HIV control strategies for sex worker-client contact networks.

Controlling the spread of HIV among hidden, high-risk populations such as survival sex workers and their clients is becoming increasingly important in the ongoing fight against HIV/AIDS. Several sociological and structural factors render general control strategies ineffective in these settings; instead, focused prevention, testing and treatment strategies which take into account the nature of survival sex work are required. Using a dynamic bipartite network model of sexual contacts, we investigate the optimal distribution of treatment and preventative resources among sex workers and their clients; specifically, we consider control strategies that randomly allocate antiretroviral therapy and pre-exposure prophylaxis within each subpopulation separately. Motivated by historical data from a South African mining community, three main asymmetries between sex workers and clients are considered in our model: relative population sizes, migration rates and partner distributions. We find that preventative interventions targeted at female sex workers are the lowest cost strategies for reducing HIV prevalence, since the sex workers form a smaller population and have, on average, more sexual contacts. However, the high migration rate among survival sex workers limits the extent to which prevalence can be reduced using this strategy. To achieve a further reduction in HIV prevalence, testing and treatment in the client population cannot be ignored.

Changing risk behaviours and the HIV epidemic: a mathematical analysis in the context of treatment as prevention.

BACKGROUND: Expanding access to highly active antiretroviral therapy (HAART) has become an important approach to HIV prevention in recent years. Previous studies suggest that concomitant changes in risk behaviours may either help or hinder programs that use a Treatment as Prevention strategy. ANALYSIS: We consider HIV-related risk behaviour as a social contagion in a deterministic compartmental model, which treats risk behaviour and HIV infection as linked processes, where acquiring risk behaviour is a prerequisite for contracting HIV. The equilibrium behaviour of the model is analysed to determine epidemic outcomes under conditions of expanding HAART coverage along with risk behaviours that change with HAART coverage. We determined the potential impact of changes in risk behaviour on the outcomes of Treatment as Prevention strategies. Model results show that HIV incidence and prevalence decline only above threshold levels of HAART coverage, which depends strongly on risk behaviour parameter values. Expanding HAART coverage with simultaneous reduction in risk behaviour act synergistically to accelerate the drop in HIV incidence and prevalence. Above the thresholds, additional HAART coverage is always sufficient to reverse the impact of HAART optimism on incidence and prevalence. Applying the model to an HIV epidemic in Vancouver, Canada, showed no evidence of HAART optimism in that setting. CONCLUSIONS: Our results suggest that Treatment as Prevention has significant potential for controlling the HIV epidemic once HAART coverage reaches a threshold. Furthermore, expanding HAART coverage combined with interventions targeting risk behaviours amplify the preventive impact, potentially driving the HIV epidemic to elimination.

Coarsening to chaos-stabilized fronts.

We investigate a model for pattern formation in the presence of Galilean symmetry proposed by Matthews and Cox [Phys. Rev. E 62, R1473 (2000)], which has the form of coupled generalized Burgers- and Ginzburg-Landau-type equations. With only the system size L as a parameter, we find distinct "small-L" and "large-L" regimes exhibiting clear differences in their dynamics and scaling behavior. The long-time statistically stationary state contains a single L-dependent front, stabilized globally by spatiotemporally chaotic dynamics confined away from the front. For sufficiently large domains, the transient dynamics include a state consisting of several viscous shocklike structures that coarsens gradually, before collapsing to a single front when one front absorbs the others.

Anomalous scaling on a spatiotemporally chaotic attractor.

The Nikolaevskiy model for pattern formation with continuous symmetry exhibits spatiotemporal chaos with strong scale separation. Extensive numerical investigations of the chaotic attractor reveal unexpected scaling behavior of the long-wave modes. Surprisingly, the computed amplitude and correlation time scalings are found to differ from the values obtained by asymptotically consistent multiple-scale analysis. However, when higher-order corrections are added to the leading-order theory of Matthews and Cox, the anomalous scaling is recovered.

Scale and space localization in the Kuramoto-Sivashinsky equation.

We describe a wavelet-based approach to the investigation of spatiotemporally complex dynamics, and show through extensive numerical studies that the dynamics of the Kuramoto-Sivashinsky equation in the spatiotemporally chaotic regime may be understood in terms of localized dynamics in both space and scale (wave number). A projection onto a spline wavelet basis enables good separation of scales, each with characteristic dynamics. At the large scales, one observes essentially slow Gaussian dynamics; at the active scales, structured "events" reminiscent of traveling waves and heteroclinic cycles appear to dominate; while the strongly damped small scales display intermittent behavior. The separation of scales and their dynamics is invariant as the length of the system increases, providing additional support for the extensivity of the spatiotemporally complex dynamics claimed in earlier works. We show also that the dynamics are spatially localized, discuss various correlation lengths, and demonstrate the existence of a characteristic interaction length for instantaneous influences. Our results motivate and advance the search for localized, low-dimensional models that capture the full behavior of spatially extended chaotic partial differential equations. (c) 1999 American Institute of Physics.