Instructor: Hao Wang


Office: CAB 539

Office Hours:

11:00AM - 12:30PM

Tuesday & Thursday

or by appointment

MATH 371 Q1

Mathematical Modeling in the Life Sciences

Winter Term, 2018

Classroom: CAB 281

Time: 9:30AM - 10:50AM

Tuesday & Thursday

Jan 8 - Apr 13, 2018

TEXTBOOK: A Course in Mathematical Biology, by G de Vries, T Hillen, M Lewis, J Mueller, B Schoenfisch. SIAM Publishing, Philadelphia, 2006.




COURSE DESCRIPTION: Model development, computation, and analysis for problems in the life sciences. Models include discrete-time models and differential equation models. Model evaluation and prediction. Applications are chosen from epidemiology, ecology, population biology, physiology, and medicine.


EXAMINATIONThe Midterm exam will be given in class on February 27, Tuesday.


HOMEWORK ASSIGNMENTS: The assignment problems will be posted in class and on my MATH 371 website. Late assignments will not be marked and a grade of zero will be assigned.


GRADING: Assignments and class participation (30%), Midterm (30%), Final presentation (10%), Final project (30%).


An overall course mark of 60% or more guarantees a passing grade of at least D.



Chapter 1. Introduction

Chapter 2. Discrete-Time Models

Chapter 3. Ordinary Differential Equations

Chapter 4. Partial Differential Equations

Chapter 5. Parameter Estimation




Final presentation schedule:

April 5: Group 1, Group 2, Group 3, Group 4

April 10: Group 5, Group 6, Group 7 (30 mins)

April 12: Group 8, Group 9, Group 10


Final presentations are given on April 5, April 10, April 12. Each group gives a 20-min presentation, however, Group 7 with four members will give a 30-min presentation. Please send me your presentation file before 9:00PM in the previous day.


Matlab sessions in NRE 2-125 from 9:30AM to 10:50AM on March 6 and 8


Group assignment for the final project


Please think of selecting a topic from Chapter 9 of textbook or any research topic relevant to my publications (see my website) for your final project:

Lemming project:
[1] (with Yang Kuang), Alternative models for moss-lemming dynamics, Mathematical Biosciences and Engineering, Vol. 4: 85-99 (2007).
[10] Revisit brown lemming population cycles in Alaska: examination of stoichiometry, IJNAM-B, Vol. 1: 93-108 (2010).

Indirectly transmitted infectious disease project:
[4] (with Richard I. Joh, Howie Weiss, Joshua S. Weitz), Dynamics of indirectly transmitted infectious diseases with immunological threshold, Bulletin of Mathematical Biology, Vol. 71: 845-862 (2009).
[23] (with Jude D. Kong, William Davis), Dynamics of a cholera transmission model with immunological threshold and natural phage control in reservoir, Bulletin of Mathematical Biology, Vol. 76: 2025-2051 (2014).
[25] (with Jude D. Kong, William Davis, Xiong Li), Stability and sensitivity analysis of the iSIR model for indirectly transmitted infectious diseases with immunological threshold, SIAM Journal on Applied Mathematics, Vol. 74: 1418-1441 (2014).
[33] (with Jinhuo Luo, Jin Wang), Seasonal forcing and exponential threshold incidence in cholera dynamics, Discrete and Continuous Dynamical System Series B, Vol. 22: 2261-2290 (2017).

Coral reef and refuge project:
[5] (with Wendy Morrison, Abhinav Singh, Howie Weiss), Modeling inverted biomass pyramids and refuges in ecosystems, Ecological Modelling, Vol. 220: 1376-1382 (2009).
[13] (with Abhinav Singh, Wendy Morrison, Howie Weiss), Modeling fish biomass structure at near pristine coral reefs and degradation by fishing, Journal of Biological Systems, Vol. 20: 21-36 (2012).
[22] (with Xiong Li, Zheng Zhang, Alan Hastings), Mathematical analysis of coral reef models, Journal of Mathematical Analysis and Applications, Vol. 416: 352-373 (2014).
[39] (with Silogini Thanarajah, Philippe Gaudreau), Refuge-mediated predator-prey dynamics and biomass pyramids, Mathematical Biosciences, Vol. 298: 29-45 (2018).

Stoichiometry project:
[9] (with Xiong Li), A stoichiometrically derived algal growth model and its global analysis, Mathematical Biosciences and Engineering, Vol. 7: 825-836 (2010).
[24] (with Angela Peace, Yang Kuang), Dynamics of a producer-grazer model incorporating the effects of excess food-nutrient content on grazerí»s growth, Bulletin of Mathematical Biology, Vol. 76: 2175-2197 (2014).

Bacterial movement project:
[18] (with Silogini Thanarajah), Competition of motile and immotile bacterial strains in a petri dish, Mathematical Biosciences and Engineering, Vol. 10: 399-424 (2013).

Industrial pollution project:
[19] (with Qihua Huang, Laura Parshotam, Caroline Bampfylde, Mark A. Lewis), A model for the impact of contaminants on fish population dynamics, Journal of Theoretical Biology, Vol. 334: 71-79 (2013).
[26] (with Qihua Huang, Mark A. Lewis), The impact of environmental toxins on predator-prey dynamics, Journal of Theoretical Biology, Vol. 378: 12-30 (2015).

Species invasion project:
[29] (with Qihua Huang, Anthony Ricciardi, Mark A. Lewis), Temperature- and turbidity-dependent competitive interactions between invasive freshwater mussels, Bulletin of Mathematical Biology, Vol. 78: 353-380 (2016).

Project Guidelines

Final report should be in a standard report format. Final report in presentation format (slides) is NOT acceptable.

3 students per group. Each group submits one report, but all group members need to present some parts in the final presentation.

Data fitting guidance:

Data fitting simulations Math 371

Matlab sample programs:

Matlab Tutorial

Matlab Course

The program for a system of two difference equations: TwoDifferenceEquations.m

The programs for a system of three differential equations: rigid.m and ThreeDifferentialEquations.m

(please save both files in the same folder and run ThreeDifferentialEquations.m to obtain results. Here,

rigid.m defines the model and ThreeDifferentialEquations.m compute and plot the solution.)

The toolbox program for a system of two differential equations to plot a user-friendly phase plane: pplane10.m

The program for a scalar PDE: SinglePDE.m

The program for a system of two PDEs: TwoPDEs.m

The programs for data fitting using the central difference derivative approximation:

CentralDifferenceDerivativeApprox.mlv.m, and lvSolve.m

The programs for data fitting using the direct least-square method:

lvpe.mlverr.m, and LeastSqaureDataFitting.m


Assignment #1: Ex 1.4.1(a)(b)(c)(d), Ex 2.4.5, Ex 2.4.8, Ex 2.4.10(a)(b), Ex 2.4.15, Ex 2.4.16, Ex 2.4.18, Ex 2.4.19(a)(b), Ex 3.9.3, Ex 3.9.4, Ex 3.9.5 (a), Ex 3.9.6(a)(b)(c)

(Due date: February 15, Thursday)

Solution to Assignment #1

Assignment #2: Ex 3.9.12, Ex 3.9.7, Ex 3.9.8, Ex 3.9.9, Ex 3.9.10, Ex 3.9.11, Ex 3.9.16, Ex 3.9.17, Ex 4.5.1, Ex 4.5.2, Ex 4.5.5(a)(b)

(Due date: April 5, Thursday)

Final project report is due in class on April 12 (the last lecture).

Solution to Assignment #2