| Monday: EA 285 |
Wednesday: BE 134A |
Friday: BE 134A |
| Mar 30
Chemical Kinetics
Mass action law
Michaelis-Menten and Hill type kinetics
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Apr 1
Basic ODE thoery
existence
uniqueness by successive iterations
examples
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Apr 3
Stability of steady state for one ODE
Phase portraits in the plane
Nullclines and Bistability
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| Apr 6
Runge Kutta Method
Solving f(x)=0
Computation: XPPAUT introduction
Math865L_example1.ode
Math865L_example2.ode
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Apr 8
Bifurcation diagram
Bistability and hystereris
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Apr 10
Hopf bifurcation
Singular perturbation
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| Apr 13
Computation:
XPPAUT for computing bifurcation diagrams
Computation: XPPAUT introduction II
Math865L_example3.ode
Math865L_example4.ode
Math865L_example5.ode
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Apr 15
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 17
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 20
Numerical experiments of virus dynamics, SIR, and SEIR
Computation: XPPAUT introduction III
Math865L_example6.ode
Math865L_example7.ode
Math865L_example8.ode
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Apr 22
Cell cycle
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Apr 24
The Goldbetter model
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| Apr 27
Simulation of the Goldbeter model
Computation: XPPAUT introduction IV
Math865L_example9.ode
Math865L_example10.ode
Math865L_example11.ode
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Apr 29
Reaction Diffusion equations
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May 1
Hyperbolic systems
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| May 4
Simulation for parabolic and hyperbolic equations
Matlab pdepe help
pdex1.m
pdex4.m
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May 6
Free boundary Problem
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May 8
A Viral therapy of tumor; A mathematical model
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| May 11
Simulations for viral therapy of tumor
Wang_Tian_paper_ex1_array.m
tridiagSolve.m
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May 13
Cell differentiation; the Yates-Callard-Stark (YCS) model of Th0 differentiation into Th1 and Th2
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May 15
Cell differentiation (continued), asymptotic behaviour
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| May 18
Numerical simulation for cell differentiation
Codes
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May 20
Tumor model with several cell types
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May 22
A model of radially symmetric tumor and it stationary solution
Stability/instability of the stationary solution
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| May 25
Memorial Day: no class
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May 27
Computation of Tumor Model
Tumor.m
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May 29
Introduction on how to present final project
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| Jun 1
Presentation by Ying Wang and Jeong Sook Im
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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Jun 3
Presentation by Shu Su and Justin Wiser
Project II: Math. Biol.Modeling immunotherpy of the tumor--immune iteraction by Denise Kirschner and John Carl Panetta, J. (1998)37: 235-252
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Jun 5
Presentation by Jim Adduci and Ozge Ozcakir
Project III: A mathematical model for collagen fibre formation during foetal and adult dermal wound healing by 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
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Jun 10
(Jun 11 Thursday: BE 134A, 11:30pm-1:18pm)
Presentation by Jung Eun Kim and Hao Ying
Project IV: SEIRS Model, Implusive Vaccination of an SEIRS Model with Time Delay and Varying Total Population Size by Shujing Gao, Lansun Chen and Zhidong Teng, Bulletin o Mathematical Biology (2007) 69:731-745
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Jun 12
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Project V: A Delay Differential Model for Pandemic Influenza with Antiviral Treatment by Murray E. %%%Alexander, Seyed M. Moghadas, Gergely Rost, Jianhong Wu, Bulletin of Mathematical Biology (2008) 70:% 382-397
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