Daniel Kim Shelby Hassberger

Taylor GuffeyHarry Han

Lauren MorganElizabeth Morris

Rachel PatelRadu Reit

ZOMBIFICATION!

BackgroundOriginated in the Afro-Caribbean spiritual belief

system (a.k.a Voodoo) Modern Zombies follow a standard:

Are mindless monsters Do not feel pain Immense appetite for human flesh Aim is to kill, eat or infect peopleFast-moving

Problem StatementDevelop a mathematical model illustrating what

would happen if a Rage epidemic began at the primate facility at Emory University.

Identify an optimal, and the most scientifically plausible strategy for keeping the spread of zombies under control.

ClassificationFive classes

Susceptibles (S): Individuals capable of being infected Immune (I): Individuals incapable of being infectedZombies (Z): Infected, symptomatic individualsCarriers (C): Infected, asymptomatic individualRemoved (R): Deceased (both infected and

uninfected) incapable of being resurrected*

One-minute infection rate Infections:

Immunity exists Only Susceptible humans can become Zombies or Carriers Asymptomatic Carriers and Zombies can infect Susceptibles The Removed cannot be infected and resurrected Every Susceptible has the same chance of becoming infected

(regardless of demographics) Means of Removal:

Zombies can die of starvation Immune and Carriers can be eaten Susceptibles cannot be eaten, only infected

Heterochromia Iridium determines Carrier class Carriers < 250,000

Rage Virus Assumptions

Birthrate = Deathrate Constant Population (Closed System)

The United States is modeled as an equally distributed population, without geographic divisions

Jurisdiction is restricted to the United States, so strategies can only be implemented within the U.S.

General Model Assumptions

Basic Model

dqZ

I C

S Z R

αSZ + g1SC

βSZ + g2SC dqZ

bIZ

bCZ

Assumptions• Susceptibles can become a Zombie through infection by a Zombie or a Carrier• Zombies are infected, symptomatic individuals• Some Susceptibles may never be infected• b is the rate at which one Zombie will defeat (in this case infect) one individual in dayFormulaS Z = βSZ + g2SC

Valuesb = 0.0017g2= 2.00 E -5

I C

S Z R

αSZ + g1SC

βSZ + g2SC dqZ

bIZ

bCZ

Assumptions• Susceptibles can become a Carrier through infection by a Zombie or a Carrier• Carriers are infected, asymptomatic individuals

Valuesa = .000001g1= 1.67 E -8

FormulaS C = αSZ + g1SC

I C

S Z R

αSZ + g1SC

βSZ + g2SC dqZ

bIZ

bCZ

Assumptions• Zombies decease by starvation • If (I+C) is less than 1 million, zombies die at their natural death rate dq • Of the human population, only Immune and Carriers are factors because they can be eaten• Flesh is the equivalent to food, thus Zombies can die in 3 days from starvation

Valuesdq= 0.033

FormulaZ R = dqZ/(I+C)

I C

S Z R

αSZ + g1SC

βSZ + g2SC dqZ

bIZ

bCZ

Assumptions• b is the rate at which one Zombie will defeat (in this case eat) one Carrier in a day

Valuesb= 0.0017

FormulaC R = βCZ

I C

S Z R

αSZ + g1SC

βSZ + g2SC dqZ

bIZ

bCZ

Assumptions• b is the rate at which one Zombie will defeat (in this case eat) one Immune in a day

Valuesb= 0.0017

FormulaI R = βIZ

Basic Model Equations

S’ = -βSZ - αSZ - g1SC - g2SCZ’ = βSZ + g2SC – dqZC’ = αSZ + g1SC - βCZR’ = βCZ + βIZ + dqZI’ = -βIZ

Basic Model Plot• Susceptibles quickly turn• Zombie population grows sporadically; then Zombies die off• Immune population dies• Removed grows exponentially, and then stabilibizes• Doomsday Scenario

Model With Quarantine

dqZ

I C

S Z R

αSZ + g1SC

βSZ + g2SC

Q

bIZ

bCZ

(dqZ)

qZ(I+C+S)

dqQ

Assumptions

Formula

Valuesq=

Z Q = qZ(C+I+S)

• Immune, Carriers, and Susecptibles all quarantine Zombies at the same rate• Quarantine Zombies cannot escape

I C

S Z R

αSZ + g1SC

βSZ + g2SC

Q

bIZ

bCZ

dqZ

qZ(I+C+S)

dqQ

Assumptions

Formula

Valuesdq= 0.033

Q R = dqQ

• Zombies die in quarantine from starvation

Model With Quarantine EquationsS’ = -βSZ - αSZ - g1SC - g2SCZ’ = βSZ + g2SC + qZ(C+I+S) – dqZC’ = αSZ + g1SC - βCZR’ = βCZ + βIZ + dqZ + dqQQ’ = qZ(C+I+S) - dqQI’ = -βIZ

Model With Quarantine Plot

• The Susceptible Population drops but and then stabilizes• The Immune Population drops but then stabilizes• The Zombie Population grows but is captured and dies out• Removed population grows exponentially, then stabilizes • Humans Survive

Model With Cure

dqZ

I C

S Z R

αSZ + g1SC

βSZ + g2SC

dkZ(I+S+C)

bCZ

bIZ

dqZ

Assumptions

FormulaZ I = dkZ(I+S+C)

Valuesdk=• A cure turns a Zombie into an

Immune

Model With Cure Equations

S’ = -βSZ - αSZ - g1SC - g2SCZ’ = βSZ + g2SC - dqZ – dkZ(C+I+S)C’ = αSZ + g1SC - βCZR’ = βCZ + βIZ + dqZI’ = -βIZ + dkZ(C+I+S)

Model With Cure Plot

• Zombie Population grows, but decreases as they are being cured. However they continue to attack and they eventually starve to death• Susceptible Population is turned•The Immune Population slightly grows as more zombies are cured but eventually dies out•Removed grows exponentially, then stabilizes

Model With Extermination

dqZ+ kZ(I+C+S)

I C

S Z R

αSZ + g1SC

βSZ + g2SC dqZ + k(I+C+S)

bIZ

bCZ

Assumptions

FormulaZ R = dqZ + k(I+C+S)

• The extermination starts after 35 days • All Immunes, Carriers, and Susceptibles are armed

Valuesdq=k=

Model With Extermination Plot

• Zombie Population dies out• Susceptible Population survives at about 50% of original population•The Immune Population slightly decreases •Removed grows exponentially, then stabilizes

Model With Extermination

EquationsS’ = -βSZ - αSZ - g1SC - g2SCZ’ = βSZ + g2SC – dqZ – k(I+C+S)C’ = αSZ + g1SC - βCZR’ = βCZ + βIZ + dqZ + k(I+C+S)I’ = -βIZ

Choosing the ModelAlgorithm: Categories are from a scale of 1-10

0.5 x Number of People Survived + 0.3 x Practicality + 0.2 x Morality behind Treatment < 10

No Treatment: 0.5(0) + 0.3(10) + 0.2(4)= 3.8Quarantine: 0.5(2) + 0.3(5) + 0.2(7)= 3.9Cure: 0.5(0) + 0.3(2) + 0.2(10)= 2.6Extermination: 0.5(6) + 0.3(7) + 0.2(2)= 5.5

Conclusions• Model with Extermination is optimal

• Chose because:1. Most people survived2. Most realistic of the treatments3. Ranked low on morality, but time of crisis

References*will enter later

Questions..?