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1-009-ICUSpread-ModelingScenario

Author(s): Brian Winkel

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

Keywords: logistic sum of square errors Intensive Care Unit hospital spread

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Abstract

Resource Image We offer students the opportunity to model the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units during the period of 1958-1974.

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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

Suppose we let P(t) be the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units at time t = 0$. Assume the units for t are in years and t = 0 corresponds to year 1958.

Give an argument for why the logistic differential equation,

P'(t) = r P(t) 100/(100 - P(t))

is a good candidate for modeling this data. Be sure to address the meanings of the rate of change in P(t), the value of 100, the parameter r, and the algebraic nature of the right hand side of the differential equation.

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Authors

Author(s): Brian Winkel

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

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