Math 865


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Course Description: Click here for details in a PDF file


Course Syllabus: Click here for details in a PDF file


Course: Mathematical Modeling of Biological Processes


References: (1) Models of Cellular Regulation by Baltazar Aguda and Avner Friedman

bulletHandout: Lecture Notes
bulletOffice Hours: MW and by appointment
bulletGrading: HW(60%),final project and oral presentation(40%)
bullet Policy: Late Homework and project will be no credit.
bulletTentative Schedule: updated regularly


Monday: EA 285 Wednesday: BE 134A Friday: BE 134A
Mar 30

Chemical Kinetics

Mass action law

Michaelis-Menten and Hill type kinetics


Apr 1

Basic ODE thoery


uniqueness by successive iterations



Apr 3

Stability of steady state for one ODE

Phase portraits in the plane

Nullclines and Bistability


Apr 6

Runge Kutta Method

Solving f(x)=0

Computation: XPPAUT introduction



Apr 8

Bifurcation diagram

Bistability and hystereris

Apr 10

Hopf bifurcation

Singular perturbation

Apr 13


XPPAUT for computing bifurcation diagrams

Computation: XPPAUT introduction II





Apr 15

Virus dynamics

Ref: Leenheer & Smith, Virus Dynamics: A Global Analysis

SIAM J. Appl. Math Vol 63, No.4 pp 1313-1327, 2003

Basic reproduction number


Apr 17

Epidemiological models

SIR model

SIER model

Reference book: Mathematical epidemiology by Fred Brauer, Pauline Van den Driessche, Jianhong Wu and Linda J. S. Allen, Springer, 2008


Apr 20

Numerical experiments of virus dynamics, SIR, and SEIR

Computation: XPPAUT introduction III




Apr 22

Cell cycle

Apr 24

The Goldbetter model

Apr 27

Simulation of the Goldbeter model

Computation: XPPAUT introduction IV




Apr 29

Reaction Diffusion equations

May 1

Hyperbolic systems

May 4

Simulation for parabolic and hyperbolic equations

Matlab pdepe help



May 6

Free boundary Problem

May 8

A Viral therapy of tumor; A mathematical model


May 11

Simulations for viral therapy of tumor



May 13

Cell differentiation; the Yates-Callard-Stark (YCS) model of Th0 differentiation into Th1 and Th2

May 15

Cell differentiation (continued), asymptotic behaviour

May 18

Numerical simulation for cell differentiation


May 20

Tumor model with several cell types

May 22

A model of radially symmetric tumor and it stationary solution

Stability/instability of the stationary solution

May 25

Memorial Day: no class

May 27

Computation of Tumor Model


May 29

Introduction on how to present final project

Jun 1

Presentation by Ying Wang and Jeong Sook Im

Project I: first reference: Dictyostelium discoideum: cellular self-organization in an excitable biological medium by Thomas Hofer, Jonathan A. Sherratt and Philip K. Maini, Proc R. Soc Lon. B (1995) 259, 249-257

second reference: Cellular pattern formation during Dictyostelium aggregation by Thomas Hofer, Jonathan A. Sherratt and Philip K. Maini, Physica D 85 (1995) 425-444
Jun 3

Presentation by Shu Su and Justin Wiser

Project II: Math. Biol.Modeling immunotherpy of the tumor--immune iteraction by Denise Kirschner and John Carl Panetta, J. (1998)37: 235-252
Jun 5

Presentation by Jim Adduci and Ozge Ozcakir

Project III: A mathematical model for collagen fibre formation during foetal and adult dermal wound healing by Paul D. Dale , Jonathan A. Sherratt and Philip K. Maini, Proc R. Soc Lond B (1996) 263, 653-660
Jun 8

Jun 10

(Jun 11 Thursday: BE 134A, 11:30pm-1:18pm)

Presentation by Jung Eun Kim and Hao Ying

Project IV: SEIRS Model, Implusive Vaccination of an SEIRS Model with Time Delay and Varying Total Population Size by Shujing Gao, Lansun Chen and Zhidong Teng, Bulletin o Mathematical Biology (2007) 69:731-745

Jun 12

Project V: A Delay Differential Model for Pandemic Influenza with Antiviral Treatment by Murray E. %%%Alexander, Seyed M. Moghadas, Gergely Rost, Jianhong Wu, Bulletin of Mathematical Biology (2008) 70:% 382-397