An Introduction to Quantitative Modeling
Department of Biological Sciences
University of Calgary
Students assume the roles of CDC researchers who must determine how to most effectively stop an impending Zombie apocalypse. The story line leads students through the process of developing a mathematical model of a Zombie outbreak, which they then use to evaluate different "management" strategies to ensure human survival. Students are introduced to a flow diagram, learn how to derive equations from a flow diagram, and evaluate predictions of the model. Comparisons to the spread of invasive species, infectious disease outbreaks, and predator-prey relationships help the students to see how important biological processes can be modeled quantitatively. Since the focal species (zombies) is fictitious, this case is an ideal way to introduce students to the process of mathematical modeling without worrying about the system-specific details of any particular organism. Originally designed for a second year introductory ecology course, this case is also appropriate for an epidemiology course, advanced population ecology courses, applied ecology courses, and quantitative biology/mathematical biology courses.
- Define a flow diagram, mass action, state variable, and parameter.
- Use a flow diagram to explain the meaning of the coupled ordinary differential equations describing the rates of change of state variables.
- Develop and hypothesize links between the zombie model and real biological problems, such as predator-prey interactions, rates of spread of disease, rates of spread of invasive species, etc.
- Explain the value of using a mathematical model to develop predictions for biological problems and evaluating potential management solutions.
- Examine the trade-off between complexity and reality in modeling biological problems.
KeywordsMathematical modeling; invasive species; disease modeling; quantitative modeling; predator-prey; population ecology
Topical AreasScientific method
Educational LevelUndergraduate lower division, Undergraduate upper division
Type / MethodsAnalysis (Issues), Discussion, Interrupted, Role-Play
Subject HeadingsBiology (General) | Ecology | Environmental Science | Epidemiology | Mathematics | Medicine (General) | Science (General) |