Syllabus: Click here for details in a PDF file Course: Math 350, Introduction to Mathematical Biology, TR 11:00am-12:18pm Texts: Primary textbook: (L) Mathematical Models in Biology by Leah Edelstein-Keshet,SIAM, 2005 Supplementary textbooks: (A) Modeling the Dynamics of Life: Calculus and Probability for Life Scientists by Frederick R. Adler (AF) Modeling of Cellular Regulation by Baltazar D. Aguda and Avner Friedman Topics: Population dynamics, Spread of disease, Competition model, Dynamics of a Neuron, Enzyme Kinetics Office Hours: Chiu-Yen Kao @MW410 by appointment Grading: HW (50%) and final project (50%). The letter grade will be with an approximately 90(A)-80(B)-70(C)-60(D) scale. Policy: NO make-up exams without doctor's excuse. Late Homework will be no credit. Tentative Schedule: updated regularly

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 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 Apr 1 Numerical solutions of ODE (2x2 system or 2nd order equation) Handout 1 and HW Apr 6Chemostate Problems: bacterial growth, drug deliver glucose-insulin kinetics, compartment analysis, (L)121-130, (L)143-152 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 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 Apr 20 Spread of disease, SIR models (L)242-248 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 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 May 4 Action potential in neurons, Fitghugh-Nagnmo model, (A)475-481 (also (A)317-326 as reference) May 6 Simulation of potential in a cell Fitzhugh-Nagumo Equations main_potential_eqn.m May 11 Bifurcation, Hopf bifurcation, singular perturbation, (AF)25-33 May 13 Hopf Bifurcation Simulations main_Hopf.m May 18 Cancer model with three species, proliferation cell, quiescence cell, death cell May 20 Numerical simulation of cancer model Cancer Reference 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) May 27 The G1 Checkpoint. J.D. Murray, Mathematical Biology I: An introduction, first edition, p.363--365 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 June 3 AIDS: Modeling the Transmission Dynamics of the Human Immunodeficiency Virus, p.333-341, (option: p.342-p.344) June 8 Final exam week June 10 Final exam week Spring commencement