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6-007-FunctionsAndDerivativesInSIRModels-ModelingScenario

Author(s): Meredith Greer

Bates College, Lewiston ME USA

Keywords: epidemiology species interactions derivatives visualization infection SIR models Law of Mass Action

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Abstract

Resource Image Given a system of differential equations, how do the solution graphs compare with the graphs of the differential equations? Students tackle this question using SIR models for well-known infectious diseases.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

The students view graphs both of solution curves and of the differential equations in the model. Students determine which graphs show solutions, which show derivatives, and which correspond to each compartment (S, I, and R) in the model. Students are then encouraged to update the model to demonstrate non-autonomous infection terms, such as incorporating changed health policy within the timeframe of an outbreak.

Solutions are provided for all exercises, including sample solutions to open-ended questions. A table of data makes it easy to change the given SIR model to represent measles, smallpox, or different influenza outbreaks. This scenario works best if the professor or students have access to software that can numerically solve and graph solutions to systems of ordinary differential equations.

Article Files

Authors

Author(s): Meredith Greer

Bates College, Lewiston ME USA

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