ZOMBIFICATION!

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

Parameters Defined g1- %Carrier infecting

Susceptible to Carrier

g2- %Carrier infecting susceptible to Zombie

q- %Quarantine of zombies

SZ- Infections of Susceptibles to Zombie per day

SZ- Infections of Susceptibles to Carrier per day

dzZ- Zombie Death by starvation

- % Zombies infecting Susceptible to Carrier

- % Zombie infecting Susceptible to Zombie

dz- % Zombie starvation

Basic Model

I C

S Z R

αSZ + g1SC

βSZ + g2SC (dqZ)/(I+C)

IZ

CZ

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• is the rate at which one Zombie will defeat (in this case eat) one individual in dayFormulaS Z = βSZ + g2SC

Values=g2=

I C

S Z R

αSZ + g1SC

βSZ + g2SC (dqZ)/(I+C)

IZ

CZ

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

Values=g1=

FormulaS C = αSZ + g1SC

I C

S Z R

αSZ + g1SC

βSZ + g2SC (dqZ)/(I+C)

IZ

CZ

Assumptions• Zombies decease by starvation • If (I+C) is less than 1 million, zombies die at their natural death rate dq

Valuesdq=

FormulaZ R = dqZ/(I+C)

I C

S Z R

αSZ + g1SC

βSZ + g2SC (dqZ)/(I+C)

IZ

CZ

Assumptions• Susceptibles can become a Zombie through infection by a Zombie or a Carrier• Some Susceptibles may never be infected

Values=

FormulaC R = βCZ

I C

S Z R

αSZ + g1SC

βSZ + g2SC (dqZ)/(I+C)

IZ

CZ

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

Values=

FormulaI R = βIZ

Basic Model Equations

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

Basic Model Plot• Susceptibles quickly turn• Zombie population grows sporadically; then Zombies die off• Immune population remains constant• Removed grows exponentially• =Doomsday

Model With Quarantine

I C

S Z R

αSZ + g1SC

βSZ + g2SC

Q

IZ

CZ

(dqZ)/(I+C)

qZ(I+C+S)

dqQ

Assumptions

Formula

Values=

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

IZ

CZ

(dqZ)/(I+C)

qZ(I+C+S)

dqQ

Assumptions

Formula

Valuesdq=

Q R = dqQ

• Zombies die in quarantine from starvation

Model With Quarantine Equations

S’ = -βSZ - αSZ - g1SC - g2SCZ’ = βSZ + g2SC + qZ(C+I+S) - dqZ/(C+I)C’ = αSZ + g1SC - βCZR’ = βCZ + βIZ + dqZ/(C+I) + 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

Model With Cure

I C

S Z R

αSZ + g1SC

βSZ + g2SC

dkZ(I+S+C)

CZ

IZ

(dqZ)/(I+C)

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 grow exponentially

Conclusions

References*will enter later

Questions..?