Microbiology/Immunology 510 - Mathematical Modeling of Infectious Diseases

NOTE: THIS COURSE IS USUALLY OFFERED EVERY OTHER FALL TERM. Please note that it will not be offered in the Fall of 2004.

This is a 3 credit hour course.

A cartoon rendering of HIV-1. A mathematical model predicting disease outcome in HIV-1 infection

Course Director:

  • Dr. Denise Kirschner
  • EMAIL for Dr. Kirschner: kirschne@malthus.micro.med.umich.edu
  • Department of Microbiology and Immunology
  • Class meets: 10:00-11:30am on tuesday and thursdays there are 2 classrooms..one is set up for computer use (5631 Med Sci II), the other is a regular classroom (2813 Med Sci II in the LRC area). Both are in Medical Science Bldg II and easy to find. The first class will meet in 5631.

    Things of interest for this course will be posted here.


    The objective of this course is to present a detailed introduction to modeling host-pathogen interactions. We will briefly discuss modeling at the population level, as these models represent some of the most classical results. We will then focus on host-pathogen interactions within the host. We will explore such pathogens as HIV, Mycobacterium tuberculosis, Helicobacter pylori . We will focus mainly on in-host models of viral infections, as most of the modeling has been done in this area in the past decade. We will however, discuss models of bacterial and parasitic infections as well. Current literature will be assigned and discussed in class throughout the course.


    Our specific goals for the course as outlined as follows:

  • 1. Illustrate the broad range of infectious disease problems which can be modeled mathematically.
  • 2. Learn the skill of gleaning and synthesizing the literature to study a particular question.
  • 3. Create mathematical models from non-mathematical descriptions of problems.
  • 4. Interpret the results of models and evaluate their biological implications.
  • 5. Show the necessity of simplification and approximation in models and identify their effects.
  • 6. Enhance computer skills and the use of the internet through email and the world wide web.
  • Background Some basic understanding of Biology
  • pre-requisites As this course is intended for a broad audience, it will include solid introductions to the mathematics, microbiology and immunology as needed. Student will be required to have Calculus I and II, but it will be helpful to have some experience with differential equations and/or linear algebra. NOTE: If you are NOT sure of your background, then contact instructor for approval.
  • Text/Readings:

  • There is no required textbook for the course.
  • There will be outside daily reading assignments from journal articles, book chapters and notes that I hand out in class.
  • Background reading in specific areas are listed below. Most are available in the bookstore or on reserve in the library.
  • Modeling text: by Leah Edelstein Keshet: Mathematical Models in Biology, Birhauser ISBN-0-07-554950-6
  • Immunology text: by Janeway and Travers: Immunobiology, 3rd or 4th edition ISBN 0-8153-2818-4
  • Microbiology text: "Mims' Pathogenesis of Infectious Diseases" authors: Mims, Dimmock, Nash, and Stephen. Academic Press. Paperback cost roughly $23.00.
  • Mathematics texts: There are two. If you have not had differential equations (in a while or ever) then Boyce and DiPrima "Elementary differential equations", 6th edition. It is a good background book that reads easily. If you have had DE, then I suggest (my favorite math book) By Steve Strogatz entitled: nonlinear dynamics and Chaos with applications to Physics, Biology, Chemistry and Engineering, ISBN-0-201-54344-3.
  • One strongly recommended general reading for everyone is by Laurie Garrett, entitled: The Coming Plague (soft cover). It costs about 12 dollars, and really gives an exciting "big picture" humanistic aspect of the subject.

  • Week 1: Intro to mathematical modeling
  • Week 2: Intro to Immunology
  • Week 3: Intro to Pathogenesis : Bacterial, Viruses and fungi & protozoa
  • Week 4: Intro to basic deterministic modeling techniques
  • Weeks 5&6: Intro to solving and exploring mathematical systems
  • Weeks 7&8&9: Mathematical Modeling of HIV-immune system
  • Weeks 10&11: Contrast with modeling biology systems: H. pylori and TB
  • Week 12: Intro PDE modeling
  • Grades Class attendance and participation will make a difference in your grade. There may be short homework assignments; and the course will have a written, in-class midterm and a final project that you should be working on during the entire semester. These will be presented in both written and oral form on the last day of class, December 10th.
  • First HOMEWORK ASSIGNMENT: Write a summary about yourself including the following information: name, classification, major, e-mail address. I also would like to know what your (academic) interests are, and why you are taking this class. What are your ultimate career goals with your degree? What is your math background? Anything else you would like to share/add about yourself is welcomed. Don't forget, as part of this assignment, you MUST send this as an e-mail message to me (email address above) before the second class meeting.
  • Participation I encourage you all to feel free to contact me over e-mail for ANY questions you may have. I enjoy and expect an interactive classroom, we hope that you all will participate, taking advantage of a small class size, and will be challenged by this exciting course.

  • Mathematica code for population growth
  • Mathematica code for competition
  • Mathematica code for LHS
  • Mathematica code for computing eigenvalues and eigenvectors
  • Mathematica code for predator prey model
  • Mathematica code for chemostat model
  • Mathematica code for S-I-R model