One of our key strengths as a small consultancy is the people that work here and their personalities. We know that our customers enjoy working with us because they can get to know us as a whole and the individual consultants working on their project. We also know that there is no place to hide so the best candidates are able to think for themselves, be passionate about what they do and have a personality that fits in with the team. This is why, as part of our second interview stage we ask candidates to give us a presentation about something that interests them. Greg Olenski, who joined the team in Spring 2016 combined his love of data analysis with his even greater love of zombies to show us what would happen if there was a Zombie outbreak in our home of Wakefield.
So this is what Greg presented to us ‘ A Mathematical Model of the Zombie Apocalypse.’ How long would you survive?
Introduction
What is a Zombie
?
- Oxford English Dictionary:
- A corpse revived by witchcraft;
- A reanimated corpse that feeds on human flesh.
- Origins of the word?
- Caribbean term for ghost, “Jumbie;
- Congolese for spirit of a dead person, “Nzambi”;
- Creole for someone who has died and come back to life without speech or free will, “Zonbi”.
- How to model the Zombie Apocalypse?
- Humans can be infected by:
- A zombie bite or scratch;
- Dying and reanimating as a zombie.
- Zombies can be killed by destroying the brain stem
The Model
- Parameters
- Rate at which H are turned to Z (α)
- Rate at which Z are R (β)
- Reanimation rate (ρ)
- Death Rate (δ)
- Classes:
- Humans (H)
- Zombies (Z)
- Dead (D)
- Removed (R)
- Equations
- H′= – αHZ – δH
- Z′ = αHZ + ρD – βHZ
- D′ = δH – ρD
- R′ = βHZ
-
The Model: Calibration
- In “reality” parameters α, β, ρ, δ estimated by observational data
- α > β (at least in short run) for following reasons:
- Element of surprise;
- Insufficient knowledge;
- Moral and compassionate grounds.
The Model: Equilibrium Conditions
- ¢Recall equations:
- H′= – αHZ – δH = 0
- Z′ = αHZ + ρD – βHZ = 0
- D′ = δH – ρD = 0
- R′ = βHZ = 0
- ¢If H = 0, doomsday equilibrium scenario:
- ¢If Z = 0, zombie free equilibrium scenario:
- Human-Zombie coexistence impossible!
Dawn breaks over Wakefield, West Yorkshire
- Wakefield, initial population H = 325,000, Z = 1
- Choose α such that initially ~3 humans turn to zombies per zombie per day.
- ODEs solved in Excel using Euler’s Method.
How the Zombie attack unfolded over 2 weeks
The zombie outbreak leads to the collapse of the human population in Wakefield within nine days.
- Small number of survivors;
- Parameters likely to change in longer run.
Can extend the model to include:
- Latent infection;
- Quarantine;
- Vaccine;
- Longer time period.
Further Conclusions
- Demonstrates flexibility of mathematical modelling;
- Shows the insight gained from analysis.
With thanks to
Munz et al. “When Zombies Attack!:
Mathematical Modelling of an Outbreak of Zombie Infection”
Infectious Disease Modelling Research Progress 2009, pp. 133-150 Nova Science Publishers, Inc.
And also thanks to Ben and his team at Authentic Recruitment for encouraging an engaging, exciting and different presentation that fit the brief.
