Mathematical Modeling of Biological Systems
Subject to revisions until January 1 2017
- Instructors: Tim Lewis, Bob Guy, Sebastian Schreiber
- Prerequisites: Algebra II/Trig
- Typical Field Trips: TBD
This cluster will introduce students to a wide variety of mathematical models used in biology. Students will learn how to construct mathematical models and use mathematical techniques to analyze these models in order to gain insight to biological phenomena. Mathematical topics covered include difference equations, differential equations and game theory, and biological topics range from ecology and epidemiology to physiology and cell biology. No prior knowledge in these mathematical modeling methods or the biological topics is necessary, but a strong interest in both mathematics and biology is essential. In addition to the core courses described below, this cluster will have weekly guest lectures by UC Davis faculty working at the interface of mathematics and biology.
Core Courses (4 Weeks)
Dynamics of Biological Systems: Patterns in Time and Space
Most biological systems are dynamic, producing fascinating patterns in both time and space. Examples include outbreaks of epidemics, the development of spots on a leopard, the synchronization of flashing fireflies, and pathological rhythms in the heart. Identifying the mechanisms that underlie the “spatio-temporal” dynamics of biological systems can not only lead to better understanding of natural phenomena but also help us to design more effective interventions when necessary. Mathematical modeling plays a fundamental role in identifying these mechanisms. In this course, students will use computer simulation and mathematical analysis to explore the dynamics in models of a variety of biological processes and to gain insight into the mechanisms that produce complex temporal and spatial patterns.
Networks and Games in Biology
Biological systems often involve many interacting components that form complex networks. These networks occur at all biological scales ranging from genes to ecosystems. Network theory provides a collection of mathematical and computational methods to understand the structure and function of these networks. When networks consist of interacting individuals, individuals within these networks may play different strategies to increase their reproductive success. Strategies exhibiting greater reproductive success are more likely to spread through the population. Evolutionary game theory examines the long-term outcomes of these interactions and has provided important insights into the evolution of cooperation, social learning, animal conflicts, and language. In this course, students will learn the fundamentals of network theory, probability, and evolutionary game theory. Computer simulations and mathematical analysis will be used to explore evolutionary games, the structure and function of biological networks, and disease dynamics on social networks.