Schedule  Text books  Matlab programs  Requirements  Links 
Massaction kinetics will be first discussed in various biological contexts. Modeling assumptions, scaling, and some qualitative studies of the dynamics will be presented for these problems. We will then use some of these ideas to discuss population dynamics with applications to ecology, cells dynamics, epidemiology and the immune system. These and other methodologies will be utilized to describe some of the current mathematical approaches to cancer modeling.
Date  Topics 
Homework  Reading 
31/10/12 
1. Introduction: motivation, modeling & examples  single species models.  [EK] pg 152154 ex 5,7 
[EK] Ch 4.14.6,
[M] Ch 1 
7/11/12  2. Modeling: nondimensionalization, pi theorem, one dimensional models  [F] Ch 2 and
appendix 2 The Buckingham Pi Theorem 

14/11/12 
3. Population dynamics  axiomatic models, bifurcations, ecology, infections  Homework
2 
[F] Ch 2 and
appendix 2 [p3] [p4] 
21/11/12  4. 2d and nd models, Stability, bifurcations, structural stability and robustness  [EK] pg 154157 ex 13, 14, 25, 26 

28/11/12 
5. Population dynamics  interactions, innate immune system  Find a research paper on MathBiology/Medicine that interests you and uses low dimensional ODE model. Write the ODE model and explain the main assumptions and the main results of the paper. [submit after completing next week assignment]  [M] Ch 3 [p5] [p6] 
5/12/12 
6. Population dynamics  difference equations, chaos  [continuation] Which analytical/computational tools are utilized in the paper? Discuss the robustness of these to inaccuracies in the model (please attach the paper you considered).  [M] Ch 2.22.4 Any of the DS books, most extended exposition Devaney (D). 
12/12/12  7. Population dynamics  spatial effects  partial differential equations approach  Find a research paper on MathBiology/Medicine that interests you and uses a PDE model. Follow the same instructions as above (if possible, find a paper on the same subject as before and compare the results). A twoweeks assignment.  [EK] 
19/12/12  8. Population dynamics  PDEs  Turing instability. Stochastic models (small populations and/or mutations).  [WE]  
26/12/12  9. Population dynamics stochastic models  Find a research paper on MathBiology/Medicine that interests you and uses a stochastic model. Follow the same instructions as above (if possible, find a paper on the same subject as before and compare the results). A twoweeks assignment.  [WE],[p7] and references therein 
2/1/13  10. Mass action kinetics & robustness of networks (one hour lecture)  [M] Ch 5, [p8] , [p2]  
9/1/13  11. Mass action kinetics  
16/1/13  12. Cancer and the innate immune system  Start working on the final assignment, see instructions below  [p1], [p3p6] 
23/1/13  13. Cancer models  review.  [p1], [p9],[p10]  
30/1/13  14. Optimal Control in math
biology models (lecture by Shalev Itzkovitz) 



Exam 13/2/13  Final assignment 
[p2] Design principles for robust biochemical reaction networks:..., G. Shinar, M. Feinberg, 2011.