Background Information
 Species: Variola virus
 Large and brick-shaped, measuring
302-350 nm by 244-270nm
 Linear double stranded DNA
 Unique among other DNA viruses
because it replicates in the cytoplasm
and not inside the nucleus
 Can be transmitted through airborne variola virus, direct contact
with infected bodily fluids or objects, prolonged face to face
contact
 Cause of death unclear, has to do with multiple organs
 Those who recover are usually disfigured for the rest of their lives
Background Information
 Earliest credible evidence: Egyptian
mummies of people who died 3000
years ago
 Disease likely emerged around 10,000
BC
 General symptoms are flu-like
-Fever
-Headache
-Severe fatigue
-Severe body aches
-Overall discomfort
 Followed by formation of red spots on
extremities, face, and trunk that
become filled with pus, which then
become scabs and fall off, leaving deep
pitted scars
 Variolation practiced as early as 1000
BC, Vaccine discovered in 1796
Background Information
 Some statistics on Smallpox
-In Europe, an estimated number of 80 million
deaths occurred from Smallpox in the 18th century
-An estimated number of 300 million deaths
occurred from Smallpox in the 20th century globally
-The last naturally occurring case developed in
Somalia in 1977
Background Information
 Smallpox eradicated by 1979
Vaccination ceased gradually afterwards
 Official stocks of virus remain in TWO
locations
-CDC in Atlanta, Georgia, USA
-VECTOR in Novosibirsk, Russia
 Fear of bioterrorism
Questions of Interest
 What is a reasonable estimate for the R0 of
a modern-day smallpox outbreak?
 How did socio-economic conditions, herd immunity,
and public health interventions affect the R0 of a
given historical outbreak?
 How can the same factors listed above affect the R0
of a modern-day smallpox outbreak?
Methods
 For Boston, Burford, Chester, Warrington cases
 Epidemic modeling
Similar to S-I-R model, the SEIU model
 Epidemic Model based on the following differential
equations
- dS/dt: -βϕSI
- dEn/dt: βϕSI-αEn
-dI/dt: αEn-γI
-dU/dt: γI
• Solve for R0 using the provided formula
β=R0γ/φN
Methods
Susceptible
Infectious
Resistant
Methods
Susceptible Exposed Infectious
(U): Dead
and
Recovered
Methods
Differential Equations
-dS/dt: -βϕSI
-dEn/dt: βϕSI-αEn
Susceptible
βφSI
Exposed
-dI/dt: αEn-γ
-dU/dt: γI
αEn
Infectious
γI
(U): Dead
and
Recovered
Variables
S:Susceptible
En: Exposed
I: Infectious
U: Dead and Recovered
β: Rate at which potential infectious contacts occur
ϕ: Proportions of contacts infected
α: Average rate latent become infectious or
(latency period)-1
γ: Rate at which individuals infected cover or die or
(infectious period)-1
Results
Boston R0: 4.3
Chester R0: 4.8
Warrington R0: 4.7
Burford R0: 3.4
a.
Boston Monthly Deaths
b. Chester Monthly Deaths
c. Warrington Monthly Deaths d. Burford Daily Deaths
Results
London (1836-1870)
-Endemic smallpox in London
from 1836 to 1870
-Analysis of individual
epidemics not possible due to
lack of and quality of data
-Lower bound of R0 is 5
Results
Results
 The interesting case of KOSOVO
(1972)
 Epidemic model more complex,
included factors such as
vaccination, herd immunity,
quarantine, socioeconomic
conditions
Methods
-
Differential Equations for Kosovo
dS/dt: χ2(1-ε1)Ci – β(ϕ+ρ-ϕρ)SI
-dI/dt: α(1-ε2)En-γI
dEn/dt: βϕ(1-ρ)SI-αEn
-dQ/dt: α(1-ε2)Ei +
αθEn-χ2Q
dEi/dt: βϕρSI-(χ1ε2 + α(1-ε2))Ei
-dU/dt: γI + χ2Q
dCi/dt: βρ(1-ϕ)SI-χ1Ci
-dV/dt: χ1(ε2Ei +
ε1Ci)
S: Susceptible
Eii: Individuals exposed, but not found
En:: Individuals exposed and found
Ci: Individuals not exposed, but not found
I: Infectious
U: Dead and recovered
V: Vaccination
Q: Quarantine
and leave community
β:Rate at which potentially infectious contacts occurs
φ: Proportion of contacts infected
(1-φ): Proportion of contacts NOT infected
ρ: Proportion of contacts found through tracing
(1-ρ): Proportion of contacts NOT found through tracing
ε1: Vaccine efficacy for those uninfected
ε2: Vaccine efficacy for those infected
α: Rate at which individuals become infectious
θ: Daily rate at which exposed individuals leave enter quarantine
(1-θ): Daily rate at which exposed individuals enter infectious class
χ1: Rate at which quaratined traced contacts successfully
vaccinated and released back into community
χ2: Rate at which proportion quaratined enter U
Methods
Susceptible
Exposed
Vaccination
Infectious
Quarantine
(U) Dead
and
Recovered
Χ1(1-ε2)
Methods
Susceptibl
e
Ei: Untraced latent
ρ
β
ε1
En: Traced latent
(1-ϕ)
ϕ
(1-ρ)
ε2
ρ
Ci: Traced Uninfected
α
α (1-θ)
Infectious
(U): Dead
and
Recovered
γ
Χ1
1-ε2
(1-ρ)
θ
Vaccination
Quarantine
χ2
Results
 The interesting case of KOSOVO
(1972)
 Epidemic model more complex,
included factors such as
vaccination, herd immunity,
quarantine, socioeconomic
conditions
 Predicted R0 of 10---Why?
-Estimated 50% vaccination rate
-Outbreak went unrecognized until
second generations of infection
-Hospital acquired cases
-β estimated to be 50
-Interventions implemented 31 days of
index case
Results
Analysis of 32 European Smallpox outbreaks post 1950
Implications
 Contemporary outbreaks in industrialized
communities with low vaccination levels have an
estimated R0 of 4-6
 Important factors that can significantly lower the
risk of a Smallpox epidemic
-Early recognition
-Unwavering herd immunity
-Effective public health interventions