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AdS2007 - (6 Harvesting a single population(7 Two-species...

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Spring 2007 UNDERGRADUATE/GRADUATE COURSE ANNOUNCEMENT Course title MODELING IN MATH. BIOLOGY Course number MAP5489/MAP4484 (Section 6537/6532 ) Schedule, Room MWF 5 , LIT 201 Instructor Maia Martcheva [email protected] http://www.math.ufl.edu/ maia Main themes Differential equations Mathematical Biology Books: (1) Linda J. S. Allen, An Introduction to Mathematical Biology, Prentice Hall, 2006. (2) Fred Brauer, Carlos Castillo-Chavez, Mathematical Models in Population Biol- ogy and Epidemiology, Springer, 2001. (3) Nicholas F. Britton, Essential Mathematical Biology, Springer, 2003. Syllabus: (1) Deriving single species differential equation models – Malthus model and logistic growth. (2) Linear differential equations - definitions, notation, first order linear differential equations. Gompertz growth. (3) First-Order Linear Systems. Pharmacokinetics model. (4) Non-linear ordinary differential equations - basic definition and notation. (5) Local stability in first-order equations. Application to population growth models.
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Unformatted text preview: (6) Harvesting a single population (7) Two-species models. Two species logistic model. Lotka-Volterra predator-prey models - introduction to predator-prey models. (8) Local stability in first order systems. Phase-plane analysis. (9) Periodic solutions. (10) Bi±urcations. (11) Predator-prey model - analysis. Periodic solutions. Predator-prey models with logistic growth in the prey in the absence o± predator. Modeling predator ±unc-tional response. (12) Two species Lotka-Volterra competition models. (13) Spruce budworm model. (14) Epidemic models. Cellular dynamics o± HIV. (15) Metapopulation and patch models. (16) Chemostat modeling. (17) Excitable systems. (18) Partial diferential models. Continuous age-structured model. Prerequisites: Diferential equations and linear algebra. Grading: Grades will be based on (1) Attendance; (2) Four take-home exams (3) Term paper (±or graduate students only). 1...
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