MAT 4996: Mathematical Modelling of Zombies (Winter 2012)

Professor: Dr. Robert Smith?

Professor Robert Smith? (the question mark is part of my name) Office 585 King Edward (KED), Room 205 G Phone 562-5800 x3864 Email rsmith43 (at) uottawa.ca Lectures Mondays 2:30-4:00, VNR 5070 Wednesdays 2:30-4:00, VNR 5070 Dates January 9-March 28, 2012 Office hours Mondays after class

Texbook: Braaaiiinnnsss! From Academics to Zombies, edited by Robert Smith?

Syllabus: A formal syllabus can be downloaded from here, although it's almost identical to the first part of this webpage.

Course Content: mathematical models, differential equations, individual-based modelling, zombie swarming, statistical estimation, fuzzy decision-making, network theory, discrete-time models, diffusion of the undead, adaptive strategies for zombie attacks.

We will also look at how modelling can advise government policy, how theoretical results can be communicated to a non-mathematical audience and how models can be formulated with only limited information. By understanding how to combat zombies, students will see an introduction to a wide variety of modelling techniques, which are applicable to other real-world issues (such as diseases, ecology etc) but which engage the imagination.

Course Objectives: Our specific goals for the course as outlined as follows:

1. Illustrate the broad range of mathematical methods to tackle the zombie invasion

2. Learn the skill of gleaning and synthesising the literature to study a particular question.

3. Create mathematical models from non-mathematical descriptions of problems.

4. Interpret the results of models and evaluate their biological implications.

5. Show the necessity of simplification and approximation in models and identify their effects.

Prerequisites: Second-year differential equations. No pre-knowledge in zombie knowledge is assumed, but students must have basic calculus and ordinary differential equations. Other topics will be reviewed in class as we go.

Assessment:

Assignments 10% Midterm 10% Presentations 20% Participation 30% Project 30%

Each week, we will read two chapters from the book (in order). Someone will present an overview of one of the chapters to the class in a 20 minute presentation. (You may do this in groups if you wish.) The remainder of the classtime will be discussing both this and the other chapter.

You are expected to keep up to date with the readings and discuss them in class, whether or not you are formally presenting them that week. As a result, class attendance is mandatory.

Assignments will be posted here, or given in class. One of the assignments will be an essay.

Plagiarism: The university takes plagiarism very seriously. This includes copying other assignments, or reproducing any work from another source without citation.

Note: Any changes or announcements will appear on the course website. You should check the website regularly for updates. Note that I will not answer math questions by email.

Essay: The choice of topic is up to you. It should involve zombies and society in some way. It must discuss the scientific, ethical and sociological implications of your topic. 2000-3000 words. (Draft due Feb 27. Final version due Mar 26. You must hand in your draft with your final essay.)

For the essay, I expect it to be well written. When you get out into the real world (or even if you stay in academia), writing reports is going to be the bread and butter of what you do. There's no getting away from it: writing is the backbone of almost every professional industry. So the more practice you get, the better. This is a good chance to hone your skills. So you should have an introduction, a coherent argument and a conclusion. I cannot emphasise how important this is - or how much it will help you in the long run.

References: Both your essay and your project should have between 12 and 50 academic references (cited in full), in addition to non-academic zombie works or websites. It is crucial to situate your work within the literature.

Project: The final assessment will be a project. This can be done in groups. Your project must be related to mathematical models of zombies, but is otherwise open.

A one-page project proposal must be submitted by January 30.

A one-page outline of the model (with the equations) and the assumptions is due by Feb 13. (Basically, this should be everything preceding the analysis.)

A 20 minute presentation will take place during the last few classes .

Projects are due by the end of semester May 1st. Note that I will be away in April, but please leave them for me at the math department secretariat.

Lectures

Introduction

When Zombies Attack! Mathematical modelling of an outbreak of zombie infection

The Undead: A plague on humanity... or a powerful new tool for epidemiological modelling?

Is it safe to go out yet? Statistical inference in a zombie outbreak model

How long can we survive? Modelling zombie movement with diffusion

When humans strike back! Adaptive strategies for zombie attacks

Is there a zombicidal maniac near you? You'd better hope so!

The Social Zombie: Modelling Undead Outbreaks on Social Networks

Zombie Demographics in the United States

An Evolvable Linear Representation for Simulating Government Policy in Zombie Outbreaks

Zombie Infection Warning System Based on Fuzzy Logic

Assignments

Assignment 1 Due January 25th.

Assignment 1 solutions

Assignment 2 solutions

Assignment 3 solutions

Note: You can work on assignments in groups. Just make sure everyone who worked on the assignment has their name on it. The next few assignments will be given in class rather than on here.

Download a helpful summary sheet that you can use when doing class readings This is a useful way of navigating an academic article so that you understand its arguments and ideas.

Note: These should be handed in every Wednesday. A number of you missed that for Jan 25th (which I announced in class Jan 18th), so I'll consider the first round to be bonus. But they're due each Wednesday.

Announcements

The CBC News item on our class (2 min)

Check your mark! (thus far)

I've calculated the pre-project percentage you're currently sitting on. These are now online on Virtual Campus, so you can check your mark. Please do note that the project is worth 30% so these marks could potentially go up or down, depending on how you do; I've simply taken your mark out of 70 thus far and converted it to a mark out of 100.

On that note, if your mark is low, it's probably because you didn't contribute much in class. Some people contributed a lot and some barely at all. I recorded everyone's degree of participation each week and it varied enormously. Remember that participation was worth 30%! However, so is the project, so you should probably take that as an incentive to do an especially good job on it in order to bring your mark up.

I actually built in quite a few bonus marks, especially around participation, and gave everyone a "free" week (on the basis that you presented one week), so any participation you contributed then was bonus. Thus, some of you are sitting at more than 100%. Congratulations if so! I also counted the reading summaries towards your participation.

Technical note: two people (you know who you are) aren't on Virtual Campus. But you're both sitting at 90 or higher.

Bonus poster

Some people have asked me about earning some bonus marks and suggested a poster. I think that's a great idea, so if you want to do a poster on your project feel free. This would be in addition to your written report, of course.