Brandy L. Rapatski Juan Tolosa Richard Stockton College of NJ A Model for the Study of HIV/AIDS

Classic Model – Compartment Model SIR Susceptible Infected Recovered Removed/Recovered Class Immunity (can’t infect or be infected) Death Isolation

Assumptions An average infective makes contact sufficient to transmit infection with  N 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  N (S/N)I =  SI There is no entry into or departure from the population except possibly through death from the disease. A fraction  of infectives leave the infective class per unit time.

SIR

Qualitative Approach

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.

Progression of Infection by Stage We investigate how infectivity varies with stage of infection. 1/6 Year 7 Years3 Years First Stage Second Stage Third Stage including AIDS Death Before modern medical intervention AIDS is roughly the last year of the third stage

Progression of Infection by Stage an alternative set of durations Infectivity varies by stage of the disease 1/6 Year 7 Years2 Years First Stage Second Stage Third Stage* AIDS & Death Before modern medical intervention *Here last year of AIDS is omitted due to sexual inactivity

[ nd Stage ] [1 st Stage][ rd Stage----] Anderson, R. M. “The spread of HIV and sexual mixing patterns,” pp 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). Untreated Viral Loads

Modes of HIV Transmission  Sexual Contact  IV Drug Use  Vertical Transmission (Mother to Child)  Blood Transfusion

Modeling SF Gay Population: the Data  HIV exploded in San Francisco between the years 1978 and  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.

San Francisco

San Francisco Transmission Dynamics Analysis of 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 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.

Simple Transmission Dynamics

Multiple Group Transmission Dynamics: from Group j to group i

Go to Six-Group Models

Six-Group Models

Current Work Test and Treat US MSM HIV/AIDS population

Go to Test and Treat Model

Juan’s Stuff

Contact Information

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.