# SHORT COURSES ON THE MATHEMATICS OF BIOLOGICAL COMPLEXITY

## University of Tennessee, Knoxville

## Supported by National Institutes of Health Award GM59924-01

### Optimal Control Theory in Application to Biology: July 9-12, 2003

The short course leaders were:
Dr. Suzanne Lenhart,
Dr. Renee Fister,
and Dr. Hem Raj Joshi.

This course gives an introduction to optimal control techniques for systems of
ordinary differential equations. These techniques are applied to a variety of
biological and medical examples. Models with one differential equation and one
control are treated first and then the extension to systems of differential
equations and multiple controls is given. Examples include disease, cancer,
bioreactor, bear and fishery models. Bang-bang and singular control cases
are covered. To illustrate an extension to a hybrid system of discrete time
and continuous space variables, an integro-difference population model paper is
presented.

Below are links to four lectures given at the short course and
several papers on the material presented at the course.

There are also MATLAB examples to illustrate the ideas. The "lab" examples
are designed to be user-friendly.

- Short Course Lecture Schedule
Text file
- Introductory Lecture, lecture by Lenhart
PDF file
- Introductory Lecture part II, lecture by Lenhart
PDF file
- Lecture on Bang-Bang and Singular Controls, lecture by Lenhart
PDF file
- Lecture on Systems, lecture by Fister
PDF file
- Two-strain Tuberculosis Model, paper by Jung, Lenhart, and Feng
PDF file
- HIV Immunology Model, paper by Joshi
PDF file
- Integro-difference Population Model, paper by Joshi, Lenhart, and Gaff
PDF file
- References
Text file

The file, *labsheets.pdf*, gives the explanations for 10 examples
of optimal control problems. The examples are designed to
request the appropriate inputs interactively and display the resulting graphs.
To work these examples, you
need to download the 15 *.m* files below and use them with MATLAB (version 6 or
newer). Note that five examples have 2 parts, for example *lab1.m* and *labone.m*.
These examples were prepared by John Workman and Suzanne Lenhart.

- labsheets.pdf,
lab1.m,
labone.m,
lab2.m,
lab3.m,
lab4.m,
lab5.m,
labfive.m,
lab6.m,
lab7.m,
lab8.m,
labeight.m,
lab9.m,
labnine.m,
lab10.m,
labten.m

Return to Short Course Home Page

`http://www.tiem.utk.edu/courses/`

Last Modified: October 1, 2003