MTH 428/528: Stochastic Elements in Mathematical Biology

Winter 2022



Instructor: Yevgeniy Kovchegov
e-mail: kovchegy @math. oregonstate.edu
Office: Kidder 60
Office Phone No: 7-1379
Office Hours: MW 5-6 via Zoom or by appointment



Instructions: MWF 1:00pm to 1:50pm in STAG 213 or via Zoom.

Course description: This course is an introduction to stochastic modeling of biological processes. Stochastic models covered may include Markov processes in both continuous and discrete time, urn models, branching processes, and coalescent processes. Biological applications modeled may include genetic drift, population dynamics, genealogy, demography, and epidemiology. Mathematical results will be qualitatively interpreted and applied to the biological process under investigation.

The course will cover the following topics:

A variety of mathematical techniques will be covered when analyzing these models.

Syllabus:  PDF



Schedule:
Monday, January 3  Review of probability. Conditional probability. Bayes’ Theorem. Lectures 1-3 slides (PDF)
Wednesday, January 5  Review of probability. Conditional probability. Bayes’ Theorem. Independent events. Lectures 1-3 slides (PDF)
Friday, January 7  Review of probability. Bayes’ Theorem. Independent events. Examples. Lectures 1-3 slides (PDF)
Monday, January 10  Review of combinatorics. Permutations and combinations. Generalized combinations. Binomial theorem. Lecture 4 slides (PDF)
Wednesday, January 12  Introduction to random variables. Binomial random variable. Expectation of a random variable. Wright-Fisher Model. Lecture 5 slides (PDF)
Friday, January 14  Binomial random variable. Expectation of a random variable. Wright-Fisher Model. Poisson random variable. Geometric random variables. Variance and standard deviation. Lecture 6 slides (PDF)
Wednesday, January 19  Variance and standard deviation of discrete random variables. Markov and Chebyshev inequalities. Lecture 7 slides (PDF)
Friday, January 21  Introduction into Markov chains. Wright-Fisher model as a Markov chain. Birth-and-death processes. Moran process. Lectures 8-11 slides (PDF)