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Department of Mathematics College of Liberal Arts and Sciences

MAP 6488 Biomathematics Seminar 2 (Spring 2026)

MAP 6488 Biomathematics Seminar 2 (25654)

Instructor: Sergei S. Pilyugin 

https://people.clas.ufl.edu/pilyugin/courses/map6488_s2025/

  • Announcements: The lectures will be delivered live in LIT 0217.
  • Time and Room: MWF 6 (12:50 – 1:40 p.m.), LIT 0217.
  • Textbook: The Theory of the Chemostat: Dynamics of Microbial Competition by H. L. Smith and P. Waltman, Cambridge University Press, 1995 (ISBN 0-521-47027-7).
  • Critical dates: Jan. 12 (classes begin), Apr. 22 (classes end).
  • Holidays: Jan. 19 (MLK Day), Mar. 14–21 (Spring Break).
  • Office Hours: MWF 4 – in LIT 458 or in zoom by appointment. Please, use e-mail: pilyugin@ufl.edu for communication. For more details, see my schedule.
  • Description and Objectives of the Course: In this course, I plan go through select chapters from the Smith and Waltman book on the chemostats and a few research papers covering the following topics:

    1. Basic equations of microbial growth, batch vs. chemostat, analysis of growth equations, exploitative competition, competitive exclusion, mutations, plasmids, competition modulated by the presence of additional factors.

    2. Trophic chains, multi-prey and multi-predator ecosystems, long food chains, competition for multiple resources.

    3. Structured models of growth: size-structured and age-structured model of microbial growth.

    4. Variable-yield models: Droop cell-quota model, phenomenological variable yield models.

    5. Periodically forced chemostats: competitive coexistence in time-varying environments, achieving coexistence via control theory.

    6. Removing the well-mixedness hypothesis: gradostats, unstirred chemostats.

    7. Additional topics (if time permits)
  • Grading System: The grade is determined by the average of the homework scores. The resulting score determines the letter grade according to the following table
    Letter Grade
    A
    A-
    B+
    B
    B-
    C+
    C
    C−
    D+
    D
    Score 100 – 93 92 – 88 87 – 83 82 – 77 76 – 71 70 – 65 64 – 59 58 – 53 52 – 47 46 – 40
  • Course policies: This course complies with all UF academic policies. For information on those polices and for resources for students, please use this link.