1. Modeling the population dynamics of HIV/AIDS Brandy L. Rapatski James A. Yorke Frederick Suppe

2. 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.

3. Modeling SF Gay Population We model the San Francisco population as described by the San Francisco City Clinic Cohort Study (SFCCC).

4. 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

5. Infectivity Per Contact Conclusions 2/3 Year 7 Years3 Years First Stage Infectivity 0.015 Second Stage Infectivity 0.006 Third Stage Infectivity 0.223 Death Total infections = 0.721 0.015*2/3=0.0100.006*7=0.0420.223*3=0.669

6. First StageSecond StageThird Stage Previous variable-infectivity SFCCC models (Jacquez-Koopman et al. 1994) 0.050-0.300 ~0.125 0.0001-0.0010.001-0.010 ~0.005 Our SFCCC variable- infectivity model 0.014-0.024 ~0.020 (factor of 1/6) 0.000-0.0080.126-0.493 ~0.300 (factor of 60) Infectivity Comparison

7. Viral Loads Variable viral loads over the course of a typical untreated individual’s HIV infection. [------------------2 nd Stage-------------------] [1 st Stage][-----3 rd Stage----] Our infectivities correspond to viral loads

8. The infectivities reflect the pattern of semen infectivity. Though infectivity depends on mode of transmission, third stage remains most infectious.

9. Person-to-Person Transition Rate Africa: 1 person to 1,000,000 in approximately 40 years (1950-1990) ModelMean Transmission Time Infections caused per individual Previous variable- infectivity SFCCC models Our SFCCC variable- infectivity model 1.3 years 6.9 years 1.6 10 ~31 generations in 40 years ~6 generations in 40 years

10. Contact Information BLR@math.umd.edu http://www.killi.com/brandy