| Tuesday: EA 295 |
Thursday: EA 295 |
| Mar 30
Chemical Kinetics
Mass action law
Michaelis-Menten and Hill type kinetics
Basic ODE thoery
existence
uniqueness by successive iterations
examples
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Apr 1
Stability of steady state for one ODE
Phase portraits in the plane
Nullclines and Bistability
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| Apr 6
Bifurcation diagram
Bistability and hystereris Hopf bifurcation
Singular perturbation
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Apr 8
Euler Method: Convergence and Stability
Computation: XPPAUT introduction
Math865L_example1.ode
Math865L_example2.ode
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| Apr 13
Virus dynamics
Ref: Leenheer & Smith, Virus Dynamics: A Global Analysis
SIAM J. Appl. Math Vol 63, No.4 pp 1313-1327, 2003
Basic reproduction number
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Apr 15
HW: (1) pick f_1 and f_2 you like to generate similar figure as Fig.3.5 in p.27 (handout) and describe the behavior of equalibrium points
Solve the virus model with N = 15 and N = 30. Discuss the biological meanings.
Computation: XPPAUT introduction II
Numerical experiments of virus dynamics
Math865L_example3.ode
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Apr 20
Epidemiological models
SIR model
SIER model
Reference book: Mathematical epidemiology by Fred Brauer, Pauline Van den Driessche, Jianhong Wu and Linda J. S. Allen, Springer, 2008
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Apr 22
Computation: XPPAUT introduction III
Math865L_example4.ode
Math865L_example5.ode
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| Apr 27
Cell cycle
The Goldbetter model
Reaction Diffusion equations
Hyperbolic systems
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Apr 29
Simulation of the Goldbetter model
Computation: XPPAUT introduction IV
Math865L_example6ode
Math865L_example7.ode
Math865L_example8.ode
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| May 4
System of Diffusion Reaction Model
Tumor model
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May 6
Simulation for parabolic and hyperbolic equations
Matlab pdepe help
pdex1.m
pdex4.m
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| May 11
Tumor model with several cell types
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May 13
Simulations for viral therapy of tumor
Wang_Tian_paper_ex1_array.m
tridiagSolve.m
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| May 18
Tumor model with several cell types
A model of radially symmetric tumor and it stationary solution
Stability/instability of the stationary solution
Cell differentiation; the Yates-Callard-Stark (YCS) model of Th0 differentiation into Th1 and Th2
Cell differentiation (continued), asymptotic behaviour
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May 20
Numerical simulation for cell differentiation
Codes
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| May 25
Project I: first reference: Dictyostelium discoideum: cellular self-organization in an excitable biological medium by Thomas Hofer, Jonathan A. Sherratt and Philip K. Maini, Proc R. Soc Lon. B (1995) 259, 249-257
second reference: Cellular pattern formation during Dictyostelium aggregation by Thomas Hofer, Jonathan A. Sherratt and Philip K. Maini, Physica D 85 (1995) 425-444
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May 27
Project II: Malaria model with periodic mosquito birth and death rates. Bassidy Dembele, Avner Friedman and Abdul-Aziz Yakubu, Journal of Biological Dynamics, Vol 3, No. 4, July 2009, 430-445
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| Jun 1
Project III: Reference I,
A mathematical model of tumor-immune evasion and siRNA treatment. J.C. Arciero, T.L. Jackson, and D.E. Kirschner. Discrete and Continuous Dynamical Systems-Series B, Vol 4, No. 1, Feb 2004, 39-58
Project III: Reference II, Modeling immunotherpy of the tumor--immune iteraction by Denise Kirschner and John Carl Panetta, J. Math. Biol. (1998)37: 235-252
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Jun 3
Project IV: Reference I,
A Mathematical Model for Collagen Fibre Formation during Foetal and Adult Dermal Wound Healing. Paul D. Dale,; Jonathan A. Sherratt and; Philip K. Maini, Proc. R. Soc. Lond. B (1996) 263, 653-660
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| Jun 8
Project V: Leukocytes. James Keener, James Sneyd. Mathematical Physiology. Vol II: Systems Physiology, Chapter 16, 495-507.
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Jun 10
Project VI: Respiration. James Keener, James Sneyd. Mathematical Physiology. Vol II: Systems Physiology, Chapter 17, 516-527.
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