METHODS: Five graph models were fit using data from 1574 people who inject drugs in Hartford, CT, USA. We used a degree-corrected stochastic block model, based on goodness-of-fit, to model networks of injection drug users. We simulated transmission of HCV and HIV through this network with varying levels of HCV treatment coverage (0%, 3%, 6%, 12%, or 24%) and varying baseline HCV prevalence in people who inject drugs (30%, 60%, 75%, or 85%). We compared the effectiveness of seven treatment-as-prevention strategies on reducing HCV prevalence over 10 years and 20 years versus no treatment. The strategies consisted of treatment assigned to either a randomly chosen individual who injects drugs or to an individual with the highest number of injection partners. Additional strategies explored the effects of treating either none, half, or all of the injection partners of the selected individual, as well as a strategy based on respondent-driven recruitment into treatment.
FINDINGS: Our model estimates show that at the highest baseline HCV prevalence in people who inject drugs (85%), expansion of treatment coverage does not substantially reduce HCV prevalence for any treatment-as-prevention strategy. However, when baseline HCV prevalence is 60% or lower, treating more than 120 (12%) individuals per 1000 people who inject drugs per year would probably eliminate HCV within 10 years. On average, assigning treatment randomly to individuals who inject drugs is better than targeting individuals with the most injection partners. Treatment-as-prevention strategies that treat additional network members are among the best performing strategies and can enhance less effective strategies that target the degree (ie, the highest number of injection partners) within the network.
INTERPRETATION: Successful HCV treatment as prevention should incorporate the baseline HCV prevalence and will achieve the greatest benefit when coverage is sufficiently expanded.
FUNDING: National Institute on Drug Abuse.
MATERIALS AND METHODS: This study included 64 sets of digitised maxilla and mandible dental casts obtained from a sample of dental arch with normal occlusion. For human evaluation, a convenient sample of orthodontic practitioners ranked the photo images of dental cast from the most tapered to the less tapered (square). In the mathematical analysis, dental arches were interpolated using the fourth-order polynomial equation with millimetric acetate paper and AutoCAD software. Finally, the relations between human evaluation and mathematical objective analyses were evaluated.
RESULTS: Human evaluations were found to be generally in agreement, but only at the extremes of tapered and square arch forms; this indicated general human error and observer bias. The two methods used to plot the arch form were comparable.
CONCLUSION: The use of fourth-order polynomial equation may be facilitative in obtaining a smooth curve, which can produce a template for individual arch that represents all potential tooth positions for the dental arch.