Monday: EA 285 
Wednesday: BE 134A 
Friday: BE 134A 
Mar 30
Chemical Kinetics
Mass action law
MichaelisMenten and Hill type kinetics

Apr 1
Basic ODE thoery
existence
uniqueness by successive iterations
examples

Apr 3
Stability of steady state for one ODE
Phase portraits in the plane
Nullclines and Bistability

Apr 6
Runge Kutta Method
Solving f(x)=0
Computation: XPPAUT introduction
Math865L_example1.ode
Math865L_example2.ode

Apr 8
Bifurcation diagram
Bistability and hystereris

Apr 10
Hopf bifurcation
Singular perturbation

Apr 13
Computation:
XPPAUT for computing bifurcation diagrams
Computation: XPPAUT introduction II
Math865L_example3.ode
Math865L_example4.ode
Math865L_example5.ode

Apr 15
Virus dynamics
Ref: Leenheer & Smith, Virus Dynamics: A Global Analysis
SIAM J. Appl. Math Vol 63, No.4 pp 13131327, 2003
Basic reproduction number

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

Apr 20
Numerical experiments of virus dynamics, SIR, and SEIR
Computation: XPPAUT introduction III
Math865L_example6.ode
Math865L_example7.ode
Math865L_example8.ode

Apr 22
Cell cycle

Apr 24
The Goldbetter model

Apr 27
Simulation of the Goldbeter model
Computation: XPPAUT introduction IV
Math865L_example9.ode
Math865L_example10.ode
Math865L_example11.ode

Apr 29
Reaction Diffusion equations

May 1
Hyperbolic systems

May 4
Simulation for parabolic and hyperbolic equations
Matlab pdepe help
pdex1.m
pdex4.m

May 6
Free boundary Problem

May 8
A Viral therapy of tumor; A mathematical model

May 11
Simulations for viral therapy of tumor
Wang_Tian_paper_ex1_array.m
tridiagSolve.m

May 13
Cell differentiation; the YatesCallardStark (YCS) model of Th0 differentiation into Th1 and Th2

May 15
Cell differentiation (continued), asymptotic behaviour

May 18
Numerical simulation for cell differentiation
Codes

May 20
Tumor model with several cell types

May 22
A model of radially symmetric tumor and it stationary solution
Stability/instability of the stationary solution

May 25
Memorial Day: no class

May 27
Computation of Tumor Model
Tumor.m

May 29
Introduction on how to present final project

Jun 1
Presentation by Ying Wang and Jeong Sook Im
Project I: first reference: Dictyostelium discoideum: cellular selforganization in an excitable biological medium by Thomas Hofer, Jonathan A. Sherratt and Philip K. Maini, Proc R. Soc Lon. B (1995) 259, 249257
second reference: Cellular pattern formation during Dictyostelium aggregation by Thomas Hofer, Jonathan A. Sherratt and Philip K. Maini, Physica D 85 (1995) 425444

Jun 3
Presentation by Shu Su and Justin Wiser
Project II: Math. Biol.Modeling immunotherpy of the tumorimmune iteraction by Denise Kirschner and John Carl Panetta, J. (1998)37: 235252

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, 653660

Jun 8

Jun 10
(Jun 11 Thursday: BE 134A, 11:30pm1:18pm)
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) 69:731745

Jun 12

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:% 382397


