The authors have declared that no competing interests exist.
Conceived and designed the experiments: DAR RSD EM PP GR MH. Performed the experiments: DAR. Analyzed the data: DAR RSD RJ. Wrote the paper: DAR RSD RJ EM PP GR MH. Designed simulation software: DAR. Reviewed treatment/vaccination literature: DAR.
Hepatitis C virus (HCV) chronically infects over 180 million people worldwide, with over 350,000 estimated deaths attributed yearly to HCV-related liver diseases. It disproportionally affects people who inject drugs (PWID). Currently there is no preventative vaccine and interventions feature long treatment durations with severe side-effects. Upcoming treatments will improve this situation, making possible large-scale treatment interventions. How these strategies should target HCV-infected PWID remains an important unanswered question. Previous models of HCV have lacked empirically grounded contact models of PWID. Here we report results on HCV transmission and treatment using simulated contact networks generated from an empirically grounded network model using recently developed statistical approaches in social network analysis. Our HCV transmission model is a detailed, stochastic, individual-based model including spontaneously clearing nodes. On transmission we investigate the role of number of contacts and injecting frequency on time to primary infection and the role of spontaneously clearing nodes on incidence rates. On treatment we investigate the effect of nine network-based treatment strategies on chronic prevalence and incidence rates of primary infection and re-infection. Both numbers of contacts and injecting frequency play key roles in reducing time to primary infection. The change from “less-” to “more-frequent” injector is roughly similar to having one additional network contact. Nodes that spontaneously clear their HCV infection have a local effect on infection risk and the total number of such nodes (but not their locations) has a network wide effect on the incidence of both primary and re-infection with HCV. Re-infection plays a large role in the effectiveness of treatment interventions. Strategies that choose PWID and treat all their contacts (analogous to ring vaccination) are most effective in reducing the incidence rates of re-infection and combined infection. A strategy targeting infected PWID with the most contacts (analogous to targeted vaccination) is the least effective.
Hepatitis C virus (HCV) is a blood-borne virus which chronically infects over 180 million people worldwide
Current treatment for HCV generally ranges from 24–48 weeks of pegylated interferon and ribavirin depending on the HCV genotype, IL28B genotype and stage of hepatic fibrosis. Increasingly, HCV treatment is becoming “response based” with the length of treatment varying based on how quickly a patient’s viral load becomes undetectable. Current treatments are estimated to be effective in about 60%
Over the next five years there will be major changes in HCV treatment. With the advent of direct-acting antiviral medications, treatment will become more efficacious, of shorter duration and will have less severe side effects. As well as benefiting individual patients, recent mathematical modelling suggests that treating PWID can lead to a considerable reduction in HCV prevalence over time due to a decrease in HCV transmission within the PWID community
Previous models of HCV transmission have typically made some assumption of “mixing” rather than consider the contact network of PWID (e.g.
Most of the research into network-based interventions to limit disease transmission has involved network contact modification such as isolation (e.g., for SARS
In practice, the entire network is usually unknown, so strategies requiring local information are most clinically relevant. Research into these strategies usually assumes the contact network has rare nodes with very large numbers of contacts (e.g., “scale-free” networks
The study by Porco et al.
Simulation models provide an effective method to investigate disease transmission and to conduct controlled experiments to explore the potential benefits of possible treatment strategies. Here we explore HCV transmission and possible treatment strategies on empirically grounded simulated PWID contact networks. Our work builds on our previous efforts creating both an individual-based transmission model
Our network model
This work studies HCV transmission and treatment in the context of empirically grounded contact networks. In the context of treatment we investigate an anticipated HCV treatment rather than preventative vaccines, starting in a situation where HCV is essentially endemic, infecting about half the network. We directly compare a number of network-based interventions in this population, including ring vaccination with secondary contacts. In the context of transmission we investigate the role of the number of contacts and injecting frequency on time to primary infection and the role of spontaneously clearing nodes on incidence rates. Importantly, in this study the PWID contact network model is empirically grounded and the transmission model includes “imported infections” which recognise both the limitations around including all network partners in empirical studies and the limitations of using a static network to model time intervals longer than those used to define a contact.
Details of our transmission model have appeared elsewhere
A feature of our model is that a fraction (25%
Model calibration for
Details of our contact network model have been described elsewhere
Using this empirical network and results from social network analysis
Parameter | Parameter Value |
Edge | −8.384 |
Isolates | −9.308 |
Alternating- |
0.611 |
Alternating- |
1.707 |
Alternating- |
−0.563 |
Same location | 2.111 |
Same gender | 0.280 |
Same age<25 | 0.787 |
Same daily user freq. | 0.429 |
Specification for the PWID contact network ERGM. The first five parameters model network structure while the last four model homophily effects: location (1, 2, 3), gender (M/F), age (less than 25, greater than 25), and injecting frequency (less than daily, at least daily). Positive homophily parameters indicate a propensity for two PWID to share a network tie when they have that attribute in common.
For the results reported here we use 100 simulated networks, each of which has 274 nodes. We form these networks by using the ERGM to simulate many networks with 524 nodes, and keep the first 100 largest components that have 274 nodes. The size 274 was chosen simply because it was the mode of the distribution of largest component sizes across 48,000 simulated networks reported previously
We conducted three sets of simulations. The first set was designed to investigate the role of network features on the time to primary infection in the baseline transmission model. (Throughout, an infection is “primary” if the node was never previously infected, including in the burn-in phase. Otherwise, an infection is counted as a “re-infection”.) Key parameter values are listed in
Model Parameter Definition | Value | Reference |
Prob. of transmission from one sharing event ( |
0.00995 | |
Rate of importing infection into a node ( |
varies | |
Proportion of spontaneously clearing nodes | 0.25 | |
Prevalence at end of burn-in phase | 0.56 | |
Edgewise weekly probability of sharing (both less-frequent users) | 0.19 | |
Edgewise weekly probability of sharing (one less-frequent user) | 0.18 | |
Edgewise weekly probability of sharing (two more-frequent users) | 0.24 | |
Incidence rate ratio for imported infections of freq. vs. non-freq. users | 1.3 | |
Mean time to chronic spontaneous clearance (years) | 200 | |
Duration of latent period (weeks) | 2 | |
Mean time to acute spontaneous clearance (weeks) | 7 | |
Duration of acute phase (weeks) | 26 | by definition |
Key model parameters used for transmission and treatment simulations. Less-frequent users have injecting behaviour less than weekly (on average) while more-frequent users have injecting behaviour at least weekly (on average). Rate of importing infection
The second set of simulations was designed to investigate the impact of network features (e.g., arrangement of spontaneously clearing nodes, number of spontaneously clearing nodes) on the incidence rate of total infection (i.e., primary or re-infection) in the baseline transmission model. Again, no community treatment strategies were included. By creating sets of nested simulations and fixing certain features (e.g., spontaneously clearing group, number of spontaneously clearing nodes, etc.) we can isolate their effect on the incidence rate of total infection. First, groups of spontaneously clearing nodes were created (referred to as S1, S2,
The third set of simulations was designed to investigate the effect of treatment strategies on both the incidence rate of infection and prevalence. For each of the nine treatment strategies, 500 simulations were performed (a different burn-in for each) for each of seven treatment initiation frequencies (i.e, treatment “epochs” to find and begin treating new people are regularly spaced every 1, 2, 4, 8, 13, 26 or 52 weeks.) This is equivalent to treatment coverage varying from 3.7–190 treatment initiations per 1000 PWID per year if each epoch corresponds to one treatment initiation. These simulations cover a period of 156 weeks (i.e., three years) following burn-in which provides enough time that differences between the strategies emerge. We made the following assumptions about treatments based on projected characteristics of direct-acting antivirals that are currently under development
For these simulations, different burn-ins have different random collections of spontaneously clearing nodes, different random collections of nodes for whom treatment is effective, and different random arrangements of infected nodes at the end of burn-in. By averaging over the 500 simulations the differences between strategies can be separated from random “noise”. Averaging over the 100 networks has a similar effect on the random selection of networks. To further minimise the effects of random noise, the post-burn-in simulations were also organized as a series of controlled experiments, where the control group was the baseline simulations using the results from the 50 000 burn-ins (500 per network, 100 networks) as initial configurations. Simulations for each of the nine treatment strategies used the same 50 000 burn-ins as initial configurations. In total, the investigation of treatment strategies involved over 3 million post-burn-in simulations (500 simulations×9 strategies×7 frequencies×100 networks).
We consider nine treatment strategies in all. One strategy uses no network information, two strategies use “global” information about the network, and six use information local to individual nodes. We further describe these strategies here. They are summarised in
Strategy | Short Name | Node Selection at each Treatment Epoch |
Decreasing node degree | dec. degree | Choose node avail. for treatment with largest node degree. |
Increasing node degree | inc. degree | Choose node avail. for treatment with smallest node degree. |
Random node selection | random | Choose avail. ego randomly. Treat ego. |
Acquaintance, degree ≥5 | acq5 | Choose avail. ego randomly. Treat ego & ego’s avail. contacts with node degree ≥5. |
Acquaintance, degree ≥3 | acq3 | Choose avail. ego randomly. Treat ego & ego’s avail. contacts with node degree ≥3. |
Primary contacts | ring | Choose avail. ego randomly. Treat ego & ego’s avail. contacts. |
Primary & some sec. contacts | 2-ring | Choose avail. ego randomly. Treat ego, avail. prim. contacts and some avail. sec. contacts. |
Primary and all sec. contacts | 2-ring all | Choose avail. ego randomly. Treat ego, avail. prim. contacts, and all avail. sec. contacts. |
Contacts of uninfected nodes | naive ring | Choose uninfected ego randomly. Treat all of ego’s avail. prim. contacts. |
Abbreviations: “avail.”: available, “prim.”: primary, “sec.”: secondary.
Treatment strategies considered. In all cases, only infected nodes not currently in treatment and without a history of treatment failure are “available” for treatment.
The treatment strategy (“random”) selects a node at random at each treatment epoch from the collection of available nodes. Thus, no network information is used. For this strategy there is a clear, non-random relationship between the treatment frequency and the mean number of treatment starts per 1000 PWIDs. For example, new treatment epochs every fourth week would see 13 people treated per year or about 47 people yearly per 1000 in a network component of size 274.
We consider two treatment strategies that use “global” information about the network. That is, at each treatment epoch, the strategies rank the available nodes in priority order for treatment, either by order of increasing (“inc. degree”) or decreasing (“dec. degree”) node degree and choose the highest ranked node for treatment. Taking nodes in decreasing order is analogous to targeted vaccination. Since knowing all node degrees and knowing the current infection status of all nodes in the PWID network will both generally be impossible, these are not practical strategies. However, they can serve as useful benchmarks. Indeed, amongst vaccination strategies the best known strategy on scale-free networks is believed to be targeted vaccination
By analogy with ring vaccination, for ring treatment (“ring”), at each treatment epoch one node (“ego”) is chosen at random from those available for treatment, and treated. In addition, all of ego’s primary contacts (i.e., ego’s “ring”) which are available for treatment, are treated. Across simulations the number of treatment initiations will vary depending on node degrees and the number of neighbours actually infected.
We also consider two treatment strategies, analogous to enhanced acquaintance immununization, in which we treat ego, chosen at random, and certain members of ego’s ring that are available for treatment. The criteria for their treatment is that their number of contacts (i.e., node degree) is at least some cutoff: either 5 (“acq5”) or 3 (“acq3”). Note that unlike enhanced acquaintance immununization, we also treat ego. Also note that “acq
We consider two treatment strategies that include primary and secondary contacts. There are two strategies because a secondary contact could be defined as all the additional neighbours of
Thus the four strategies “random”, “acq5”, “acq3”, and “ring” capture a spectrum of strategies that begin with a randomly chosen ego at each treatment epoch and treat an increasing fraction of ego’s primary contacts, while the “2-ring” and “2-ring all” strategies go even further by treating an increasing fraction of ego’s secondary contacts too.
Finally, we consider an additional treatment strategy (“naive ring”) which treats the infected primary contacts of randomly selected HCV-naive (i.e., never infected) nodes. This is the only strategy for which the randomly chosen node is not available for treatment. We caution that results for this strategy must be viewed as preliminary. Our network model does not explicitly model the contacts of new injectors. Thus, it assumes their contacts are similar to more experienced injectors, and so results for this strategy will be the most sensitive to departures from this assumption. We discuss this further in the Discussion.
Network visualisation was created using Pajek
As expected, both increased numbers of contacts (i.e., node degree) and increased injecting frequency play key roles in reducing the time to primary infection.
Boxplots are for results for each of 12 categories (node degrees 1–6; two injecting frequencies) over 100 networks. Injecting behaviour frequency is denoted as “less” (i.e., less than daily) or “more” (i.e., at least daily). For each network, results are formed from 3000 HCV simulations as the median for each node as both a less frequent and a more frequent injector, and then the median for each of the 12 groups. Boxes show the 25-th and 75-th percentiles. The central line denotes the median, the whiskers show the range of data not considered outliers, and outliers are shown individually. More frequent injecting behaviour is approximately equivalent to being a less frequent injector with one additional network contact.
We investigated the role of spontaneously clearing nodes on the incidence rate of total infection (i.e., primary or re-infection) using analysis of variance (ANOVA) and nested models in which the burn-in group is nested within the particular group of spontaneously clearing nodes. The number and locations of spontaneously clearing nodes varies randomly across the groups of spontaneously clearing nodes. For a single fixed network of size 274, simulation results from 15 randomly chosen groups of spontaneously clearing nodes (
We repeated the nested ANOVA analysis using simulation results from nine additional networks of size 274 chosen at random, to make ten in total. For all ten networks the spontaneously clearing group was a significant effect in determining the incidence rate of total infection (i.e.,
Vertical coordinate shows the mean incidence rate of total infection in weeks 131–156, calculated as the mean incidence rates across 500 simulations and then the mean (with 95% confidence interval) across 100 networks. Horizontal coordinate shows the mean number of treatments started in weeks 1–156, calculated as the means across 500 simulations per network, then the mean across 100 networks, and then the mean across 3 years. Strategies that choose nodes at random and ignore the infection status of some (“acq5”) or all (“dec. degree”, “random”) primary contacts have the largest incidence rate of infection. Conversely, the 2-ring strategies and “naive ring” have the lowest incidence rate of infection. Mean treatment starts for “naive ring” are smaller because there are limited numbers of infected nodes available for treatment around randomly chosen uninfected nodes.
The use of the network strategies can be seen as a way of reducing the number of treatments to achieve a desired effect. For example, the effect from treating 47 randomly chosen infected people per 1000 PWID (i.e., 13 in a network of 274) is approximately the same as treating 35 infected people per 1000 using the ring strategy. This difference increases as the treatment frequency increases.
Vertical coordinate shows the mean incidence rate of re-infection infection in weeks 131–156, calculated as the mean incidence rates across 500 simulations and then the mean (with 95% confidence interval) across 100 networks. Horizontal coordinate shows the mean number of treatments started in weeks 1–156, calculated as the means across 500 simulations per network, then the mean across 100 networks, and then the mean across 3 years. Strategies that choose nodes at random and ignore the infection status of some (“acq5”) or all (“dec. degree”, “random”) primary contacts have the largest incidence rate of infection. Conversely, the 2-ring strategies have the lowest incidence rate of infection. Mean treatment starts for “naive ring” are smaller because there are limited numbers of infected nodes available for treatment around randomly chosen uninfected nodes.
Vertical coordinate shows the mean incidence rate of primary infection in weeks 131–156, calculated as the mean incidence rates across 500 simulations and then the mean (with 95% confidence interval) across 100 networks. Horizontal coordinate shows the mean number of treatments started in weeks 1–156, calculated as the means across 500 simulations per network, then the mean across 100 networks, and then the mean across 3 years. Differences between strategies are smaller than for the incidence rate of total infection and re-infection. The “naive ring” strategy, which treats the primary contacts of randomly-chosen never infected nodes (if they exist) is quite effective. Mean treatment starts for “naive ring” are smaller because there are limited numbers of infected nodes available for treatment around randomly chosen uninfected nodes.
Secondly, except for “naive ring”, an ordering of the strategies using the incidence rate of re-infection is the same as one using the incidence rate of total infection. (Recall that “naive ring” is specifically designed to protect never-infected individuals from infection by treating their contacts.) To better understand the effect of treating nodes but not their infected contacts, and to distinguish the effect of network transmission from the effect of imported infections,
Vertical coordinate shows the mean proportion of new infections in weeks 131–156 that are network-based (i.e., not imported), calculated as the mean proportions across 500 simulations and then the mean (with 95% confidence interval) across 100 networks. Horizontal coordinate shows the mean number of treatments started in weeks 1–156, calculated as the means across 500 simulations per network, then the mean across 100 networks, and then the mean across 3 years. Strategies that choose high-risk nodes (i.e., more primary contacts) at random while ignoring the infection status of some (“acq5”) or all (“dec. degree”, “random”) primary contacts show a larger fraction of network-based infections. At higher treatment frequencies, “inc. degree” shows an increasing fraction of network-based infections as higher-risk nodes are treated. The “naive ring” strategy, which treats the primary contacts of randomly-chosen never infected nodes (if they exist), effectively reduces network-based transmission.
Thirdly, with the exception of “naive ring”, the differences in the rate of primary infection between the strategies are negligible. For “naive ring”, a trade-off is at work. By focussing on never infected nodes, the incidence rate of primary infections can be lowered, but at the expense of a higher incidence rate of re-infection for other nodes. Whether there is a net benefit from this trade-off is a different matter, but
Finally, we note that the additional benefit from “ring” to “2-ring” is small. In practice, the benefit from using a 2-ring strategy may be outweighed by the additional complexity of finding and treating secondary contacts. Cost-benefit analysis comparing these strategies is left for future work.
Vertical coordinate shows the mean chronic prevalence (defined as the proportion of nodes infected constantly for the last 26 weeks, calculated as the mean proportions across 500 simulations and then the mean (with 95% confidence interval) across 100 networks. Horizontal coordinate shows the mean number of treatments started in weeks 1–156, calculated as the means across 500 simulations per network, then the mean across 100 networks, and then the mean across 3 years.
We conducted a number of additional analyses to assess the sensitivity of our results to various assumptions. Since we use a static network model, we assessed the sensitivity of our treatment results to the choice of the particular weeks after burn-in used for reporting results. Specifically, we limit the time period of interest to the first 52 weeks following burn-in. On this shorter period the assumption of a static network is more realistic. To do this we calculate the incidence rate of total infection for each of the nine strategies on weeks 27 to 52 which provides 26 weeks for the treatments to produce an effect. We calculate the number of treatments on weeks 1 to 52. Results for the treatment strategies are qualitatively similar. That is, a ranking of the strategies from most to least effective is the same. The main difference is that the size of the impacts were not as great, due to a smaller period for treatment to have an effect. This is not shown for brevity. Importantly, this shows that even over a shorter time period in which the assumption of a static network is more realistic, our conclusions ranking the various treatment strategies do not change.
We conducted additional simulations to account for uncertainty in input parameters to our model. In total, 14 additional scenarios were investigated under five treatment strategies (decreasing degree, random, ring, 2-ring, naive ring). These are described in
Finally, to investigate the suitability of our assumption of a static network, we performed additional analysis on the duration of edges in our empirical network
Our results demonstrate the PWID network plays an important role in hepatitis C transmission through both the number of contacts and the attributes of one’s sharing partners. Understanding the PWID network is likely to play an important role in the effective and efficient roll out of HCV treatment of PWID over the next 20 years. In this study, strategies that include treatment of both primary and secondary contacts are the most effective in reducing incidence rates of re-infection and total infection, for similar numbers of treatment starts.
We have shown that the number of network partners plays an important, direct role in determining the time to primary infection. The time to primary infection for someone with six contacts may be less than half that of someone with one contact. Our network model also suggests location, age and frequency of injecting contribute to the configuration of the network, thus playing an indirect role in risk of infection too. We have also shown that the difference in time to primary infection between “less-frequent” and “more-frequent” injector is roughly the same as having one additional network contact. Thus, it may be more effective for health promotion campaigns to focus on the social context in which risk behaviours take place (e.g., with whom, with how many different people), rather than simply focusing on the behaviours themselves (e.g., sharing injecting equipment).
In the context of treatment, treating an individual without treating their contacts leaves a reservoir of virus as a source of re-infection (in the absence of acquired immunity) and so those treated are at high risk of re-infection. Treatment strategies that take advantage of the contact network of PWID are more effective in lowering both the incidence rates of re-infection and total infection. For similar numbers of treatment starts above about 20 per year per 1000 PWID, the most effective strategies at lowering incidence rates of re-infection in this study treat infected primary and secondary contacts of infected PWID as well (i.e., “2-ring”, “2-ring all”). The strategy treating primary contacts but not secondary contacts (“ring”) was almost as effective. The least effective strategies treat infected PWID selected at random (“random”), or chosen by decreasing numbers of primary contacts (“dec. degree”). The lack of effectiveness of “dec. degree” as a treatment strategy is in stark contrast to the widespread belief that targeted vaccination is the most effective
A common way to think of an infectious disease spreading is to imagine the disease spreading away from an index case at the start (e.g. SARS, influenza) or end (e.g. smallpox eradication) of an outbreak. In the context of HCV in Melbourne, Australia, where half or more of the population of interest (PWIDs) are already infected, it may more more helpful to think of infection transmitted
We have demonstrated a reduction in chronic prevalence through treatment. Martin et al. (
In the context of HCV transmission we have shown that the number (and proportion) of spontaneously clearing nodes has a statistically significant effect on the network-wide incidence rate of total infection. On the other hand, for a fixed number of such nodes, their arrangement within the network does not have a statistically significant effect on incidence rate of total infection. This suggests that apart from their risk of re-infection, the effect of spontaneously clearing nodes is a local effect
Our work is novel for a number of reasons. 1) Our study investigates an anticipated HCV treatment, rather than preventative vaccines. 2) Unlike other network-based intervention studies we do not consider the beginning or the end of an epidemic. Rather, HCV is essentially endemic, infecting about half the network. 3) We directly compare a number of network-based interventions in this population, including ring vaccination with secondary contacts. 4) The contact network model of PWID is empirically grounded
This study has several limitations. We have modelled a three year period following burn-in using a static network, which we recognise is an approximation. As described in Welch et al.
We deliberately considered the use of a treatment rather than a vaccine because this is a major issue with the considerable advances in direct-acting antiviral agents, and there is currently no vaccine for HCV. Necessarily, treatment is targeted at sero-positive PWID. This differs from the results in Hahn et al.
We have not explicitly modelled the arrival of new injectors to the network. This means our results on the time to primary infection and “naive ring” treatment strategy assume the contacts of new injectors are similar to others in the network. Our results on “naive ring” in particular highlight the need for a dynamic network model as future work, with special emphasis on new members to the drug-injecting scene. Those people represent a pool of uninfected people. How they form contacts early in their injecting careers must play a key role in both their risk of primary infection and strategies to prevent primary infection. Such a model would also give an indication of the role of population turnover in the infecting scene as newer, never-infected people enter the injecting scene while more experienced, infected people leave.
The treatment strategies considered here do not explicitly target recent infections or new PWID. As a result differences in the rate of primary infection between the strategies are negligible (with the exception of the “naive ring” strategy). We leave study of such strategies for future work.
We have assumed the probability of infection is constant throughout the duration of an infection. Currently there is no consensus on the variability in infectivity following infection, and we feel any other choice would be arbitrary in the absence of supporting data. We think the role of increased infectivity in the first acute phase of infection would be minor over short durations when over 50% of nodes in the network have already been infected by the end of burn-in. We also suspect increased infectivity in the acute phase will be more important for a dynamic model where the arrival and early days of HCV-uninfected people in the network are explicitly modelled.
Our transmission model assumes no acquired immunity. Under this assumption, “boomerang” infections, in which A infects B, A becomes uninfected, then B infects A, can play an important role in re-infection. We feel this is a conservative assumption in the context of a model of the effects of treatment on HCV incidence and prevalence. Results from empirical studies of HCV re-infection following spontaneous clearance of prior HCV infection have been variable, with some reporting much lower rates of re-infection compared to primary infection
The imported infections included in the transmission model provide a way to model risk of infection from sources other than primary contacts. It is a modelling device that reflects limitations in modelling the contact network, which in turn reflects difficulties with collecting data on this difficult-to-reach population of individuals. Since this risk of infection is independent of the contact network and lacks heterogeneity (except for the difference in incidence rate between less-frequent and more-frequent injectors), our results should be conservative with respect to differences between network-based treatment strategies.
Our investigation of contact referral strategies like ring treatment assumes all infected contacts are treated. In reality, only a fraction of those contacts would be treated. For example, some contacts may be unwilling to have their HCV status determined, while others may reject treatment despite being infected. Although we have not explicitly modelled these effects, a number of aspects of our simulation mitigate these differences. We assume the treatments are only effective in 80% of people, so incomplete elimination of infection in primary contacts is already included. Futher, we include importing of infection which means a node continues to have risk even if all contacts are uninfected. Finally, the acquaintance immunisation strategies “acq3” and “acq5” treat only a fraction of a node’s primary contacts, thus giving a sense of the difference incomplete treatment of primary contacts can make (albeit when untreated primary contacts are not randomly chosen, but chosen by node degree.).
It would be interesting to do a direct comparison of our network based HCV model treating random nodes, for example, with a deterministic mixing model using similar treatments and similar treatment numbers. This would help aid interpretation of results from mixing models. This is left for future work.
(DOC)
The authors are grateful to the field workers who collected the data that made this study possible. The authors wish to thank Jodie McVernon and James McCaw for providing helpful computing resources. Finally, the authors wish to thank the six reviewers for their helpful feedback on the manuscript.