ZOMBIFICATION!

1. ZOMBIFICATION! Daniel Kim Shelby Hassberger Taylor Guffey Harry Han Lauren Morgan Elizabeth Morris Rachel Patel RaduReit

2. 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

3. 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.

4. 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*

5. Rage Virus Assumptions • 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

6. General Model 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.

7. Parameters Defined • SZ- Infections of Susceptibles to Zombie per day • SZ- Infections of Susceptibles to Carrier per day • dzZ- Zombie Death by starvation • a- % Zombies infecting Susceptible to Carrier • b- % Zombie infecting Susceptible to Zombie • dz- % Zombie starvation • g1- %Carrier infecting Susceptible to Carrier • g2- %Carrier infecting susceptible to Zombie • q- %Quarantine of zombies

8. Basic Model

9. bIZ I C bCZ αSZ + g1SC S (dqZ)/(I+C) Z R βSZ + g2SC Assumptions Values • 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 eat) one individual in day b= g2= Formula S Z = βSZ + g2SC

10. bIZ I C bCZ αSZ + g1SC S (dqZ)/(I+C) Z R βSZ + g2SC Assumptions Values • Susceptibles can become a Carrier through infection by a Zombie or a Carrier • Carriers are infected, asymptomatic individuals a= g1= Formula S C = αSZ + g1SC

11. bIZ I C bCZ αSZ + g1SC S (dqZ)/(I+C) Z R βSZ + g2SC Assumptions Values • Zombies decease by starvation • If (I+C) is less than 1 million, zombies die at their natural death rate dq dq= Formula Z R = dqZ/(I+C)

12. bIZ I C bCZ αSZ + g1SC S (dqZ)/(I+C) Z R βSZ + g2SC Assumptions Values • Susceptibles can become a Zombie through infection by a Zombie or a Carrier • Some Susceptibles may never be infected b= Formula CR= βCZ

13. bIZ I C bCZ αSZ + g1SC S (dqZ)/(I+C) Z R βSZ + g2SC Assumptions Values • b is the rate at which one Zombie will defeat (in this case eat) one individual in day b= Formula IR= βIZ

14. Basic Model Equations • S’ = -βSZ - αSZ - g1SC - g2SC • Z’ = βSZ + g2SC - dqZ/(C+I) • C’ = αSZ + g1SC - βCZ • R’ = βCZ + βIZ + dqZ/(C+I) • I’ = -βIZ

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

16. Model With Quarantine

17. bIZ C I bCZ αSZ + g1SC S R Z (dqZ)/(I+C) βSZ + g2SC Assumptions Values qZ(I+C+S) • Immune, Carriers, and Susecptibles all quarantine Zombies at the same rate • Quarantine Zombies cannot escape b= Q dqQ Formula Z Q = qZ(C+I+S)

18. bIZ C I bCZ αSZ + g1SC S R Z (dqZ)/(I+C) βSZ + g2SC Assumptions Values qZ(I+C+S) • Zombies die in quarantine from starvation dq= Q dqQ Formula QR = dqQ

19. Model With Quarantine Equations • S’ = -βSZ - αSZ - g1SC - g2SC • Z’ = βSZ + g2SC + qZ(C+I+S) - dqZ/(C+I) • C’ = αSZ + g1SC - βCZ • R’ = βCZ + βIZ + dqZ/(C+I) + dqQ • Q’ = qZ(C+I+S) - dqQ • I’ = -βIZ

20. 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

21. Model With Cure

22. bIZ I C bCZ αSZ + g1SC S Z R βSZ + g2SC (dqZ)/(I+C) Values Assumptions dkZ(I+S+C) dk= • A cure turns a Zombie into an Immune Formula Z I = dkZ(I+S+C)

23. Model With Cure Equations • S’ = -βSZ - αSZ - g1SC - g2SC • Z’ = βSZ + g2SC - dqZ – dkZ(C+I+S) • C’ = αSZ + g1SC - βCZ • R’ = βCZ + βIZ + dqZ • I’ = -βIZ + dkZ(C+I+S)

24. 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

25. Conclusions

26. References • *will enter later

27. Questions..?