Modelling hepatitis C transmission over a social network of injecting drug users

Abstract

Hepatitis C virus (HCV) is a blood-borne virus that disproportionately affects people who inject drugs (PWIDs). Based on extensive interview and blood test data from a longitudinal study in Melbourne, Australia, we describe an individual-based transmission model for HCV spread amongst PWID. We use this model to simulate the transmission of HCV on an empirical social network of PWID. A feature of our model is that sources of infection can be both network neighbours and non-neighbours via “importing”. Data-driven estimates of sharing frequency and rate of importing are provided. Compared to an appropriately calibrated fully connected network, the empirical network provides some protective effect on the time to primary infection. We also illustrate heterogeneities in incidence rate of infection, both across and within node degrees (i.e., number of network partners). We explore the reduced risk of infection from spontaneously clearing cutpoint nodes whose infection status oscillates, both in theory and in simulation. Further, we show our model-based estimate of per-event transmission probability largely agrees with previous estimates at the lower end of the range 1–3% commonly cited.

Introduction

Hepatitis C is a blood-borne virus that is estimated to infect 200 million people worldwide. Approximately 80–90% of HCV infections in Australia occur in PWID (NCHECR, 2006). The proportion of people infected with HCV who develop persistent or chronic infection is in the range of 50–70% (NCHECR, 2006). A subset of those with chronic infection is at risk of developing cirrhosis, liver failure and hepatocellular carcinoma. Mathematical modelling of the spread of HCV has a large role to play in projecting the future course of the epidemic (e.g., NCHECR, 2006, Vickerman et al., 2009, Hutchinson et al., 2006), assessing the benefits of possible behavioural interventions (e.g., NCHECR, 2009, Vickerman et al., 2007), and exploring the benefits and deployment strategies of potential vaccines and treatments (e.g., Hahn et al., 2009). Kretzschmar and Wiessing (2008) provide an overview of contemporary challenges in modelling HCV.

Previous models of HCV transmission have typically made some assumption of “mixing” (e.g., Mather and Crofts, 1999, Pollack, 2001, Esposito and Rossi, 2004, Salomon et al., 2002, Vickerman et al., 2007, Vickerman et al., 2009, Hahn et al., 2009, also Murray et al., 2003, NCHECR, 2009, NCHECR, 2006 in the Australian context). That is, members of a population are assumed to have contact with all other members of the population (Anderson and May, 1991). Typically these models are deterministic, using differential equations to model quantities such as the total numbers of susceptibles and infectives in “compartments” (e.g., Pollack, 2001, Murray et al., 2003, Esposito and Rossi, 2004, Salomon et al., 2002, Vickerman et al., 2007, Vickerman et al., 2009), although some use stochastic simulation (e.g., Mather and Crofts, 1999, Hutchinson et al., 2006, Hahn et al., 2009, Moneim and Mosa, 2009). As our understanding of HCV has grown, these models have become increasingly sophisticated. Yet, while mixing has proven to be a useful simplifying assumption, particularly for modelling large populations, these models lack empirically grounded, disease relevant contact patterns (networks), and so fail to capture individual heterogeneity. (Hutchinson et al., 2006 is noteworthy for using a basic non-mixing approach that randomly assigns and removes sharing partners to create a simple random network which varies from year to year.) It is increasingly recognised that contact networks are relevant for understanding the transmission dynamics of various viruses like HCV. (See Welch et al., 2011 and references therein for an overview.)

While there is a large body of research on social networks (primarily sexual contact networks) relevant to HIV transmission (e.g., Morris, 2004 and references therein), networks-based research in HCV is in its infancy (Aitken et al., 2004, Brewer et al., 2006, Wylie et al., 2006, De et al., 2007, Aitken et al., 2008, Miller et al., 2009). In the context of HCV, the contact network of PWID formed by sharing needles/syringes is arguably most relevant. (The importance of sharing of other related equipment such as filters and spoons is less certain. See De et al., 2008 for a review.) Only recently have data on PWIDs been collected with both blood samples and a social network component (e.g., Aitken et al., 2008, Miller et al., 2009) that allow estimating incidence rates in conjunction with creating/estimating the network itself.

Individual-based (or agent-based) stochastic models of disease transmission have become increasingly popular (e.g., Hutchinson et al., 2006, Hahn et al., 2009 for HCV). They appear well-suited both to modelling individual heterogeneity and to modelling the spread of disease on networks. Unfortunately, these models for HCV lack an empirically grounded contact network.

This paper describes the first individual-based stochastic model of HCV transmission based on an empirical social network of PWID. Our model was created: (1) to explore the role of the network in HCV transmission, and (2) to investigate epidemiological differences between using the latest developments in social network modelling with other common network models and compartmental (i.e., non-network) models. Our main quantities of interest are the incidence rate of primary and secondary infection and the time to primary infection. Our model, parameter estimates and social network are based on data collected in Melbourne, Australia in the “Networks 2” study of the Burnet Institute (Aitken et al., 2008, Miller et al., 2009). The empirical social network is based on extensive interview data and its derivation is described below. Sources of infection in our model include both network neighbours and a source of “imported infections” which is independent of the social network. The rate of imported infections is estimated from empirical data.

In this paper we investigate HCV transmission on our empirical network and on a fully connected network which represents a mixing assumption. We demonstrate a protective effect, on the time to primary infection, of the social network in comparison with a mixing assumption. We illustrate heterogeneities in rate of infection, both across and within node degrees. We explore the attenuated risk of infection from gateway nodes whose infection status oscillates, both in theory and in simulation. Further, our model-based estimate of per-event transmission probability is shown to largely confirm the estimate of Hahn et al. (2009) at the lower end of the range 1–3% commonly cited. A number of upcoming additional investigations are described in Discussion.

The rest of this paper is organized as follows. Section 2 describes the data, the social network, and how various parameters were estimated. Section 3 describes the individual-based model in detail and describes how calibration was used to determine the probability of transmission from a single sharing event. Section 4 describes results from numerous simulations and a theoretical treatment of the reduced risk of gateway nodes whose infection status oscillates, followed by a discussion in Section 5.