** Course description:** Mathematical and quantitative modeling of biological phenomena has become a necessary
approach at studying living organisms. Mathematical biologists work towards identifying
unified frameworks that describe biological phenomena in different levels of complexity.
It ranges from small entities such as viruses and bacteria, cells in tissues and, ecological
models where animals compete for resources in a habitat. This course introduces basic concepts
of mathematical biology with modern applications in mind. We use dynamical systems tools to
model mechanisms of cell growth and cell- cell interaction as well as complex evolution of
species. We discuss subjects such as microbial growth, cancer evolution and virus dynamics
and epidemiology.

**Course time:** 2020 Winter 2A (2:25-4:15)

**Course Location:** Kemeny 004

**Instructor:** Kamran Kaveh

(Office: Kemeny 244, Email: kkaveh@dartmouth.edu)

**Prerequisites:** Math 3. Familiarity with programming (for example: MATLAB, Python or Mathematica).
Basic probability highly recommended.

**Grading:** Projects (50%), Problem sets (40%), Attendance & Participation (10%)

**Projects:** Approximately 4 weeks are given to complete the project.
The instructor will suggest project ideas in the third week, but you are
allowed to propose your own, which has to be approved by the instructor in the
fourth week at the latest. Each project presentation is limited to 15 minutes and
preferably in the style of TED talks.

**Late policy:** By “deadline” we mean it.
On the condition of accepting the penalty for turning in
homework late (that is, 5% each additional day), however,
an extension of maximum 2 days will be granted on a case-by-case basis.

**Collaboration policy:** Collaborations on problem sets
are permitted, but you are required to disclose the names of the other students with
whom you collaborated and discussed. You are encouraged to work in groups for course
projects (but no more than 2 individuals per project).

**Textbooks:** Mainly notes. Useful references are “Evolutionary Dynamics”, M. A. Nowak (2006).
“Mathematical Biology”, J. D. Murray (2003).

## Syllabus

** Day 1: Introduction & Overview **

** Day 2: Population dynamics **

How to write ODE for biological dynamics

Fixed points and steady states

Example: Logistic growth

** Day 3: Population Dynamics II **

Natural selection

Replicator equation

Discrete Time models

**Day 4: Interacting populations **

Cell-cell interaction and signaling

Predator-prey equation. Evolutionary games

Replicator equation revisited

Stability analysis of complex populations

(Problem set 1: Growth models)

**Day 5-6: Evolution of antibiotic resistance **

Mechanisms of antibiotic resistance

Death-Galaxy experiment

Mutation-selection processes

Mutational pathways

**Day 7: Migration and dispersal **

Cell motility

Random walks in bacteria

Chemotaxis

(Problem set 2)

** Day 8: Stochastic models of growth and competition **

Branching process

Moran process

Fixation probability

Time to fixation

** Day 9-10: Growth and competition in tissues and networks **

Moran process on networks

death-birth vs birth-death processes

(Problem set 3)

**Day 11: Cancer modeling. I **

Oncogenes and Tumor suppressor genes

Moran models of cancer initiation

**Day 12: Cancer modeling. II **

Tumor microenvironment

Spatial models of tumor growth

**Day 13: Stem cell dynamics **

Self-renewal vs. differentiation

Population dynamics of stem cells

Stem cells in cancer

(Problem set 4)

**Day 14: Infectious disease models. I **

S-I model

Basic reproduction number

Dynamics of Immune response

** Day 15: Infectious disease models. II **

Evolution of virulence

HIV dynamics

Drug resistance in HIV

(Problem set 5)

** Day 16: Epidemiology and network models **

S-I model on networks

Vaccination strategies

** Day 17: Viruses meets Cancer cells: Oncolytic viral therapy **

Oncolytic virus dynamics

Spatial models of oncolytic viral therapy

**Days 18-19: Project Presentations **