Daniel Kim Shelby Hassberger Taylor Guffey Harry Han Lauren Morgan Elizabeth Morris Rachel Patel Radu Reit ZOMBIFICATIO N!

Background Originated 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 people Fast-moving

Problem Statement Develop 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.

Classification Five classes Susceptibles (S): Individuals capable of being infected Immune (I): Individuals incapable of being infected Zombies (Z): Infected, symptomatic individuals Carriers (C): Infected, asymptomatic individual Removed (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 dqZdqZ

IC S Z R αSZ + g 1 SC βSZ + g 2 SC dqZdqZ  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 infect) one individual in day Formula S Z = βSZ + g 2 SC Values  = g 2 = 2.00 E - 5

I C S Z R αSZ + g 1 SC βSZ + g 2 SC dqZdqZ  IZ  CZ Assumptions Susceptibles can become a Carrier through infection by a Zombie or a Carrier Carriers are infected, asymptomatic individuals Values  = g 1 = 1.67 E - 8 Formula S C = αSZ + g 1 SC

IC S Z R αSZ + g 1 SC βSZ + g 2 SC dqZdqZ  IZ  CZ Assumptions Zombies decease by starvation If (I+C) is less than 1 million, zombies die at their natural death rate d q 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 Values d q  Formula Z R = d q Z/(I+C)

IC S Z R αSZ + g 1 SC βSZ + g 2 SC dqZdqZ  IZ  CZ Assumptions  is the rate at which one Zombie will defeat (in this case eat) one Carrier in a day Values  Formula C R = βCZ

I C S Z R αSZ + g 1 SC βSZ + g 2 SC dqZdqZ  IZ  CZ Assumptions  is the rate at which one Zombie will defeat (in this case eat) one Immune in a day Values  Formula I R = βIZ

Basic Model Equations S’ = -βSZ - αSZ - g 1 SC - g 2 SC Z’ = βSZ + g 2 SC – d q Z C’ = αSZ + g 1 SC - βCZ R’ = βCZ + βIZ + d q Z I’ = -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 dqZdqZ

I C S Z R αSZ + g 1 SC βSZ + g 2 SC Q  IZ  CZ (d q Z) qZ(I+C+S) dqQdqQ Assumpti ons Formula Values q= 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 + g 1 SC βSZ + g 2 SC Q  IZ  CZ dqZdqZ qZ(I+C+S) dqQdqQ Assumpti ons Formula Values d q = Q R = d q Q Zombies die in quarantine from starvation

Model With Quarantine Equations S’ = -βSZ - αSZ - g 1 SC - g 2 SC Z’ = βSZ + g 2 SC + qZ(C+I+S) – d q Z C’ = αSZ + g 1 SC - βCZ R’ = βCZ + βIZ + d q Z + d q Q Q’ = qZ(C+I+S) - d q Q I’ = -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 dqZdqZ

I C S Z R αSZ + g 1 SC βSZ + g 2 SC d k Z(I+S+C)  CZ  IZ dqZdqZ Assumpti ons Formula Z I = d k Z(I+S+C) Values dk=dk= A cure turns a Zombie into an Immune

Model With Cure Equations S’ = -βSZ - αSZ - g 1 SC - g 2 SC Z’ = βSZ + g 2 SC - d q Z – d k Z(C+I+S) C’ = αSZ + g 1 SC - βCZ R’ = βCZ + βIZ + d q Z I’ = -βIZ + d k Z(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 d q Z+ kZ(I+C+S)

I C S Z R αSZ + g 1 SC βSZ + g 2 SC d q Z + k(I+C+S)  IZ  CZ Assumpti ons Formula Z R = d q Z + k(I+C+S) The extermination starts after 35 days All Immunes, Carriers, and Susceptibles are armed Values d q= 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 Equations S’ = -βSZ - αSZ - g 1 SC - g 2 SC Z’ = βSZ + g 2 SC – d q Z – k(I+C+S) C’ = αSZ + g 1 SC - βCZ R’ = βCZ + βIZ + d q Z + k(I+C+S) I’ = -βIZ

Choosing the Model Algorithm: Categories are from a scale of x Number of People Survived x Practicality x Morality behind Treatment < 10 No Treatment: 0.5(0) + 0.3(10) + 0.2(4)= 3.8 Quarantine: 0.5(2) + 0.3(5) + 0.2(7)= 3.9 Cure: 0.5(0) + 0.3(2) + 0.2(10)= 2.6 Extermination: 0.5(6) + 0.3(7) + 0.2(2)= 5.5

Conclusions Model with Extermination is optimal Chose because: 1.Most people survived 2.Most realistic of the treatments 3.Ranked low on morality, but time of crisis

References *will enter later

Questions..?