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AdS2012 - analysis(7 Two-species models Two species...

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Spring 2012 UNDERGRADUATE/GRADUATE COURSE ANNOUNCEMENT Course title MODELING IN MATH. BIOLOGY Course number MAP5489/MAP4484 Schedule, Room MWF 3 , LIT 127 Instructor Maia Martcheva [email protected] http://www.math.ufl.edu/ maia Main themes Differential equations Mathematical Biology Books: (1) Fred Brauer, Carlos Castillo-Chavez, Mathematical Models in Population Biol- ogy 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.
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Unformatted text preview: analysis. (7) Two-species models. Two species logistic Lotka-Volterra model. Global stability via Lyapunov ²unction. (8) Predator-prey models with periodic solutions. Modeling predator ²unctional re-sponse. (9) Epidemic modeling. (10) Two species Lotka-Volterra competition models. (11) Mutualism (12) Cellular dynamics o² 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 di±erential models. Continuous age-structured model. (17) Partial di±erential models with di±usion. Prerequisites: Di±erential equations and linear algebra. Grading: Grades will be based on (1) Attendance; (2) Two exams (3) Homeworks (4) Term paper and presentation (²or graduate students only). 1...
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  • Spring '08
  • Martcheva,M
  • Mathematical Models in Population Biology and Epidemiology, possible presentation topic, Differential equations Mathematical Biology

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