Network Firewall Dynamics and the Subsaturation Stabilization of HIV

Abstract

In 2001, Friedman et al. conjectured the existence of a “firewall effect” in which individuals who are infected with HIV, but remain in a state of low infectiousness, serve to prevent the virus from spreading. To evaluate this historical conjecture, we develop a new graph-theoretic measure that quantifies the extent to which Friedman's firewall hypothesis(FH)holds in a risk network. We compute this new measure across simulated trajectories of a stochastic discrete dynamical system that models a social network of 25,000 individuals engaging in risk acts over a period of 15 years. The model's parameters are based on analyses of data collected in prior studies of the real-world risk networks of people who inject drugs (PWID) in New York City. Analysis of system trajectories reveals the structural mechanisms by which individuals with mature HIV infections tend to partition the network into homogeneous clusters (with respect to infection status) and how uninfected clusters remain relatively stable (with respect to infection status) over long stretches of time. We confirm the spontaneous emergence of network firewalls in the system and reveal their structural role in the nonspreading of HIV.

The Interaction of Risk Network Structures and Virus Natural History in the Non-spreading of HIV Among People Who Inject Drugs in the Early Stages of the Epidemic

“…Here, it would seem, high infectiousness takes advantage of the small world nature of PWID networks (43,45), where a low network distance between clusters creates short paths between any two randomly chosen nodes. This small world character is partly due to the presence of network hubs: individuals with high numbers of partners.…”

“…All of this takes place in simulations within which infection from chronically infected nodes remains possible, but (much) less likely than would be the case for infection from acutely infected nodes (42,43). To the extent that these two infection probabilities equalize, the firewall effect dissipates, and sub-saturation stabilization disappears.…”

“…Each simulation began with a HIV prevalence rate of 0.01%, which generally grew quickly to roughly 50-60% before stabilizing within that range. The simulation algorithm is presented elsewhere in greater detail (43). …”

Acute HIV infection transmission among people who inject drugs in a mature epidemic setting

“…Other reasons include distinct network characteristics and dynamics (e.g., distribution and prevalence of concurrent relationships, total number of partners, rate of partner turnover), which have been shown to influence the transmission and spread of HIV infection among at-risk persons [43, 44], and thus may determine, in part, the contribution of AHI. For instance, the theory that chronically-infected individuals may act as network ‘firewalls,’ buffering acutely-infected individuals from the rest of the population, has been previously demonstrated [44, 45]. Further study is needed to determine whether this ‘firewall’ principle limited the contribution of AHI infection in the model.…”

Integrating molecular epidemiology and social network analysis to study infectious diseases: Towards a socio-molecular era for public health

“…Populations with assortative mixing of individuals are more likely to experience a rapid epidemic growth early on, while outbreaks in populations with disassortative mixing are more likely to grow into larger epidemics. Later the so-called “firewall” effect was introduced which in theory can be observed when the HIV long-term infected individuals “protect” susceptible individuals from getting in contact with highly infectious acutely infected individuals, inducing saturation at a lower prevalence than the one predicted by a panmictic model (Friedman et al, 2000, Khan et al, 2013, Dombrowski et al, 2013). Improvements in computational capacities have facilitated such advanced epidemiological modeling that takes more complicated population network structures into account (Danon et al, 2011).…”