Predicting Human Papilloma Virus Prevalence and Vaccine Policy Effectiveness

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Predicting Human Papilloma Virus Prevalence and
Vaccine Policy Effectiveness
Courtney Corley and Armin R. Mikler Computational
Epidemiology Research Laboratory Department of
Computer Science and Engineering University of
North Texas
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Motivation

• Why is a computer scientist interested in the
  spread of diseases?
• Infection dynamics in complex networks
• Bridge the gap between the public health domain
  and mathematical epidemiologists

3
Human Papilloma Virus

• Sexually Transmitted Virus which can lead to
  cervical dysplasia (cancer).

Found in 99.7 of all cervical cancers
Types 16,18,31,45 account for 75 of cervical
cancer
80 of the sexually active adult population will
contract HPV cdc
U.S. spent over 1.6 billion in treating symptoms
of HPV
2004
5-6 billion spent on screening tests such as pap
smears.
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Human Papilloma Virus
U.S. estimates 13,000 cases of cervical cancer
2005
More than 5,000 will die from cervical cancer

• Exciting news!

Several candidate vaccines are in phase III
testing with the FDA and broad phase IV trials
have begun
Drug companies are currently in licensing
arbitration
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Modeling Epidemics

• Susceptibles- can be infected
• Infectives are infectious
• Removed- incapable of transmitting disease

• Let ß be the transmission rate based on contact
  rate and infectivity
• Let ? be the rate of infectives becoming
  non-infectious

Susceptible S
Infectives I
Removed R
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Sexually Transmitted Disease Modeling

• Sexual activity and sexually active populations

• Transmission Dynamics
• Contact rates and activity groups
• Risk of Transmission

• Sexual mixing
• Demographic Stratification

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HPV
Total Sexually Active Population (?)
Vaccinated Vkl
Vaccinated Infectious VIkl
Recovered Rkl

• Note A constant population is maintained. Every
  year/update in the model a proportion of the
  population
• Enters or ages-in as susceptibles
• Leaves or ages-out

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Who do we model?

• We model the individuals who are currently
  sexually active (?)
• and able to contract the disease

We define the sexually active population age
range (1/µ) as
The range in years (1/µ) in which an individual
changes sexual partners more than once per year
on average
Age (years)
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Transmission Dynamics
Contact Rates

• Modeling sexually transmitted diseases is similar
  to modeling other infectious diseases, they
  depend on

Population Mixing
The contact-rate (cl) is the number of partner
changes per year
High
We define three sexual activity groups by
contact-rates
Moderate
Low
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Risk of Transmission

• The risk of transmission (ß) is based on two
  factors

The average number of sexual encounters with one
partner (?)
The risk of transmission in one sexual encounter
(?)
The transmission risk is a binomial with ß(1-
?)?

• The average is taken to determine the relative
  risk for HPV infection
• Male-to-Female 80
• Female-to-Male 70

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Demographic Stratification

• To accurately model geographic regions, we
  categorize the population further

Demographics
Low
We have our three activity groups
Moderate
High

• Now we combine
• a demographic trait
• the sexual activity classes
• to represent the demographically stratified
  population where ?l is the proportion of ? in
  each sub-group

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Example Stratification

• HPV
• Age range 15-30 years
• Stratify at 5 year intervals (1/?)
• Different contact rates can be assigned to each
  group
• The sub-groups (l) are numbered 0 to 8 in this
  example

8
9
9.5
2.5
3.5
3
1
1.25
1.5
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Population Interaction

• A contact can take place between an individual in
  a subgroup demographic, sexual activity class
  and an individual
• In the same subgroup
• or
• In a different subgroup

• Consider our HPV population example

Let ? be a matrix of size l by l Where the entry
in ?lm defines the proportion of interactions
that occur between subgroup l and subgroup m
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Population Interaction Example
What proportion of interactions will a 23 year
old in the moderate activity class have with the
population?

• Consider this sample interaction matrix

l4
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More about mixing and infection
Where e is between 0 and 1
Assortative Mixing (like with like) e 0 Random
Mixing (like with unlike) e 1

• Where ? is the infectivity of gender k and
  sub-group l

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• So far . . .
• Sexual Activity Classes
• Demographic Stratification
• Transmission Dynamics
• Contact Rates
• Population Interaction

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Population States

• Now, we need to keep track of

• Who is susceptible to the disease
• Who has the disease and is infectious
• Who has recovered from the disease

Also for HPV

• Who has been Vaccinated
• Who has the disease and been vaccinated,
  Vaccinated Infectious

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Total Sexually Active Population (?)
Susceptible Skl
Vaccinated Vkl
Susceptible individuals in the first age-group
Infectious Ikl
Vaccinated Infectious VIkl
Recovered Rkl

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Susceptible Skl
Vaccinated Vkl
Susceptible individuals in the all other
age-groups Let n be the number of sexual
activity classes
Infectious Ikl
Vaccinated Infectious VIkl
Recovered Rkl

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Total Sexually Active Population (?)
Individuals in the first age-group
Susceptible Skl
Vaccinated Vkl

Infectious Ikl
Vaccinated Infectious VIkl
Recovered Rkl
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Individuals in all other age-groups
Susceptible Skl
Vaccinated Vkl

Infectious Ikl
Vaccinated Infectious VIkl
Recovered Rkl
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Application

• Our goal is to bridge the gap between the
  mathematical epidemiologists and professionals in
  industry and public health officials

We have developed a computer application
interface to this model, which simulates endemic
prevalence of a disease
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Application Interface

• Input parameters
• Disease
• Population
• Vaccine

Output Populations in each state over length
of simulation
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HPV Application Demo

• The following parameters are used in this demo

• Age range 15-30, 5 year group interval
• Sexual activity classes of low, moderate and high
• Denton County, TX population data from the 2000
  U.S. Census
• 75 vaccine efficacy
• 90 vaccine coverage
• Vaccine is effective for 10 years

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Application Start Page
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Input Parameters
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Population Parameters
Denton County, 2000 U.S. Census Data
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Vaccine Parameters
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Application Output
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Population Graph Output
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Population Ratio Graph Output
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HPV Experiments
Proportion of population with sustained
infection
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Results

• Qualitative assessment
• Denton County would have a larger benefit in
  starting vaccination at age (15-19) than
  vaccinating high-risk minorities

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Related Material

• Our paper currently in review with the model
  description in the appendix
• http//cerl.unt.edu/corley/pub/corley.ieee.bibe.
  2005.pdf
• link to the web-application demo
• http//cerl.unt.edu/corley/hpv

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Conclusion

• Modeling these diseases with this application
  will maximize resource allocation and utilization
  in the community or population where it is most
  needed

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References
Thank You!

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