Brandy L. Rapatski

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A Model for the Study of HIV/AIDS

• Brandy L. Rapatski
• Juan Tolosa
• Richard Stockton
• College of NJ

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Classic Model Compartment Model
S
I
R
Susceptible Infected
Recovered

• Removed/Recovered Class
• Immunity (cant infect or be infected)
• Death
• Isolation

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Assumptions

• An average infective makes contact sufficient to
  transmit infection with bN others per unit time.
  (N total population).
• Probability a random contact by an infective is
  with a susceptible is S/N
• The number of new infections in unit time is
• bN (S/N)I bSI
• There is no entry into or departure from the
  population except possibly through death from the
  disease.
• A fraction a of infectives leave the infective
  class per unit time.

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S
I
R
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Qualitative Approach
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Basic Reproduction Number
The number of secondary infections caused by a
single infective introduced into a wholly
susceptible population over the course of the
infection of this single infective.
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Progression of Infection by Stage

• We investigate how infectivity varies with stage
  of infection.

1/6 Year
7 Years
3 Years
Death
First Stage
Second Stage
Third Stage including AIDS
Before modern medical intervention AIDS is
roughly the last year of the third stage
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Progression of Infection by Stagean alternative
set of durations

• Infectivity varies by stage of the disease

1/6 Year
7 Years
2 Years
AIDS Death
First Stage
Second Stage
Third Stage
Before modern medical intervention Here last
year of AIDS is omitted due to sexual inactivity
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Untreated Viral Loads
Anderson, R. M. The spread of HIV and sexual
mixing patterns, pp. 71-86 in Mann, J. and D.
Tarantola (eds.), AIDS in the World II Global
Dimensions, Social Roots, and Responses. The
Global AIDS Policy Coalition. (New York Oxford
University Press, 1996).
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Modes of HIV Transmission

• Sexual Contact
• IV Drug Use
• Vertical Transmission (Mother to Child)
• Blood Transfusion

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Modeling SF Gay Population the Data

• HIV exploded in San Francisco between the years
  1978 and 1984.
• San Francisco obtained high quality data on 6875
  gay men Infection rates and number of sexual
  contacts.
• Blood samples were taken and frozen during the
  years HIV was quietly breaking out as part of a
  hepatitis vaccine study.

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San Francisco
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San Francisco Transmission Dynamics

• Analysis of 1978-1984
• Six Activity Levels (from survey data)
• Infectiousness depends on stage (3 stages)
• Bathhouse Assumption
• Men vary in how often they visit the bathhouses
  but once inside choose partners at random.

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Model Compartments

• Individuals can be in any of four stages
  (including susceptible) and in any of six
  activity groups. So the model keeps track of
  fraction of people in each of the 4 x 6
  subpopulations.

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Simple Transmission Dynamics
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Multiple Group Transmission Dynamics
from Group j to group i
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Go to Six-Group Models
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Six-Group Models
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Current Work

• Test and Treat US MSM HIV/AIDS population

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Go to Test and Treat Model
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Juans Stuff ?
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Contact Information

• Brandy.rapatski_at_stockton.edu
• Juan.tolosa_at_stockton.edu

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Current MSM Epidemic in US

• MSM accounted for 71 of all HIV infections among
  male adults and adolescents in 2005 even though
  only about 5 to 7 of male adults and
  adolescents in the United States identify
  themselves as MSM
• Through its National HIV Behavioral Surveillance
  system, CDC found that 25 of the MSM surveyed in
  5 large cities were infected with HIV and 48 of
  those infected were unaware of their infections.
• Young black MSM in this study were more likely to
  be unaware of their infection approximately 9
  of 10 young black MSM compared to 6 of 10 young
  white men.
• Of the men who tested positive, most (74) had
  previously tested negative for HIV infection and
  59 believed that they were at low or very low
  risk.