THE COLLEGE OF STATEN ISLAND DEPARTMENTS OF MATHEMATICS/BIOLOGY COURSE OUTLINE MTH/BIO 415 (GRAD 761) MATHEMATICAL BIOLOGY SPRING 2006 4CR/4HR Textbook Mathematical Models in Biology (Classics in Applied Mathematics by Leah Edelstein-Keshet Paperback: 586 pages Publisher: SIAM: Society for Industrial and Applied Mathematics; New Ed edition ISBN-10: 0898715547 ISBN-13: 978-0898715545 Note: Each Topic will be covered over the week(s) indicated. In many cases, sections in the book will be supplemented by handouts. Week Textbook Sections Topics I 1.1 Introduction to building models: Scaling example. Introduction to MATLAB. Theory of difference equations. II-III 2.1-2.8, 3.1 Non-linear difference equations: recognition, steady states, stability Graphical methods, Applications to population dynamics. Cobwebbing using MATLAB. Density dependence in single-species populations. Chaos and its biological relevance. III-IV 1.3-1.7 Difference equations continued. Application to seed banks and insect populations. Age and stage structure. V 3.2-3.5 Host-parasitoid systems. The Nicholson-Bailey model and extensions. Discussion of applications. 1VI-VIII 4.1-4.11 Continuous processes and ordinary differential equations.: Algal growth in a chemostat. Building resource-saturation into the model. Dimensional analysis. Scaling. Linearization of nonlinear equations. Local stability analysis. Systems of equations. e.g. albatross foraging behavior-use in epidemiological models- e.g. spread of AIDS. Use of MATLAB to solve systems of differential equations. ODE23/ODE45 MIDTERM EXAM X-XI Spring Break IX, XI-XII 5.1-5.6 8.1-8.9 6.1-6.6 7.1-7.4 Phase plane methods; oscillatory systems. Neurons and neuronal models. Limit cycles, oscillations and excitable systems. Application of continuous models to population dynamics. Single and competing species models. Predator-prey models. Models for molecular events: Michaelis-Menten kinetics. Sigmoidal behavior and its implications. XIII-XV 9.1-9.7 10 Handout Role of spatial variation in biological systems. Diffusion models. More complex spatial patterns. Introduction to reaction-diffusion models. Brief introduction to stochastic models. XVI Final Project Presentations