(2) Linda J. S. Allen, An Introduction to Mathematical Biology, Prentice Hall, 2006.
(3) Nicholas F. Britton, Essential Mathematical Biology, Springer, 2003.
Spring 2012 UNDERGRADUATE/GRADUATE COURSE ANNOUNCEMENT Course title Course number Schedule, Room Instructor
Main themes
MODELING IN MATH. BIOLOGY MAP5489/MAP4484 MWF 3, LIT 127 Maia Martcheva
[email protected] http://www.math.ufl.edu/∼maia Differential equations Mathematical Biology
Books: (1) Fred Brauer, Carlos Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, 2001. (2) Linda J. S. Allen, An Introduction to Mathematical Biology, Prentice Hall, 2006. (3) Nicholas F. Britton, Essential Mathematical Biology, Springer, 2003. Syllabus: (1) Deriving single species differential equation models – Malthus model and logistic growth. (2) Harvesting single populations. (3) Single spieces discrete time population models. (4) Continuous single species population models with delay. (5) Models of interacting populations – predator-prey Lotka-Volterra model. (6) Local stability of non-linear systems of equations. Linearization. Phase-plane analysis. (7) Two-species models. Two species logistic Lotka-Volterra model. Global stability via Lyapunov function. (8) Predator-prey models with periodic solutions. Modeling predator functional response. (9) Epidemic modeling. (10) Two species Lotka-Volterra competition models. (11) Mutualism (12) Cellular dynamics of HIV (possible presentation topic). (13) Metapopulation and patch models (possible presentation topic). (14) Chemostat modeling (possible presentation topic). (15) Excitable systems (possible presentation topic). (16) Partial differential models. Continuous age-structured model. (17) Partial differential models with diffusion. Prerequisites: Differential equations and linear algebra. Grading: Grades will be based on (1) Attendance; (2) Two exams (3) Homeworks (4) Term paper and presentation (for graduate students only).
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