PDF Problem III - Langley-Tucker - D1 - Cobras

Problem III Technical Paper – BMED 1300 – December 6, 2013 – Langley/Tucker D1 Cobras 1
Abstract — For a zombie outbreak, as is true for most
epidemics as well as generalized natural or man-made
disasters, preventative measure, efficiency, and speed of
response time are key factors in minimizing cost and loss of
property or life. After running a slightly expanded SIR model
accounting for ability of susceptible individuals to either
escape or die instead of being only removed, decreased
success rate for infected individuals to propagate the disease
quickly enough to overcome their innate death rate from
susceptible-infected interaction remains vital in preventing a
disease outbreak from swelling to epidemic proportions. Costs
of implementation can range anywhere from $7 million for
erecting a barrier for a 50% estimated survival rate to nearly
100% if $1.5 billion is available for providing ammunition,
training, and protection during an outbreak.
INTRODUCTION
According to the National Strategic Plan for Public Health
Preparedness and Response, a recent publication by the CDC
in 2011, preparation for any kind of natural disaster such as
flooding stands to offer vast improvements in many other non-
related disasters including wildfire, terrorism, or pandemic
diseases. In preparing for a potential epidemic, we chose to
model an outbreak of zombie-ism for its ease of capturing
public attention and to identify general trends that can be
related to other natural disasters. Mathematical modeling has
been employed to predict the temporal transmission properties
of many diseases, including influenza, Ebola, and malaria,
often with highly accurate results (Praditsitthikorn 2013).
Once correctly fitted with available data, they also have the
potential to be powerful prognostic tools in predicting the
effectiveness of future intervention strategies (Simonsen
2013). A mathematical model also offers additional
advantages in terms of reproducibility and scale, as many
potential diseases yet un-encountered in the real world would
be prohibitively expensive and time-consuming, not to
mention potentially unethical or even illegal, to create a
controlled test environment with real subjects. The potential
epidemiological impacts of many such interventions in the
face of disease outbreak were studied, and the results as well
as a recommendation of the most effective approaches in
response to a potential epidemic are discussed below.
I. METHODS
A. Modeling an Outbreak
Because no documented zombie outbreaks currently exist, a
different source of data was needed to provide information on
initial parameters for modeling. Since the base virus cited to
cause zombie-ism was Ebola based, studies involving Ebola
infection and transmissions were deemed to be useful as a
baseline (Zaman 2009). Strategies for intervention involving a
zombie outbreak centered at Emory University in Atlanta,
Georgia were studied using a susceptible-infected-removed
(SIR) model, with assumptions of a homogenously mixed
population due to the short time span of the disease. Further
assumptions were made involving the characteristics of the
disease from the film 28 Days Later, specifically grouping the
entire population of Atlanta into a single group of equal risk of
infection regardless of age, that the virus spread only through
contact of body fluids and thus was limited to ground-based
contact with infected individuals, that infected individuals
moved slowly enough to be contained within Georgia, and that
zombies could not swim in deep running water nor scale
barbed wire fences at least 5 feet high (Retrospect 2002).
Other assumptions for infected individuals included an instant
incubation period that indicated only infected individuals
could spread the disease, complete erosion of higher thought
in favor of blind aggression, the existence of a natural carrier
with immunity to all symptoms of the disease save for a minor
infection rate and easily identifiable red mark in the left eye,
and would still be in full control of themselves and work
actively with susceptible individuals to escape. Finally,
infected individuals were assumed to both ignore and be
completely ignored by all non-primates, and were not
superhuman in strength and stamina and were still vulnerable
to death from blunt force trauma, with no possibility of
reanimation or returning to life.
Mathematical Modeling of a Zombie Virus
Epidemic
K. Bai, R. Bonagura, A. Cavallaro, K. Fierro, P. Grob, M. Lewis, E. Lobben, A. Nicaretta, E. Peek

For the basic SIR model (Figure I), the removed class was
changed to two separate groups, dead (D) and escaped (E) in
order to differentiate desired state of removal for susceptible
versus infected individuals; ideally, all susceptible individuals
during the initial outbreak would ultimately be able to escape,
while all infected that formed due to the virus would die,
either from intervention or natural causes. In addition to the
susceptible class, a carrier class (C) was also added that was a
different result from being infected by the disease; this group
was still able to keep their mental faculties intact, and would
be indistinguishable from a susceptible person aside from a
small infection rate and a characteristic red dash in the left eye
for easy identification.
Setting the moment the first infected patient escapes from
Emory, it was assumed that susceptible individuals would try
to get away from infected zombies (parameter e), while
zombies would try to infect as many people as they could,
generating more infected (parameter a), or carriers (parameter
g) if the susceptible individual was immune. During this time,
the susceptible population would still experience a natural, if
drastically altered from normal, birth (b) and death (c) rate.
Similarly, zombies would also incur a small natural death rate
from accidental injuries (d). Carriers would work with
survivors to escape (e), but also have a small chance of
infecting susceptible individuals (h). Survivors would also
resist infection by killing off zombies as they escaped (l), and
active intervention through armed individuals or army
interactions would also kill off many infected (f), moving
them into the dead group. The simulation would be run for as
long as necessary for the initial population of 10 million
susceptible people (Census 2013) and 1 infected to have all
been moved into either the dead or escaped categories. Finally,
a density-dependent parameter (k) was added to limit the
number of interactions any two groups could have with each
other in 1 day to avoid exponential crashes from assuming that
1 zombie could attack 10 million susceptible people on the
first day of the outbreak. Full equations for each population
are included in Appendix I.
Data for many parameters was not available due to lack of
zombies existing in published literature. The infection variable
(a) was estimated using the virulence of malaria, which has a
20-50% chance per bite of infected mosquito of passing the
malaria causing protist on (Ahmed 2013). Malaria was chosen
over Ebola because an infected patient with Ebola is typically
bed-bound during the course of the infection, continually
coughing up blood and drained of strength (Qiu 2013); the
disease also has a staggering mortality rate of 90% (Nakayama
2013) and is slow to spread because it incapacitates infected
individuals (Shi 2013), making it a poor model for zombie-
ism. Malaria, in contrast, is a rapidly spreading blood-based
disease that relies on a mosquito vector, which is much less
crippling on its victims and has a single-digit mortality rate in
developed countries (Lusti-Narasimhan 2013). Most
importantly, a carrier state for malaria also exists, having a
much lower infection rate and displaying no adverse effects of
the disease (Krause 2013). The estimate for parameter a was
further refined using predator hunting success rates in
Yellowstone national park, whose native wolf packs'
successful kill rate averaged 30% over the course of 4 years
(Vucitech 2011). We believed that an infected individual,
working in small packs of highly aggressive individuals and
relying primarily on their teeth and speed, would have a
similar efficiency to packs of hunting dogs if left alone with
unarmed civilians. Thus, the infection rate based on zombie-
human interactions was set at 0.33, or 33 new infected
individuals formed for every 100 encounters between a
susceptible and a zombie.
A zombie outbreak would be a calamitous event, which
would impact birth and death rates to values drastically
different from their baseline values in the United States. We
decided that increased levels of stress as well as general chaos
would push conditions closer to a second or third world
country during the short span of time as the infection spread.
Thus, the birth rate (b) was set to the birth rate of rural
Afghanistan, 20 births per thousand individuals per day (CIA
2013). Afghanistan was chosen because it was a country with
very heavy U.S. military involvement and limited GDP and
educational opportunities available for its citizens. Similarly,
the death rate (c) was also taken from this location, 21.5
deaths per 1000 individuals per day (CIA 2013), which is one
of the highest in the world due to lack of some modern
medical facilities and basic utilities like water or electricity,
which would also likely not be in full supply during an
epidemic. Innate death rates for infected individuals was
estimated based on the assumptions that animals ignored them,
but they would still be vulnerable to the same accidental
deaths that occurred for normal people, namely lightning,
machinery-related injuries, and starvation. These rates (d)
coincided with the annual death rate in the United States from
accidental deaths from injury, approximately 39.1 per 100,000
people per year (CDC 2013).
Parameters for successful escape from an area rely on being
able to successfully set up a quarantine boundary that
separates the infected from the susceptible populations, and
thus (e) was initially set to 0 in the baseline model to indicate
no escape, which was varied in later simulations. Similarly,
the (f) parameter that represented active intervention in killing
zombies through force was also set to 0 and later varied in the
base model to set up an estimate of time-span and damage a
no-intervention policy would result in.

Next, the rate at which interaction with an infected
individual would become a carrier instead of a full infected
due to natural immunity was modeled with (g); because there
was no published estimate of the carrier rate, an estimate was
derived using the movie setting of 28 Days Later, in which
only three carriers were found in the entire population of
Britain, or 3 carriers per 10 million people. While carriers
were easily identified with a red dot in the left eye and
actively helped other susceptible people escape, blood or
saliva based contact from sharing food still posed a small risk
of infection due to viruses present in bodily fluids. Hepatitis
B, a similar blood-based viral disease, also has carriers with
minor symptoms who are capable of infecting others
throughout their lives, and thus (h), the infection parameter
due to carrier interaction, was matched with published data
concerning HBV and set to 12 infections per 100 interactions
(WHO 2013).
Finally, to model interactions between the three groups of
susceptible, infected, and carriers, a parameter (l) indicating
the chance of successfully fighting off a zombie by killing it
when it attacks was chosen to match the average survival rate
in the United States from encountering a bear in the
wilderness, as there had only been two wolf attacks in the past
ten years (Wolf 2013). This value was set as 14 successes out
of 100 encounters (Geetha 2012). Interactions between
members of population were limited by time, and the final
parameter (k) was established using information from the
CDC's zombie outbreak model that limited members of all
populations to interacting with a maximum of 21 other
individuals per day, slightly less than 1 attack or encounter per
hour in order to prevent a massive exponential crash in
populations from assuming that 1 zombie would be able to
attack all 10 million susceptible people on the first day that he
or she was freed. All of the above variables are summarized in
table I.
After the baseline model with no military intervention or
escape was established, three more scenarios were explored: a
quarantine model set around the Georgia area that would allow
for escape over a wall followed by military action, an
aggressive preparation model that would arm civilians and
drill them in how to better fight off infected before escaping,
and an escape model involving decreasing the successful
infection rate of infected via an early system of warnings and
evacuation drills.
The quarantine model assumed that zombies were unable to
swim in running water deeper than five feet, ran at a
maximum of 12 miles per hour similar to an average person
(Rompottie 1972), and would be hindered by barbed wire
fence at least five feet high. A proposed containment area was
planned using a map of waterways in Georgia, with a
perimeter of 233 x 300 miles across (Georgia Ecoregion
Descriptions 2007). Estimates for cost included barbed wire
costing $1.23 per foot (Gerrish 2012) for a total of $6.9
million; this wall would take half a day to set up (t = 0.5)
(Schulte 2011), and once established, the escape rate outlined
in the Georgia Hurricane Evacuation Plan, a similar disaster
evacuation scenario, indicated that the escape rate out of the
wall would be (e = 0.2). After being alerted to the presence of
an outbreak, it was estimated that the army would take 5 days
to fully mobilize (Keegan 1999) and come in to actively
eliminate infected; their intervention was predicted to have a
65% success rate when avoiding collateral damage (t = 5, f =
0.65, (Bradley 2003)).
The second model that was run was an armed civilian
scenario. In this model, the escape routes are still present
meaning the value of ‘e’ is non-zero. Evacuation drills are
scheduled year-round meaning (e) is increased from the
quarantine model, from 0.20 to 0.35 following data from
Japan’s earthquake and typhoon evacuation plans and past
data (Bouville 2013). More importantly, the focus of this plan
is providing arms and ammunition for the adult population of
Georgia. Any healthy individual at or above the legal age to
bear arms would be provided one by the government,
averaging around 200 dollars for a 12-gauge shotgun and
ammunition per individual (Roger 1973). With an adult
population in Georgia of about 7.5 million, this would cost the
government approximately $1.498 billion dollars to
implement. The ‘l’ value in this scenario was set at 0.5
assuming that an armed individual would be able to fight off a
zombie about half the time, modeled after average kill rate for
armed individuals during annual deer hunts (U.S. Fish and
Wildlife Service, 2012).
The final model, equipping civilians to better escape, relied
on preparation drills and preventative action once the initial
outbreak started in order to prevent enough infected from
forming to overcome their natural die-off rate. In a study done
on wild wolves in Yellowstone National Park, it was
suggested that changes in annual prey migration patterns
combined with unusually thin snow during the year greatly
decreased the wolf pack's successful kill rate (a) from 33% to
15% (Metz 2011). We would seek to emulate this effect
through multiple publicized warnings on many radio and
television stations, averaging $500 for a 30-second
commercial, once an hour every day for 2 months after testing
on the virus begins gives a cost of $720 thousand in addition
to construction of the wall. The commercials would emphasize
preparedness to evacuate, with emphasis on getting inside an
automobile which is much more difficult for an infected to
break into.
For all sets of parameters, simulations were run using PLAS

with a time interval of 30 days, updating once every 0.1 days.
The initial population of susceptible people was set to 10
million, the population of Georgia (CIA 2013), initial infected
was set to 1 individual 'patient zero,' and initial escaped, dead,
and carriers were all set to 0.
II. RESULTS
The default no intervention and no escape model (graph I)
predicted a very quick population crash of susceptible people
after 5 days. The initial infected outbreak grew exponentially
starting from day 1, while the susceptible population also
experienced a mild growth rate from background birth rate.
However, by day 4, when the infected population became 30%
of the susceptible population, it took only 1 more day for the
infected to completely eliminate remaining susceptible
individuals, driving the S population to 0 while the infected
population peaked at 550,000. Remaining infected then slowly
died off over the course of 3 weeks as they had no more new
susceptible people to infect, and eventually all 10 million
initial individuals ended up in the dead population. The carrier
group remained extremely small (< 1000 individuals at all
times) and did not make any major contribution to infections
or infected death rates. The escaped population does not exist.
This model was used as our baseline.
The quarantine model (graph II) with an estimated cost of
$7 million, set the (e) parameter to 0.20 after half a day or 0.5
time units, and had a shallower susceptible crash over the
course of 4 days. With the ability to escape safely,
approximately 500,000 initial susceptible people and carriers,
or half the population, was able to make it out of the area,
while the maximum number of infected peak at only 250,000.
Our modeled military intervention did not make a huge
difference; after the population crash at 4 days, military
intervention by day 5 only made the remaining number of
infected individuals die off faster.
The aggressive intervention (graph III) with an estimated
cost of $1.5 billion completely avoided the population crash of
the previous 2 scenarios. Although the carrier population once
again did not end up contributing very much, the higher
escape and death of zombie from encounter with armed
civilians rate was projected to completely wipe out the initial
infection faster than it could reproduce itself, and thus the
maximum number of infected, 76 individuals, were unable to
reach a critical mass to overcome their die-out rate of
combined parameters (c), (l), and (f). Over 90% of the
population was able to evacuate in approximately 9 days, with
every initial susceptible escaping within 2 weeks due to lack
of risk from the infected group.
The lowered susceptibility scenario (graph IV) with an
estimated cost of $7.7 million appeared to be a combination of
the previous two scenarios. Once again, the lowered ability of
the infected group to propagate itself, this time due to a
lowered (a) value, prevented it from reaching the critical mass
of 30% required to overcome the susceptible and carrier
population’s ability to ward them off. However, because this
time susceptible people were not better equipped to fight them
off, the zombie population was able to avoid extinction,
hovering around 100 individuals. Although it was insufficient
to overcome the background birth rate, the deceased
population continued to slowly increase as a few susceptible
people were turned into infected and then promptly killed as
the others escaped. Full evacuation took 18 days, by the end of
which the dead population hovered around 2,300 individuals.
III. DISCUSSION
We investigated the results of an epidemic outbreak based
on a highly infectious blood-based pathogen and the costs,
time span, and overall effectiveness of different forms of
intervention based on their potential to reduce the death toll
due to infection. To address this question, we developed a
modified SIR model with carrier and escaped groups to predict
the various outcomes of different strategies.
For all scenarios, it appeared that the initial week after the
infected was first released among the susceptible population
was of critical importance; during this period, the infected
population must successfully attack and infect enough
susceptible people in order to overcome their own natural die-
off rate, as well as later military action that would increase
their death rate. If the infected population was ever able to
reach at least 30% of the susceptible population size, a
population crash would occur over the next day as the infected
would have enough numbers to kill or infect all remaining
members of the susceptible population before they could
escape. However, if the infected were never able to reach this
amount of individuals, the background death rate as well as
deaths from attempted attacks on escaping susceptible people
and carriers would cause their own population to quickly die
off. Thus, it appeared that no equilibrium population dynamic
between zombies and humans exists; either the susceptible
people will fight off the initial tide of infected so that they
cannot seriously hinder their escape and later die off from
hunger or military action, or the infected will quickly explode
out of control and convert all susceptible individuals into their
own group before slowly dying off due to lack of new
individuals to infect.
The background birth and death rates for susceptible people,
as well as background death rates due to accidents from
infected individuals had little to no impact on the projected

changes in population. At the best during the no intervention
scenarios or total kill scenarios of infected, the birth and death
rates were only visible after one population had been
completely wiped out, and served to increase or decrease the
population by around 5% over the course of 2 weeks until the
simulation ended. Modeled military intervention, while
efficient at quickly exterminating infected, was not able to
respond quickly enough to make a different and halt the initial
population crash if it existed, or to kill enough infected
individuals to prevent a crash in the first place. The carrier
population and its own latent infection rate had such a small
chance of forming that the carrier group was never a factor in
any of the 4 described scenarios.
The most important parameters that dictated the outcome of
an infection were (a) the infection rate, (e) the ability to escape
to a safe area, and (l), the chance of a group of survivors being
able to successfully fight off a group of zombies. Small
decreases in (a) from the default 33% kill rate of zombies had
the effect of ‘lengthening’ the time window that it took for
zombies to approach critical mass, and during that time they
would still be slowly dying off. This was most evident in
comparing the default model to the lowered susceptibility
scenario, in which the period before the susceptible population
hit 0 was extended from 5 days to around 18 days. Decreased
infection rate also greatly increased the number of individuals
able to escape as there were fewer infected interfering. Higher
escape (e) values had the effect of shortening the amount of
time it took for the population to hit 0; with a higher escape
rate, the susceptible population quickly emptied out to 0 as
carriers and susceptible people either escaped outside of
Georgia or succumbed to infection. However, because the
pool of potential infected individuals shrank so much more
quickly due to 2 separate ways of leaving the susceptible
group, the total number of infected was much lower compared
to the default model, and a significantly higher proportion of
susceptible people were able to escape, around 80%. The (l)
parameter from the last scenario indicated that doubling the
chances of survivors being able to kill an infected that
attacked them instead of becoming infected themselves was
enough by itself to avoid a zombie epidemic by making it too
‘risky’ for a zombie to attack a person. Since zombies were
only 33% successful to being with, an increase in kill rate
from 14% to 30% meant that the initial zombie was only able
to infect 3 people before he himself was killed. This strategy
attacked the infected group right at the start, and prevented
them from ever ballooning out of control. In fact, decreasing
(a) or increasing (l) was efficient enough that evacuation does
not even seem to be necessary as the infected population
crashes to 0, eliminating the threat.
With these data in mind, our recommended approach to a
localized epidemic infection such as zombie-ism would be to
have some kind of containment border around Georgia that is
at least half a day’s running distance outside of a potential
disaster ground zero area. With a base cost of around $7
million in construction costs, such a border could be quickly
established in a manner similar to the Berlin Wall once an
alarm was raised, and combined with natural barriers such as
rivers and mountains, would offer an easily enforceable barrier
that could be strengthened as needed with addition supplies.
Assuming that it was possible to tell susceptible people
from infected apart, this action alone would provide a 50%
survival rate from the disease as long as people began fleeing
when the outbreak began. Since it is much more expensive to
arm the entire population, and proactive preventions are
already established with the CDC and Emory’s biohazard
level 4 protocols, lowering infection rate seems difficult to
predict depending on strain of virus, as well as infeasible to
cover all existing experiments. Therefore, regular preparation
for evacuation such as informing citizens of optimized escape
routes (increasing e), as well as a small emergency source of
either firearms or protective equipment and supplies during a
time of crisis (increasing l), would be the most cost-efficient
approach to maximizing survival rate and minimizing costs.
We recommend enough public dispensation of information
through radio, T.V., or social media through a $700,000
budget, enough to show once on every public TV station for a
year hourly, to increase the escape rate enough through
preparation to 25% that the initial infection does not gain
enough momentum to cause a population crash. This approach
of prevention over reaction would also be likely to be very
useful in other natural disaster scenarios such as evacuating in
the face of a flood or hurricane. These results are summarized
in table II and graph V below. It should be noted that if
finances are of no concern, a $1.5 billion investment in arming
and educating the general populace is enough to ensure a
100% survival rate for this type of disaster, but real expenses
are likely to be a key deciding factor in how prepared one
chooses to be.
Overall, this study has many limitations in assuming
homogenous population density, extrapolations of disease
infection and escape rates, and somewhat unrealistic
assumptions that available food, power, medicine, or clean
water would remain unchanged during this specific type of
crisis, and that all populations of individuals are equally
vulnerable. Further studies could be targeted in an area larger
than Atlanta or Georgia, and incorporate many other risk
factors like disease, malnutrition, and unevenly distributed
population.

IV. CONCLUSION
For a zombie outbreak, as is true for most epidemics as well
as generalized natural or man-made disasters, preventative
measure, efficiency, and speed of response time are key
factors in minimizing cost and loss of property or life. After
running a slightly expanded SIR model accounting for ability
of susceptible individuals to either escape or die instead of
being only removed, decreased success rate for infected
individuals to propagate the disease quickly enough to
overcome their innate death rate from susceptible-infected
interaction remains vital in preventing a disease outbreak from
swelling to epidemic proportions. Costs of implementation can
range anywhere from $7 million for erecting a barrier for a
50% estimated survival rate to nearly 100% if $1.5 billion is
available for providing ammunition, training, and protection
during an outbreak.
APPENDIX
I. Differential Equations Used for Modeling
Figure I
Fig.1 Original SIR Model
Figure II
Fig. II Augmented SCIDE Model
Table I
*Modified in later scenarios
Table I Parameter Values for Default Model
Graph I
Graph I Default Model Survival Rate
Graph II
Graph II Quarantine Scenario Survival Rate
Parameter Meaning Value
a Zombie infection rate 0.33*
b Susceptible birth rate 0.081
c Susceptible/carrier death rate 0.00215
d Zombie death rate (natural) 0.0000391
e Escape rate 0*
f Zombie death rate (military) 0*
g Carrier from infection rate 0.0000000316
h Carrier infection rate 0.12
l Survivor fighting off zombie rate 0.144*

Graph III
Graph III Aggressive Intervention Scenario Survival Rate
Graph IV
Graph IV Lowered Susceptibility Scenario Survival Rate
Graph V
Graph V Recommended Intervention Survival Rate
REFERENCES
"00's Retrospect: Bloody Disgusting's Top 20 Films of the
Decade... Part 3". Bloody Disgusting. Archived from the
original on 24 December 2002. Retrieved 3 January 2010.
Ahmed, B. S., Phelps, B. R., Reuben, E. B., & Ferris, R. E.
(2013). Does a significant reduction in malaria risk make
lopinavir/ritonavir-based ART cost-effective for children
with HIV in co-endemic, low-resource settings? Trans R
Soc Trop Med Hyg. doi: 10.1093/trstmh/trt108
Alves, F. P., Gil, L. H., Marrelli, M. T., Ribolla, P. E.,
Camargo, E. P., & Da Silva, L. H. (2005). Asymptomatic
carriers of Plasmodium spp. as infection source for malaria
vector mosquitoes in the Brazilian Amazon. J Med
Entomol, 42(5), 777-779.
Bouville, A., Linet, M. S., Hatch, M., Mabuchi, K., & Simon,
S. L. (2013). Guidelines for Exposure Assessment in Health
Risk Studies Following a Nuclear Reactor Accident.
Environ Health Perspect. doi: 10.1289/ehp.1307120
Bradley, Graham (February 21, 2003 at A18). "Military Turns
to Software to Cut Civilian Casualties". Washington Post.
Centers for Disease Control and Prevention. Centers for
Disease Control and Prevention, 30 May 2013. Web. 06
Dec. 2013.
"Central Intelligence Agency." The World Factbook. N.p., n.d.
Web. 06 Dec. 2013.
"Evacuation Information." GEMA/Homeland Security -. N.p.,
n.d. Web. 03 Dec. 2013.
Mandal, S., Sarkar, R., & Sinha, S. (2011). Mathematical
models of malaria. Malaria Journal, 10(202), doi:
10.1186/1475-2875-10-202
Geetha, N. T., Shivakumar, H. R., Amarnath, P. U., Rajesh
Kumar, B. P., & Kirthikumar, R. (2012). Bear Maul Injuries
in Maxillofacial Region: Our Experience. J Maxillofac Oral
Surg, 11(4), 420-424. doi: 10.1007/s12663-011-0328-4
Gerrish, J., Fence Systems for Grazing Management,
University of Missouri, Forage Research Center, Linneus,
MO
Georgia Ecoregion Descriptions, Accessed November 23,
2007
"Georgia QuickFacts from the US Census Bureau." Georgia
QuickFacts from the US Census Bureau. N.p., n.d. Web. 05
Dec. 2013.
Keegan, John (1999). The First World War. New York: Alfred
A. Knopf, Inc.
Krause, A., Wainstein, T., Essop, F. B., & Goodyear, Q.
(2013). Testing for haemoglobinopathies in Johannesburg,

South Africa: A 30-year review. S Afr Med J, 103(12), 989-
993. doi: 10.7196/samj.7255
Lusti-Narasimhan, M., Pessoa-Silva, C. L., & Temmerman,
M. (2013). Moving forward in tackling antimicrobial
resistance: WHO actions. Sex Transm Infect, 89 Suppl 4,
iv57-iv59. doi: 10.1136/sextrans-2012-050910
Metz, M. C., Vucetich, J. A., Smith, D. W., Stahler, D. R., &
Peterson, R. O. (2011). Effect of sociality and season on
gray wolf (Canis lupus) foraging behavior: implications for
estimating summer kill rate. PLoS One, 6(3), e17332. doi:
10.1371/journal.pone.0017332
Nakayama, E., & Saijo, M. (2013). Animal models for Ebola
and Marburg virus infections. Front Microbiol, 4, 267. doi:
10.3389/fmicb.2013.00267
Praditsitthikorn, N., Kotirum, S., Mohara, A., Dumrongprat,
K., Velasco, R. P., & Teerawattananon, Y. (2013).
Assessing key model parameters for economic evaluation of
pandemic influenza interventions: the data source matters.
Influenza Other Respir Viruses, 7 Suppl 2, 59-63. doi:
10.1111/irv.12091
Qiu, X., Audet, J., Wong, G., Fernando, L., Bello, A., Pillet,
S., . . . Kobinger, G. P. (2013). Sustained protection against
Ebola virus infection following treatment of infected
nonhuman primates with ZMAb. Sci Rep, 3, 3365. doi:
10.1038/srep03365
Roger H. Robinson (1973). The police shotgun manual.
Thomas. pp. 91–94. ISBN 0-398-02630-0.
Rompottie, K. (1972). "A study of stride length in
running".International Track and Field: 249–56. 4
Schulte, Bennet (2011). The Berlin Wall. Remains of a Lost
Border. (Die Berliner Mauer. Spuren einer verschwundenen
Grenze). be.bra verlag, Berlin.
Shi, M., & Shen, Y. Q. (2013). [Research progress of the
molecule mechanisms of Ebola virus infection of cells].
Bing Du Xue Bao, 29(1), 71-75.
Simonsen, L., Spreeuwenberg, P., Lustig, R., Taylor, R. J.,
Fleming, D. M., Kroneman, M., . . . Paget, W. J. (2013).
Global Mortality Estimates for the 2009 Influenza
Pandemic from the GLaMOR Project: A Modeling Study.
PLoS Med, 10(11), e1001558. doi:
10.1371/journal.pmed.1001558
Sbuscio, Richard. (2011). Adrenaline and Your Self Defense
Strategy. Published on the Web
Vucetich, J. A., Hebblewhite, M., Smith, D. W., & Peterson,
R. O. (2011). Predicting prey population dynamics from kill
rate, predation rate and predator-prey ratios in three wolf-
ungulate systems. J Anim Ecol, 80(6), 1236-1245. doi:
10.1111/j.1365-2656.2011.01855.x
"Hepatitis B." WHO. N.p., n.d. Web. 05 Dec. 2013.
Wolf, B. C., & Harding, B. E. (2013). Fatalities Due to
Indigenous and Exotic Species in Florida. J Forensic Sci.
doi: 10.1111/1556-4029.12261
Zaman, G., Kang, Y. H., & Jung, I. H. (2009). Optimal
treatment of an SIR epidemic model with time delay.
Biosystems, 98(1), 43-50. doi:
10.1016/j.biosystems.2009.05.006

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