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Schedule Text books Matlab programs Requirements Links

Mathematical Modeling in Biology and Medicine

  Fall 2012

Lectures: Wednesdays, 
11:00-13:00Ziskind 1
Instructor: Vered Rom-Kedar 

Teaching assistant:   Mary Kloc email: marykloc at gmail.com

Announcements: Notice we are back to the OLD TIME 
Go to MAAA seminars on Tuesdays @ 11:00
 


Various strategies of modeling of biological and medical problems and various mathematical and computational tools for analyzing these models will be presented.

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.



To participate students must have adequate mathematical background :
Calculus 1,2,3, Linear Algebra, Ordinary differential equations and basic partial differential equation undergraduate courses
Basic knowledge and programming in Matlab will be also assumed.  

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
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

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)   

 
Exam  13/2/13 Final assignment
 

Math Biology books and lecture notes:

 Additional reading:

Relevant Journal papers:
Dynamical systems books:

Grades etc

Homework assignments will be given every week  (no late submissions).
There will be an exam.
Grade:  60% homework (best 80%) +  40% exam.

Matlab Programs

rk2  rk4
logistic map  Euler scheme circle map  lorenz lorenz w manifolds  henon pendulum standard map  pendulum w forcing

Links

Online "Labs":

Online courses

Local activities:

 Mathematical Analysis and Applications Seminar