Schedule | Text books | Matlab programs | Requirements | Links |
Mass-action 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 152-154 ex 5,7 |
[EK] Ch 4.1-4.6,
[M] Ch 1 |
7/11/12 | 2. Modeling: non-dimensionalization, pi theorem, one dimensional models | [F] Ch 2 and
appendix 2 The Buckingham Pi Theorem |
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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 154-157 ex 13, 14, 25, 26 |
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28/11/12 |
5. Population dynamics - interactions, innate immune system | Find a research paper on Math-Biology/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 2.2-2.4 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 Math-Biology/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 two-weeks 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 Math-Biology/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 two-weeks 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], [p3-p6] |
23/1/13 | 13. Cancer models - review. | [p1], [p9],[p10] | |
30/1/13 | 14. Optimal Control in math
biology models (lecture by Shalev Itzkovitz) |
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Exam 13/2/13 | Final assignment |
[p2] Design principles for robust biochemical reaction networks:..., G. Shinar, M. Feinberg, 2011.