| MWF Jennings Hall 050 |
| Mar 28
Chemical Kinetics
Mass action law
|
Mar 30
Michaelis-Menten and Hill type kinetics
|
Apr 1
Computation:
Euler's method: Consistency, Stability, Convergence
|
| Apr 4
Basic ODE thoery
existence
uniqueness by successive iterations
examples
|
Apr 6
Stability of steady state for one ODE
Phase portraits in the plane
Nullclines and Bistability
|
Apr 8
Computation:
forward and backward Euler's method code: test_euler.m
code: test_euler2.m
|
| Apr 11
Epidemiological models
SIR model
SIER model
|
Apr 13
Chemostats and Competing Populations
|
Apr 15
Computation:
solve roots of nonlinear systems
Matlab built-in function: fzero, fsolve, meshgrid, contour, gradient, quiver
|
|
Apr 18
Computation:
Numerical methods for solving eigenvalue problems
|
Apr 20
Bifurcation
|
Apr 22
Computation:
Bifurcation diagram
|
| Apr 25
Hopf Bifurcation
|
Apr 27
Singular Perturbation
Neuronal Oscillation
|
Apr 29
Computation:
Bistability and hystereris
Hopf bifurcation
Singular perturbation
code: main_potential_eqn.m
code: potential_eqn.m
code: main_FitzhughNagumo.m
code: FitzhughNagumo_eqn.m
|
| May 2
Hyperbolic systems
|
May 4
Neurofilaments Transport in Axon
|
May 6
Computation:
Simulation for hyperbolic equations
code: main_Upwind_LF.m
code: flux.m
code: exact1.m
code: bd1.m
code: IC1.m
|
| May 9
Diffusion Equations
|
May 11
Wound Healing
|
May 13
HW: Problem 11.4
Computation:
Simulation for diffusion equations
Matlab pdepe help
pdex1.m
pdex4.m
|
| May 16
Cancer
|
May 18
Cancer therapy
|
May 20
HW: 12.2
Computation:
Numerical simulation for wound healing
main_woundhealing.m
flux1_wound.m
|
| May 23
Project I (Nianpeng Li, Moussa Doumbia)
Combining cytokine signalling with T-bet and GATA-3 regulation in
Th1 and Th2 differentiation: a model for cellular decision-making by Andrew Yates, robin Callard, Jaroslav Stark, Journal of Theoretical Biology, 231 (2004), p.181-196
Models of Cellular Regulation by Baltazar D. Aguda and Avner Friedman, Oxford Graduate Texts<, p.127-133/p>
|
May 25
Project II (Oyita Udiani)
A mathematical model for chronic myelogenous leukemia (CML) and
T cell interaction by Helen Moore and Natasha K. Li
Leukocytes. James Keener, James Sneyd. Mathematical Physiology. Vol II: Systems Physiology, Chapter 16, 495-507.
|
May 27
HW: 14.2, 14.3
Computation:
Cancer therapy simulation
CancerTherapy.m
tridiagSolve.m
|
| May 30
Memorial Day: no class
|
Jun 1
Project III (Leah Campbell)
Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: a mathematical model and experiments by Yangjin Kim, Julie Wallace, Fu Li, Michael Ostrowski, and Avner Friedman, Journal of Mathematical Biology, 61 (2010), p.401-421
|
Jun 3
Project IV (Kyle Frank)
A mathematical analysis of the dynamics of prion proliferation by Meredith L. Greer, Laurent Pujo-Menjouet, Glenn F. Webb, Journal of Theoretical Biology, 242, 3, (2006), p.598-606
|
|
Project VII
|
Jun 7
(Jun 7 Tuesday: Jennings hall 050 , 9:30am -11:18am)
Project V (Laine Noble)
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 VI (Noah Brostoff)
Essential mathematical Biology by Nicholas F. Britton, Chapter 5.6,Traveling Waves Solutions of General Reaction-diffusion Equations, p.164-173
|
|
