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The HW problems need to
be turned in. HW due every Tuesday in class. It includes all assignments given in the
previous week (Tues, Thurs).
| Tuesday: 11:00-12:18, Journalism Bldg 0139
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Thursday: 11:00-12:18, 209W 18th Ave 0295 |
| Mar 30 (Spring Classes Begin)
2x2 linear system of ODEs; phase portroit; (L)138-140, (L)181-190
Stability of steady states; (L)141-142
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Apr 1
Numerical solutions of ODE (2x2 system or 2nd order equation)
Handout 1 and HW
Matlab code for directional field
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| Apr 6 Chemostate Problems: bacterial growth, drug deliver
glucose-insulin kinetics, compartment analysis, (L)121-130, (L)143-152
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Apr 8
Numerical method-- example from (L)117-125, 155-156
HW: write the code to solve the system (13 a, 13b) with Kmax = 10, Kn = 1, F = 1, V = 1; C0 = 5; alpha = 0.5 up to t=4, N(0)=5; C(0)=4
main_bacterialgrowth.m
bacterialgrowth.m
main_bacterial_nutrient.m
bacterial_nutrient_eqn.m
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| Apr 13
Population dynamics: logistic and Gompertz growth
Lotka-Volterra model
predator-prey
| Apr 15
Computation models, phase portraits, (L)212-236
HW: (1)Write the code for Gompertz Growth Model in Tumors
dN/dt=r*N, dr/dt = -alpha*r, alpha = 3
Choose several initial conditions for N and r and describe the behaviours of the solutions.
(2) Generate other cases in p.228 figure 6.8(b)-(d) and discuss the solutions
main_logisticgrowth.m
logisticgrowth.m
main_LotkaVolterra.m
LotkaVolterra.m
main_PredatorPrey.m
PredatorPrey.m
figure of PredatorPrey
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| Apr 20
Spread of disease, SIR models (L)242-248
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Apr 22
Numerical Simulations
HW:(1) Choose different parameters to illustrate stable and unstable disease free cases. Demonstrate them numerically and theoretically.
(2)Include the people who may get the disease again after they recover into the model. Discuss how this model is different or the same from the previous model theoretically and numerically.
(3) Write the code for SEIR model and discuss the solutions behaviours as above questions.
main_SIR.m
SIR_eqn.m
main_SIV.m
SIV_eqn.m
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| Apr 27
Chemical Kinetics, Enzyme dynamics, Michaelis-Menton, Hill kinetics, (AF) 18-22
Examples (L)303-308
| Apr 29
Simulation of models
Write a code to simulate the system in p.281 (20a-20e)
Try to pick the coefficients to generate similar behavior shown in Figure 7.3 in p. 280
Explain your work.
main_hum_mos.m
hum_mos_eqn.m
main_chem_kinetics.m
chem_kinetics_eqn.m
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| May 4
Action potential in neurons, Fitghugh-Nagnmo model, (A)475-481 (also (A)317-326 as reference)
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May 6
Simulation of potential in a cell
Fitzhugh-Nagumo Equations
main_potential_eqn.m
potential_eqn.m
main_FitzhughNagumo.m
FitzhughNagumo_eqn.m
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| May 11
Bifurcation, Hopf bifurcation, singular perturbation, (AF)25-33
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May 13
Hopf Bifurcation Simulations
main_Hopf.m
Hopf_eqn.m
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| May 18
Cancer model with three species, proliferation cell, quiescence cell, death cell
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May 20
Numerical simulation of cancer model
Cancer Reference
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| May 25
Modeling the Control of Testosterone Secretion and Chemical Castration, J.D. Murray, Mathematical Biology I: An introduction, third edition, p.244-253 (skip p.248-251)
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May 27
The G1 Checkpoint. J.D. Murray, Mathematical Biology I: An introduction, first edition, p.363--365
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| Jun1
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, p. 430-435
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June 3
AIDS: Modeling the Transmission Dynamics of the Human Immunodeficiency Virus, p.333-341, (option: p.342-p.344)
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| June 8
Final exam week
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June 10
Final exam week
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| Spring commencement
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