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Modeling Applications to HIV Research Problems

Within-Person HIV Dynamics

Detailed models of within-person dynamics of HIV and immune response are influential in therapeutic areas for drug development and clinical purposes (e.g., Perelson & Ribeiro 2013,43 Rivadeneira et al. 2014,44 other chapters in this book) but go beyond the scope of this chapter. Nevertheless, the overall transition models between the stages of HIV (acute, latent, end stage) are often used in individual and population-level models.

Individual Behavior Risks

Mechanistically, the majority of HIV transmission from one person to another occurs through sexual contact or syringe sharing.1 As risky behaviors accumulate so does the overall probability of transmission. Denoting the probability of HIV transmission per unprotected sex act as p, the cumulative probability P of seroconversion after N such sex acts with an HIVpositive individual becomes

The model can also accommodate different probabilities of transmission for a variety of unprotected sexual activities (e.g., oral and anal sex) and syringe sharing.45

Here M and K indicate the number of unprotected sex acts and the number of times syringes were shared. For each individual act i or j, a corresponding probability pi or pj would vary depending on the type of sex act, use of condoms, rinsing the syringe with bleach, and so on. A number of statistical models have been used to estimate individual risks of HIV transmission.40,46 An example of projection of behavior into the future is presented in Figure 10.9. These estimates were used to develop a simulation model that calculates the probability of becoming HIV infected over time (e.g., in 2 years).45 The model was applied to a cohort of discordant couples and used to identify individuals at highest risk. These models can be expanded more generally for any behavior that can potentially lead to HIV. Such a model was developed for a sample of at-risk individuals in North Carolina. Individuals at the highest risk of acquiring HIV not surprisingly either had a large number of concurrent sexual


Projections of specific behavior into the future for male-to-female transmission in a discordant couple assuming having two unprotected sex acts per week. The model emphasizes the need for the partner to be on antiretroviral therapy (ART) to reduce the chances of HIV transmission. When a couple wants to conceive a child, having unprotected sex is critical and the main protective measures become ART and Pre-Exposure Prophylaxis (PrEP).

partners or often shared syringes with strangers.47 Recently the CDC published a statistical risk calculator2,48 that uses this approach to estimate the risk of HIV if the behavior does not change and the possible effects of behavior changes.

Simulations can also be used to suggest possible behavioral conditions under which certain incidence is observed. For example, when high incidence is observed in a sample but little risky behavior is reported, the question becomes one of which behaviors are not being reported.49

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