Mathematical Modeling of Cancer

Course director: Franziska Michor, PhD

This course introduces the basics of mathematical modeling and computation in biology. Only basic mathematical knowledge (Calculus at high-school or college level) is required.

Class 1: Introduction to Mathematical Modeling in Biology.

We will study introductory models in biology, and cover the basic principles of constructing mathematical models. How do we quantitatively describe a biological system? How do we know which systems are amenable to mathematical modeling, and what kinds of questions can we answer with these techniques?

Class 2: Classic Models in Ecology and Evolutionary Biology.

We introduce basic exponential and logistic models of population growth, epidemiological models of disease spread, models of natural selection.

Class 3: Deterministic Models in Cancer Biology (I).

We discuss several deterministic models of cancer cell growth, leukemia treatment response, and other examples.

Class 4: Deterministic Models in Cancer Biology (II).

We discuss several deterministic models of cancer cell growth, leukemia treatment response, and other examples.

Class 5: Introduction to Probabilistic Models in Biology.

We introduce an example of a simple probabilistic model of population growth to motivate the next lecture.

Class 6: Probabilistic Models in Biology.

We discuss various models of population growth and birth-death models such as Wright-Fisher and Moran processes.

Class 7: Evolutionary Models in Cancer (I).

We introduce basic probabilistic models of cancer cell populations, including Moran models of stem cell compartments, birth-death models of exponentially growing tumor populations, Wright-Fisher models. We introduce an example of two-type model of sensitive and resistant cancer cells.

Class 8: Evolutionary Models in Cancer (II). Part 1.

Analytical tools for exploring our models. We use the models discussed in the previous discussion to calculate various quantities such as the probability of developing resistance in an exponentially growing tumor.

Class 9: Evolutionary Models in Cancer (II). Part 2.

Simulation tools for exploring our models. Many models are too complex to obtain analytical estimates for the quantities we are interested. We introduce basic stochastic computer simulation methods to explore these complex models.

Class 10: Mathematical Modeling of Cancer Paper Reading Session.

We will discuss recent publications in mathematical modeling of cancer.

Class 11: Mathematical Modeling of Cancer Paper Reading Session.

We will discuss recent publications in mathematical modeling of cancer.

Class 12: Mathematical Modeling of Cancer Paper Reading Session.

We will discuss recent publications in mathematical modeling of cancer.

Class 13: Mathematical Modeling of Cancer Paper Reading Session.

We will discuss recent publications in mathematical modeling of cancer.

Class 14: Mathematical Modeling of Cancer Paper Reading Session.

We will discuss recent publications in mathematical modeling of cancer.

Class 15: Mathematical Modeling of Cancer Idea Session.

We will discuss ideas to design mathematical models of cancer biology.