Mathematical Biology 

This course is meant for graduate students of the MSc program in Biomedical Engineering and Physics, offered at Cinvestav Monterrey. It's objective is to introduce the students to basic concepts and techniques in Nonlinear Dynamics and Bifurcation Theory, as well as to the fascinating world of Mathematical Modeling of Biological Systems. To this end, we study some classical examples of mathematical models of biological phenomena, at scales ranging from a single cell to ecosystems. While studying these models, new mathematical and numerical-analysis techniques are introduced. At the end, the students are expected to have a working knowledge of the subject known as Mathematical Biology.

Course outline:

  1. Introduction to ordinary differential equations.
    1. Terminal velocity.
    2. Why clouds don't fall?
    3. Why microbes swimming differs so much from that of vertebrates.
  2. Exponential growth and decay.
    1. Stochastic processes underlying these models.
    2. Growth and decay rate constants.
    3. Half time life.
    4. Life expectancy.
    5. Replication and death propensities.
  3. Logistic growth model.
  4. Competitive Lotka-Volterra equations.
  5. SIR epidemiology model.
  6. Vaccination.
  7. Gene regulation.