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1-004-MicroorganismImmigration-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: continuous immigration population death discrete

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Abstract

Resource Image We present a modeling opportunity for population death with non-constant immigration and suggest the use of both discrete and continuous models with a comparison of results.

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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

Consider a situation in which we are studying 50 microorganisms initially in the Petri dish. We lose 50% of the population each hour due to ``forces of death,'' but through a one way hatch some 10 microorganisms per hour can enter our Petri dish in the first hour, 20 microorganisms per hour can enter our Petri dish in the second hour, 30 microorganisms per hour can enter our Petri dish in the third hour, 40 in the fourth hour, etc. Model this situation with (a) a discrete difference equation model and (b) a continuous differential equation model. State all your assumptions used in the model building process. Build your model very carefully and be sure to define your variables and units. Compare your models and comment on differences and similarities.

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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