrea Bruder, Jim Powell, Brynja Kohler, and Matt Lewis

  Dead leaves, ping-pong balls or plastic golf balls are floated down a small stream. The number of leaves/balls passing recording stations along the stream are tallied. Students are then challenged to develop a transport model for the resulting data. From this exercise students gain greater understanding of PDE modeling, conservation laws, parameter estimation as well as mass and momentum transport processes.

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  Yeast Lab

  Matt Lewis and Jim Powell

  Yeast are grown in a small, capped ask, generating carbon dioxide which is trapped in an inverted jar full of colored water. The volume of carbon dioxide produced can either be measured directly or using time-lapse imagery on an iPad or similar. Students are then challenged to model the resulting data. From this exercise students gain greater understand- ing of ODE compartment models, parameter estimation, population dynamics and limiting factors.

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  Leaky Bucket Lab

  Jim Powell, Jim Haefner, and Brynja Kohler

  Students test Torrecelli’s law and develop and compare their own alternative models to describe the dynamics of water draining from perforated containers. From this exercise students gain experience and perspective using a classic model as well as greater understanding of ODE compartment models, parameter estimation and fluid flows.

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  Disease Lab

  Jim Powell and Matt Lewis

  Students use transparencies and dry erase markers to simulate the spread of a zombie virus among a fixed population. Students are then challenged to create their own "disease" and develop an ODE model for the resulting data. From this exercise students gain greater understanding of population and SIR models, disease dynamics, parameter estimation and compartment modeling.