Search strategy

We searched MEDLINE, SCOPUS, COMPENDEX, Google Scholar and Web of Science databases for studies presenting TB transmission models of human populations with contact tracing as an intervention. We limited our search to relevant English language publications from earliest date to February 2012 inclusive. For MEDLINE the search terms used were “Humans” AND (“tuberculosis” OR “latent tuberculosis” OR “tuberculosis, multidrug-resistant” OR “tuberculosis, pulmonary”) AND (“models, theoretical” OR “models, biological” OR “nonlinear dynamics”). For the other databases, which did not use hierarchical keyword structures, title searches on (“TB” OR “Tuberculosis”) and “model” were used. Titles and abstracts were screened to identify studies presenting models of TB transmission dynamics in human populations. Abstracts were then reviewed to limit results to models incorporating active case finding, population stratification or that used a heterogeneous contact structure. Full-text articles were obtained and articles were included for review if they presented models designed to incorporate contact tracing as an intervention. While a number of articles present similar models to those included, models that did not explicitly discuss contact tracing were excluded.

Search results

Of the 1285 studies identified through searching, 1114 were excluded by title search, 151 were excluded through abstract search and 15 were excluded through full text search. Five studies met our inclusion criteria and were included in the review (see Figure 1).

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Figure 1. Flow chart of document search.

https://doi.org/10.1371/journal.pone.0072470.g001

Setting of studies

Four of the studies presented models developed for low prevalence, developed world settings [19]–[22]. In these settings the background prevalence of latent TB infection is relatively low and health care systems frequently include contact tracing as a routine intervention for TB [19], [20]. Mellor et al. present a model for a high prevalence, developing world setting (Zimbabwe) where high HIV prevalence also contributes to the TB epidemic [23].

Interventions investigated

Tian et al., Ziv et al. and Aparicio et al. [22] investigate the scope of contact tracing required to eliminate TB epidemics [20], [21]. Mellor et al. compare likely scenarios for implementation of contact tracing and high risk group investigations in a specific setting to compare their potential effects on incidence, prevalence, mortality and case detection rates [23]. Guzzetta et al. built a model designed to incorporate contact tracing but do not implement the intervention [19].

Aims of the studies

All five studies primarily investigate model characteristics and appropriateness rather than focussing on projections or investigating the epidemiology of TB. For example, Guzzetta et al. and Mellor et al. investigate the improved fit to data and any increased insight provided by models with socio-demographic structure [19], [23]. However, all studies, except Guzzetta et al., did attempt to evaluate the effectiveness of contact tracing programs in a real world context [20], [21], [23].

Models used

Models of infectious disease transmission are often categorised by features such as inclusion or exclusion of random effects (stochastic vs. deterministic) and the level of aggregation (compartmental vs. individual based models).

In deterministic models there is a fixed relationship between input parameters and model outputs so that the same set of initial conditions will always lead to the same outcomes [11]. Stochastic models allow some degree of chance at each time step leading to slightly different outcomes from each simulation. In compartmental models individuals in each class are only considered at an aggregate level where the importance of chance events, including in relation to interventions such as contact tracing, is usually ignored. Individual based models [24] instead simulate each individual in a population and allow for a more realistic implementation of targeted interventions such as contact tracing. These models are always stochastic in contrast to compartmental models which are typically (but not exclusively) deterministic and can be used to gain insight at a population level or for smaller groups of individuals [11]. Individual based models can provide an added level of realism that may provide more accurate insights into disease transmission and control measures. However, they often cannot be evaluated analytically and require considerably more computational power to analyse numerically than compartmental models. The increase complexity also typically leads to larger data requirements and other challenges in parameter estimation.

Tian et al.,Ziv et al. and Aparicio et al. [22] present deterministic compartmental models of TB transmission [20], [21] with uniform mixing in homogeneous populations. Mellor et al. present an individual based stochastic model with household-level clustering. The model incorporates increased individual contact within clusters but assumes that interactions between households are random, so that there is no wider community structure. Guzzetta et al. compare three different models of increasing complexity, starting with a homogenous compartmental deterministic model, followed by two individual based stochastic models which incorporate varying degrees of stratification, clustering and geographic complexity [19]. In their most complex implementation they include workplace and school clustering in addition to household clustering [19], [23]. Guzzetta et al. also assume random interactions outside of the specified clusters but in addition restrict these interactions spatially to emphasise contacts within nearby locations [19].

Disease classes

The disease classes common to all five reviewed studies were susceptible, latently infected, and infectious. All of the studies except Aparicio et al. incorporated reactivation from latent infection into their models.Mellor et al. and Guzzetta et al. included relapse rates for recovered individuals [19], [23]. Aparicio et al. [22], Guzzetta et al. and Mellor et al. incorporate re-infection in their models and assume that latent infection or successful treatment/recovery provided some protection. None of the studies incorporated the Bacillus Calmette–Guérin (BCG) vaccination.

Tian et al. and Mellor et al. include a recovered class from which individuals may transition back to susceptible [25], [27], while only Ziv et al. assumed recovery from the disease provided full immunity against future disease [21]. Aparicio et al., Tian et al. and Mellor et al. include a treated class [20], [22], [23]. Mellor et al. and Ziv et al. include a breakdown of the latent class into early/late or fast/slow disease progression [21], [23]. Tian et al. subdivide classes by case detection status and along with Mellor et al. have classes for non-infectious active disease [20], [23].

For compartmental models such as that used in Tian et al., additional classes or compartments provide a more detailed method of incorporating contact investigation into the model. This has the potential to be more realistic than simply aggregating interventions into a detection or treatment rate but also causes a rise in model complexity. Individual based models are more readily adaptable to realistic implementations of contact tracing.

Stratification

Risk factors such as age, gender, smoking or the presence of interacting infections such as HIV may also be taken into consideration in disease transmission models. Stratifying the simulated population by risk factor enables interactions between risk factors and transitions between disease classes to be incorporated. Key examples of where this may be important include rates of re-activation and the dependence of contact patterns on age, gender or location. Age is often a key determinant in disease transmission modelling as it strongly informs patterns of infectious contact. For many diseases age also influences susceptibility to infection or disease. In TB models the absence of age may result in an underestimation of transmission rates resulting in overestimation of reactivation rates [19], [26].

[TIGHER]Age stratification was implemented in Guzzetta et al. and Mellor et al. [19], [23] while Aparicio et al., Tian et al. and Ziv et al. implemented homogenous population structures [20]–[22]. Mellor et al. made use of age, not only directly in the TB model, but also as a means of determining the impact of sexual activity on HIV as a risk factor for TB [23]. Tian et al. suggest that the model they present would be improved by the use of age stratification and recommend future modelling efforts should include this feature [20].

While none of the models include the BCG vaccine, implementation of BCG in models is challenging due to variable estimates of its efficacy as well as its apparently differential impact on disseminated (and potentially fatal) disease as opposed to pulmonary (and hence transmissible) disease [27].

Implementation of contact tracing

The practical conduct of contact tracing involves several steps, including identification of relevant contacts, decisions on the extent of tracing required and active recruiting of contacts for evaluation. Each step could be represented explicitly in models through the inclusion of additional classes and transition rates. Modelled steps would include probabilities of tracing any given contact, of contacts complying with testing, of tests detecting additional cases and the success probabilities of treatment – although these latter detection and treatment steps would also be required for regular passive detection with DOTS. Depending on the degree of complexity of the model being implemented some or all of these steps might be aggregated. For example an increased rate of detection could be implemented through an increased overall ‘treatment’ rate which incorporates both detection rates and subsequent treatment rates.

In the studies reviewed, contact tracing was implemented with varying degrees of realism. Aparicio et al. and Ziv et al. implement contact tracing at an aggregate population level in the form of increased preventative treatment rates for latently infected cases [21], [22]. Tian et al. include additional compartments for the population previously investigated through contact tracing or passive case detection [20]. Mellor et al. incorporate tracing of household level contacts using tests with specific detection parameters governing their accuracy (the tuberculin skin test (TST) and sputum microscopy) [23]. Guzzetta et al. while justifying their detailed community structure in terms of contact tracing, do not actually implement the intervention in their study [19].

Comparisons with data

In an ideal situation modellers would have at least two independent data sets, where the first data set could be used for model fitting and parameter estimation and the second as a validation set to compare with model results [28]. However as data is typically limited modellers must often make a choice between the use of the available data for parameterisation or validation, or to use data from one data set for both purposes. Approaches taken in the reviewed papers are discussed below.

Parameterization

The parameters of the model govern dynamic changes in disease classes through events such as disease transmission or recovery, as well as demographic processes such as births and deaths. All five studies made extensive use of literature to inform parameter values with additional estimation conducted through fitting models in all studies except Ziv et al. who took parameter values from previous work [21]. Epidemiological data used in parameter estimates was taken from a variety of sources including the WHO, CDC and other published studies. Mellor et al. made use of UNAIDS data and UK based sexual surveys in estimates of HIV prevalence [23]. Household surveys and census data were used for models incorporating heterogeneity in the population (age and/or household clustering) [19], [23].

Calibration of model parameters to data was attempted in four of the five papers, with Ziv et al. [21] choosing instead to use parameters taken from previous work. The method of calibration was different in each study, with maximum likelihood estimation used in Mellor et al. [23], polynomial least squares used in Aparicio et al. [22], a search optimization method in Tian et al. [20] and Latin-Hypercube samples combined with a least-squares threshold used in Guzzetta et al. [19] The source data for individual parameters in Tian et al. and Ziv et al. were not presented in their studies; Tian et al. list a number of sources for all parameter estimates while Ziv et al. state that estimates are taken directly from earlier work [20], [21].

The studies reviewed showed considerable variance in several key parameters (Table 1). For example, the number of new infections per infectious person per year varies between 7 and 18.8 infections while the mean duration of infectious period also varies from 0.3 to 2 years (Table 1). The mean survival time for TB cases also ranges from 3.3 years to 27 years. While setting dependent differences do occur in such parameters the variation in these key parameters is large and hinders model comparison. The models also incorporate treatment in different ways with Mellor et al. [23] and Tian et al. [20] using explicit detection and treatment rates while the other models use only aggregate treatment rates. When combined with the significant differences in parameter values described above, this variation makes parameter study outcomes difficult to summarise collectively. Choices in parameterization, both in terms of values and the structural form of the parameters, affect both the way interventions are implemented and their impacts with flow on effects to policy implications.

Validation of model predictions

Baseline predictions (pre-intervention) were compared to observed epidemics to validate models in Aparicio et al., Guzzetta et al. and Mellor et al. [19], [22], [23] while Tian et al. present no baseline predictions [20] and Ziv et al. present models parameterized from previous work [21]. None of the reviewed studies attempt to validate the predicted efficacy of the contact tracing intervention with data. While there is little or no RCT data available to use in this instance, some observational data should be available in settings in which contact tracing has been in place as an intervention for some time (such as the USA) [29].

Sensitivity Analysis

Aparicio et al. [22], Tian et al. and Mellor et al. discuss the sensitivity analysis conducted for the models they present [20], [23]. Aparicio et al. [22] vary the contact number (the number of secondary infections caused by an average case in a fully susceptible environment) through a realistic range. Tian et al. separately vary the number of contacts traced and mean time taken per investigation to determine how sensitive the model is to these parameters [20]. Mellor et al. find that their model is sensitive to reducing the long-term HIV prevalence, with reduced TB incidence the main impact (increases in this parameter had little effect) [23]. Ziv et al. do not perform sensitivity analysis for the model presented. Instead, they use estimates from previous work in which LHS was used in estimating parameters, but do not discuss sensitivity to this parameterization [21]. Similarly Guzzetta et al. use LHS in parameter estimation but do not discuss sensitivity [19].

Key Findings of the Studies

Tian et al. demonstrate that for a specific low burden setting there are limited gains to be made from increased levels of detection beyond a certain point. They suggest that there is an optimal level that will result in eventual epidemic elimination beyond which there are diminishing returns from increased number of investigations [20]. Aparicio et al. and Ziv et al. find that effective treatment of latent TB cases (discovered through contact tracing) should result in TB epidemic elimination in a low burden setting [21], [22]. Mellor et al. find that targeting known high risk households with HIV positive individuals may be more effective than contact tracing [23]. Guzzetta et al. compare modelling methodologies for TB and find that socio-demographic individual based models provide good fits to available data and are of a form which allows evaluation of control strategies such as contact tracing [19].

Recommendations of the Studies

The three recent studies recommend developing individual based models for the modelling of sophisticated social networks required for a detailed implementation of contact tracing [19], [20], [23]. Mellor et al. also suggests that targeted active case finding interventions in households with HIV-infected individuals may be more effective than contact tracing of TB-infected patients [23]. Tian et al. suggested that contact tracing is in a sense self-limiting and an optimal strategy could involve targeted investigations of intimate or close contacts, although their model does not provide information on the nature of contacts [25]. Aparicio et.al. and Ziv et al. suggest that using contact investigation programs to find recently infected persons may substantially contribute to the effort to control tuberculosis [21], [22], and Aparicio et al. go further to state that such a strategy may be more cost efficient than current strategies Guzzetta et al. [19] note the need for household transmission data to accurately estimate the impact of contact investigation interventions.

Recommendations

Realistic implementations of contact tracing as an intervention in TB epidemics require the development of individual based models which can incorporate the required detail of contact structure. At present it is not clear that such approaches are superior to compartmental models as the value of this added realism will be best assessed through direct comparison between such models and simplified approaches.

The settings with the most potential to gain from implementing interventions such as contact tracing in addition to existing DOTS are those with high burdens from TB epidemics in which DOTS alone has not been sufficient to control the epidemic. There is an urgent need to develop models for settings both with and without high HIV prevalence which can be used to help make decisions about which interventions to put in place.

Access to and better use of more detailed data on the implementation and impact of contact tracing as an intervention, in addition to improved demographic data on contact and household structures are likely to be important elements of progress in this field. There is a great potential for collaborative work between clinicians, epidemiologists and modellers to use field studies and routine surveillance activities to gather the data required to inform future models.