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CAMEL Question: Can Applied Math Extend Life?


Author(s)

Qinxia Li
Department of Mathematics and Computer Science
Fisk University
qli@fisk.edu
Xinyao Yang
Department of Mathematical Sciences
Xi’an Jiaotong-Liverpool University
Lauren S. Gollahon
Department of Biological Sciences
Texas Tech University
lauren.gollahon@ttu.edu

Abstract

This directed case study examines differences between the exponential and logistic growth models in biology and how they are applied to solve real life problems. The narrative follows a student returning to the United States as he tries to assess his possible exposure to Middle East Respiratory Syndrome (MERS). To better understand his risk, James needs to get up to speed on a variety of topics including the difference between infection, transmission, virulence, etc., and how these topics can be mathematically modeled not only in relation to MERS, but also with respect to Ebola and influenza. This case was designed for use in the second semester of a biocalculus course or a course involving ordinary differential equations, which are appropriate for second year undergraduate students majoring in biology, pre-med, and bio-mathematics. These students typically have completed a semester of calculus and one year of general biology. The case provides an opportunity for students to develop their understanding of differential equations and increase their appreciation of mathematics as it applies to solving a problem of biology.


Objectives

  • Understand the linear growth model and apply it to solve linear differential equations.
  • Understand the logistic growth model and apply it to solve separable differential equations.
  • Graph the solutions with graphing utilities and examine the differences in the solutions with distinct initial conditions and spreading rates.
  • Explain the solutions in a biological context.

Keywords

exponential growth, logistic growth, differential equation, spreading rate, Ebola, MERS, H3N2

Topical Areas

N/A

Educational Level

Undergraduate lower division, Undergraduate upper division

Format

PDF

Type / Methods

Directed, Discussion

Language

English

Subject Headings

Biology (General)  |   Epidemiology  |   Mathematics  |   Medicine (General)  |  


Date Posted

2/10/2017

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