Vampires & Humans…

Can They Co-exist?Caitlin Bryant

&Jennifer Davis

OutlinePurposeAssumptionsVariables and ParametersEquations and GraphsSensitivity AnalysisFuture ImprovementsSources

PurposeTo see if vampires exist in our world today.

AssumptionsGrowth rate of humans remains constantVampires only drink blood for nourishmentMust consume 1 tbsp. of blood every 2 weeks2 humans killed every 2 weeks (food & fun)At least one vampire slayerVampires want their population to remain the sameHumans are only turned if a vampire is slainAge of initial human population over 18All vampires in Atlanta are members of the AVAVampires only kill the bad guys

VariablesS: # of susceptible humansV: # of vampires

Parametersr: growth rate of humans = .0562h: rate humans are turned into vampires = .02m: rate of humans bitten and killed = 1c: rate of vampires being slain = .01q: rate of ‘hungry’ vampires = 1a: carrying capacity for vampires = 1

Motivation for our Equations:

Equations and Graphs

The NumbersInitial Population of humans : 400,000 adults

in AtlantaInitial Vampire Population: 1% of population

are members of AVATherefore:

S(0) = 100V(0) = .01

Can we Coexist??

Humans VS Vampires

Fixed Points

S = 112.399 V = .0551577

-0.0619969 + 0.228682i -0.0619969 – 0.228682i

Eigen values

Our fixed points are stable so…humans and vampires can coexist!

Sensitivity Analysis on ‘c’

How many vampires should slayers kill a year?

Between -1 and .0562 We chose c = .01 Based on c, h = .02

What if there are no vampires? Parameter values,

fixed points, & eigen values all remain the same.

Now V(0) = 0

What if there are no humans?

Now S(0) = 0 Vampires die off.

Need for Slayers? To determine if we need

slayers we let S = 100 and V = .01.

But now, c = 0, and therefore h = 0.

The fixed points become S = 0 and V = 0 (no humans and no vampires exist)

The answer is yes! We do need vampire slayers!

Future Improvements: Consider vampires that feed of other animals

besides humans. What if other nondead creatures exist?

Werewolves? Zombies?

Conclusion It is possible for

vampires to exist. Now we know they

need us, but we don’t need them!

Believe what you wish…

Sources• birth rate from http://www.infoplease.com/ipa/A0005067.html• death rate from:

http://www.indexmundi.com/united(underscore)states/death(underscore)rate.html

• vampire need 1 tablespoon every two weeks, so 26 tablespoons of blood a year:http://www.freewebs.com/lastbloodfaq/

• http://wiki.answers.com/Q/How(underscore)many(underscore)tablespoons(underscore)are(underscore) n(underscore)a(underscore)pint

• 32 tablespoons in a pint http://wiki.answers.com/Q/How(underscore)much(underscore)blood(underscore)is(underscore)in(underscore)the(underscore)human(underscore)body 10 pints of blood in a human

• Atlanta population http://www.infoplease.com/us/census/data/georgia/atlanta/demographic.html

• http://www.atlantavampirealliance.com/missionfaq.html