Modeling the population dynamics of HIV/AIDS

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Modeling the population dynamics of HIV/AIDS

• Brandy L. Rapatski
• James A. Yorke
• Frederick Suppe

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Primary Goal

• To determine how infectiousness of HIV varies as
  an untreated infected gay man progresses through
  3 stages of the disease.
• Any attempt to measure these infectivities must
  be a highly mathematical analysis of available
  data.

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Modeling SF Gay Population

• We model the San Francisco population as
  described by the San Francisco City Clinic Cohort
  Study (SFCCC).

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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.
• Model must account for 1978-1984 SF data

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Infectivity Per Contact Conclusions
2/3 Year
7 Years
3 Years
Death
First Stage Infectivity 0.015
Second Stage Infectivity 0.006
Third Stage Infectivity 0.223
0.0152/30.010
0.00670.042
0.22330.669
Total infections 0.721
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Infectivity Comparison
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Viral Loads
Our infectivities correspond to viral loads
------------------2nd Stage-------------------

1st Stage
-----3rd Stage----
Variable viral loads over the course of a typical
untreated individuals HIV infection.
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• The infectivities reflect the pattern of semen
  infectivity.
• Though infectivity depends on mode of
  transmission, third stage remains most
  infectious.

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Person-to-Person Transition Rate
Africa 1 person to 1,000,000 in approximately
40 years (1950-1990)
1.3 years
1.6
31 generations in 40 years
6.9 years
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6 generations in 40 years
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Contact Information

• BLR_at_math.umd.edu
• http//www.killi.com/brandy