BIOEE 3620 - Dynamic Models in Biology

(crosslisted) MATH 3620
(BIO-AS, MQR-AS, SMR-AS)

Spring. 4 credits. Student option grading.

Prerequisite: two majors-level biology courses and completion of mathematics requirements for biological sciences major or equivalent.

S. Ellner., A. Vladimirsky, A. Hein.

Introductory survey of the development, computer implementation, and applications of dynamic models in biology and ecology. Case-study format covering a broad range of current application areas such as regulatory networks, neurobiology, cardiology, infectious disease management, and conservation of endangered species. Students also learn how to construct and study biological systems models on the computer using a scripting and graphics environment.

Outcome 1: “Read” a dynamic model, interpreting its equations as statements about underlying processes and the biological assumptions made about the rates and consequences of those processes.

Outcome 2: Adapt existing models for applications to related systems or alternative scenarios.

Outcome 3: Write computer programs (using R or Matlab) to numerically solve low-dimensional matrix equation (deterministic and stochastic), difference equation, differential equation, partial differential equation and agent-based models of biological systems.

Outcome 4: Use the Pplane software to perform phase-plane analyses of two-dimensional dynamical systems including nullclines, local stability, computing stable and unstable manifolds of saddles, and locating stable and unstable periodic orbits and their basins of attraction.

Outcome 5: Locate equilibria, compute Jacobians, evaluate local stability through eigenvalue calculations and other linear algebraic methods, and interpret these results in terms of asymptotic system dynamics and bifurcations.

Outcome 6: Read and understand biological research papers that use modeling as a primary methodology.

Outcome 7: Formulate meaningful research questions in biology that can be addressed using dynamic models, and apply the skills learned in the course to answer those questions.