Strategic Planning for Tuberculosis Control in the Republic of Fiji

The tuberculosis (TB) health burden in Fiji has been declining in recent years, although challenges remain in improving control of the diabetes co-epidemic and achieving adequate case detection across the widely dispersed archipelago. We applied a mathematical model of TB transmission to the TB epidemic in Fiji that captured the historical reality over several decades, including age stratification, diabetes, varying disease manifestations, and incorrect diagnoses. Next, we simulated six intervention scenarios that are under consideration by the Fiji National Tuberculosis Program. Our findings show that the interventions were able to achieve only modest improvements in disease burden, with awareness raising being the most effective intervention to reduce TB incidence, and treatment support yielding the highest impact on mortality. These improvements would fall far short of the ambitious targets that have been set by the country, and could easily be derailed by moderate increases in the diabetes burden. Furthermore, the effectiveness of the interventions was limited by the extensive pool of latent TB infection, because the programs were directed at only active cases, and thus were unlikely to achieve the desired reductions in burden. Therefore, it is essential to address the co-epidemic of diabetes and treat people with latent TB infection.


Constant parameters
The constant parameters (first group in Section 2) that do not vary with the calendar time through model integration are presented in Table S1 below. The rationale and review of the relevant evidence that were used to determine these parameter values are presented in the following sections.

Epidemiological uncertainty parameters
We restrict the parameters that can be varied during calibration to TB-specific parameters that would otherwise remain constant throughout model runs. This behaviour is chosen so that the uncertainty calculations capture the considerable epidemiological uncertainty in such parameters, whereas the programmatic parameters are fitted to the best available data for each time point available. Similarly, the intervention-related and economic parameters are held constant throughout the epidemiological uncertainty simulations. The uncertainty parameters are indicated by providing a lower and upper value of the uncertainty range that may be explored. Each uncertainty parameter is varied between each simulation using a Metropolis-Hastings algorithm. When running uncertainty, the base case (i.e. without interventions other than vaccination and IPT in under five years of age applied) is run to completion, and acceptance is determined based on this simulation only. Figure S11 presents the prior distributions used for the five calibrated parameters. The parameters of the gamma and beta distributions were obtained by specifying the values of the mean and standard deviation, and the shape and scale parameters were computed accordingly. We used the following distributions: The likelihood is obtained by assuming that the country TB incidence at a given time point is normally distributed around the predicted TB incidence provided by the model for this same time point. As the time period 2010-2016 is used for calibration and because the WHO provides yearly estimates for TB incidence, this means that the likelihood is made of seven components that are all multiplied together.

Prior distributions
Posterior distributions of the parameters Figure S12 presents the posterior distributions of the five calibrated parameters.

Model initialisation
At model commencement, persons are assigned to the fully susceptible and active compartments only. The proportion of persons assigned to active TB remains constant throughout all the calibration model runs, while the total starting population is algorithmically varied to target a specified modern population. This is achieved by first calculating the ratio of the simulated modern population and the targeted modern population at each integration run. Next, the starting population is multiplied by the reciprocal of this ratio. For example, if a run over-shoots the modern population by 1%, the starting population is multiplied by 100/101 (revising the starting population down by approximately 1%).

Demographic parameters
For simulating births into the model, we assign a time-variant parameter using publicly available crude birth rate data from the World Bank [3]. The birth rate is interpreted as crude births per 1000 population (as is the case for the World Bank data) and so is multiplied by the total population of the model divided by 1000 to determine the overall rate of births entering the susceptible compartment ( Figure S1). This is then distributed between vaccinated and unvaccinated births according to Bacillus Calmette-Guérin (BCG) coverage at the time point simulated, to reflect the coverage of neonatal vaccination.
Simulating non-TB-related deaths or the background death rate is achieved with an analogous method. Life expectancy is obtained from publicly available data from the World Bank [3], and a time-variant parameter is fitted to these data points ( Figure S3). Then, population deaths are calculated as the reciprocal of this value and applied equally to every model compartment, including all the compartments for patients with active TB (in addition to TBspecific mortality), all risk groups, and all age groups.

Susceptibility/immunity to infection
The degree of susceptibility or immunity to infection among different population groups given their vaccination status, Mtb infection-related compartment, age, and treatment history is one of the most uncertain yet important parameters in TB epidemiology. We consider homogeneous susceptibility/immunity to Mtb across risk groups and age groups, assuming that the differing rates of TB disease in these groups are related to the other factors described below. By contrast, BCG vaccination and latent infection with Mtb are considered to influence the likelihood of infection after exposure to an infectious individual. The effect of BCG vaccination on immunity is described under the section on BCG vaccination below. The effect of prior latent infection on reinfection is estimated from a review of cohort studies comparing those with evidence of prior Mtb infection to those without such evidence among persons exposed to infectious TB. This study found that the rate of new episodes of TB disease in those with prior latent infection was 0.21-fold that in those without. Since the reactivation of past infection would lead to even lower values, we use this estimate as our parameter value for the relative rate of reinfection among currently latently infected persons (by comparison to the rate of infection in fully susceptible persons) [4]. Note that this only applies to the late latent compartment, as the reinfection of those in the early latent compartment will not affect their risk of progression to active disease, as these persons are already conferred the highest risk of progression to TB.
Subsequent episodes of TB disease after recovery from a prior episode are known to occur at a higher rate than that in the background population [5]. However, whether this is due to an increased host susceptibility to reinfection incurred by the previous episode or to underlying heterogeneity in rates of reinfection is unclear. In the latter case, it is feasible that recovered or treated individuals have equivalent or even decreased susceptibility to future infection than those who have never been infected [6]. We use a multiplying parameter to allow for individuals who have previously been treated for active TB to be assigned a different level of susceptibility to subsequent infection from those who have not. This multiplier is applied in addition to the parameters described above for latent infection and vaccination, such that the total level of susceptibility is the product of these two parameters. This parameter is varied during uncertainty, with its prior distribution presented in the second panel of Figure S11. For example, previously treated and latently infected persons would both have a relative risk of 0.21 compared to fully susceptible persons where this parameter is set to one.

Model of M. tuberculosis infection and progression
General approach and compartmental structure Our approach to quantifying rates of progression from latency to active disease is described in detail in two published journal articles. The first uses TB surveillance data from a very low transmission setting to estimate rates of active disease following a defined index exposure to an infectious case and evidence of exposure [7]. The second article uses the reactivation profiles from this study and from a similar epidemiological investigation [8] to determine the ideal compartmental structure and progression parameters to accurately capture progression to active TB following infection [9]. This second publication found that two latency compartments placed in series are highly effective at reproducing epidemiological observations when appropriately parameterised, and appropriate parameter values are provided. Specifically, following infection, all the latently infected individuals first progress to a high-risk "early latent" compartment, from which they may progress rapidly (within months) to active TB. Alternatively, these individuals may "stabilise", transitioning to a lowrisk "late latent" compartment, from which the progression to active TB occurs much more slowly. This configuration is also consistent with that used or recommended in other important TB modelling papers [10]. This approach requires the estimation of three epidemiological parameters: the time period spent in the early latent compartment, the proportion of individuals progressing to active disease from the early latent compartment, and the rate of progression from the late latent compartment to active disease (values presented in Table S1). Then, these are converted into three rates for early progression, stabilisation, and late progression.

Organ manifestation
We distinguish three types of organ manifestation of active TB: smear-positive pulmonary, smear-negative pulmonary cases, and extrapulmonary cases. We assume that the proportion of notified TB cases that are pulmonary or extrapulmonary, along with the proportion of pulmonary cases that are smear-positive, are constant over time. We calculate this value as the total number of notifications reported by each organ manifestation, and use this constant value for the proportion of incident cases by organ manifestation.

Natural history
Once TB disease has manifested, natural history parameters are first set to reflect outcomes in the absence of detection by the health care system. The total rates of progression to either death or spontaneous recovery are set to equal the reciprocal of the time period of untreated active disease. Next, a proportion of this total rate is then allocated to each of the two possible outcomes (death and spontaneous recovery) according to the case fatality rate (a proportion) for smear-positive TB. The smear-negative and extrapulmonary case fatality rates are then both set to be proportionately lower than the smear-positive case fatality rate by a relative multiplier parameter that remains constant throughout model runs. That is, the rate of untreated death is equal to the reciprocal of the time period untreated multiplied by the case fatality rate, while the rate of spontaneous recovery is equal to the reciprocal of the time period untreated multiplied by the complement of the case fatality rate. Parameter values and uncertainty ranges are estimated from a detailed review of pre-chemotherapy era outcomes [11].

Case detection
Obtaining the case detection ratio The case detection rate is a time-variant parameter and is a fundamental parameter determining the performance of TB programs at the country level. Estimates of the case detection rate are provided by the World Health Organization in the Global TB Report [12]. It is important to note that this "rate" is actually a ratio or proportion, and is referred to as the case detection ratio hereafter. Specifically, the case detection ratio is the proportion of all the active cases that are detected during their episode of disease, which is also expressed as the ratio of notifications to incidence in the geographical region considered. Variations in its magnitude have major impacts on disease burden that may only be realised decades later. Effective medical treatments for active TB only became available from the 1950s onwards.
Since there was no effective treatment that improved on the natural history of the disease, we apply an effective case detection ratio prior to that time of zero. As with other time-variant parameters, case detection ratio data are loaded from the Global TB Report data.

Adjustment to the case detection ratio for decentralisation
After the case detection ratio time-variant parameter has been defined as described above, it is next adjusted for the decentralisation intervention. This is described in detail in Section 17, and has the general effect of narrowing the gap between the actual, loaded case detection ratio and an idealised perfect case detection ratio.

Adjustment to the case detection ratio by organ status
We assign different values to the case detection ratio according to organ status, because it is likely that smear-positive, smear-negative, and extrapulmonary cases are diagnosed by the health care system at different rates. Smear-positive cases may be targeted by the health system, and may be easier to diagnose with the tools locally available (smear microscopy in particular). Moreover, several interventions may act to close this diagnostic gap between smear-positive and smear-negative or extrapulmonary cases. For example, GeneXpert improves the possibility of detection with smear-negative TB cases relative to smear microscopy and clinical judgement, partially closing this detection gap, as described below. In our model, the rate of detection for smear-positive cases is increased, while the rates of detection for smear-negative and extrapulmonary cases are decreased. This is calculated such that the smear-negative and extrapulmonary cases have a case detection ratio that is lower than that of the smear-positive cases by a constant specified ratio, while the weighted average case detection ratio for all the forms of TB remains equal to the unprocessed case detection ratio originally estimated.

Missed diagnosis and the accuracy of the diagnostic algorithm
In order to explicitly simulate patients who presented for care but whose diagnosis was missed, a flow rate that transitions patients from the active untreated compartment to a missed diagnosis compartments is simulated. Patients whose diagnosis has been missed suffer outcomes applicable to those in the active treatment compartment in terms of death and spontaneous recovery, but do not re-start seeking treatment for a limited period of time. To achieve this, it is considered that case detection is linked to the diagnostic algorithm, as missed cases are proportional to its complement. That is: The adjustment process for organ status described for the rate of case detection is applied in the same way to the sensitivity of the baseline diagnostic algorithm parameter in order to simulate a greater proportion of smear-positive persons being detected rather than missed under baseline conditions through clinical assessment and smear microscopy (i.e. prior to implementation of novel diagnostics, such as GeneXpert).

Treatment outcomes
Determining aggregate outcomes Treatment outcomes are derived from the Global TB Report, which reports outcomes for patients differently by strain, HIV status, sputum smear status, and treatment history, as well as changing its reporting approach for some categories after 2011. All the reported treatment outcomes are grouped into three broad categories for model interpretation: 1) treatment success, 2) death during treatment, and 3) survival with unfavourable outcomes (i.e. any outcome other than success or death, with the terminology for these pathways having changed over time).
For patients up to and including 2011, patients achieving treatment completion or cure (the latter for smear-positive patients only) are classified as treatment success, patients dying on treatment are classified as such, and patients reported as default or failure are classified into the third category. Up to 2011, relapse cases are included with retreatment cases in Global TB Report data. After 2011 for non-MDR-TB patients, loss to follow-up and failure are classified as unfavourable outcomes (as opposed to default and failure up to 2011). After 2011, relapse cases are included with new cases in official data, in contrast to the situation up to 2011. As there is no reliable way to account for this change, it should be noted that outcome parameters are fit to data that changes its characteristics after 2011, although this change is very small in magnitude.

Calculation of proportions
Once the total outcomes have been classified into the three categories described above, the proportion of patients falling into each category is calculated. Then, two time-variant proportion functions are defined. The first is the treatment success proportion, for which the numerator is successful treatment outcomes (cure and completion), and the denominator is all treatment outcomes (figures S5 and S7). The second is the proportion of unsuccessful outcomes resulting in death, for which the numerator is death outcomes, and the denominator is all the treatment outcomes other than success. Then, time-variant functions representing proportions (limited to range zero to one) are calculated for these quantities. Then, the proportion of defaults is calculated as the proportion of non-success outcomes multiplied by the proportion of unsuccessful outcomes resulting in death. Using this approach, all the treatment outcomes must consistently remain nonnegative, and the three possible outcomes always sum to one.

Treatment history
All the compartments are duplicated according to whether patients have been previously treated or not. The only exception is for the fully susceptible unvaccinated compartment(s), which is not duplicated, as there is no equivalent compartment representing fully susceptible individuals in the previously treated stratum. This is because previously treated individuals are assigned a modified level of immunity/susceptibility to future episodes of infection.

Risk of progression to active disease
The natural history of childhood TB was described in detail by Marais et al. in their 2004 publication that considered historical publications on this topic in detail [13]. The period from 1920 to 1950 was particularly informative for the study of the natural history of TB, as chest radiography had become available, but effective treatment to modify the natural history had not. Although quantitative estimates of the risk of progression to active disease and subtypes are presented, we prefer the publications by Sloot et al. and Trauer et al., as these two modern estimates employ formal survival analysis techniques and are highly consistent with one another [7,8]. Moreover, after modification of the progression rates for BCG-vaccination, these estimates are likely to be consistent with those of Marais et al.

Infectiousness
Although children are often considered non-infectious, some groups of children are likely to have the potential to transmit infection, including adolescents who more often have adulttype reactivation TB. Other potentially infectious paediatric groups include those with pulmonary cavitation, positive smears for acid fast bacilli (AFBs), laryngeal involvement, widespread pulmonary disease, and suspected congenital TB (which tends to be more extensive). However, younger children, including those with primary pulmonary TB, are unlikely to be infectious because of their low bacillary load [14] and inability to generate a sufficiently forceful cough [15]. This is supported by the observation that an infectious adult was consistently identifiable in outbreaks of TB in orphanages and children's hospitals, while such outbreaks did not occur when only a child was identified with active TB. Eight case reports of transmission from children were identified in a 2001 review, which included four children aged under one (including two with congenital TB), with the others aged three, five, seven, and nine. However, the extent of transmission was either limited or incompletely described in most of the six reports considering children aged five and below. Unpublished data recording low rates of tuberculin skin test (TST) conversion in the staff of paediatric hospitals also support this contention [16]. For these reasons, we reduce the infectiousness of children by one order of magnitude (i.e. 0.1 times that of adults) and apply this to estimates of the under-five age group. Although we maintain the division into smear-negative/smear positive and extra-pulmonary in this age group to reflect the same qualitative status as in the adult age group, we acknowledge that all of the members of this group are likely to be smearnegative most of the time, and use the (0.1-fold) multiplier to reflect this. For the age group aged 5 to 15, we assume that approximately half of these patients will have adult-type and half child-type manifestations of disease, resulting in a weighted average of 0.55 times the infectiousness of adults for this group.

Case fatality
The case fatality rate (a proportion) for children with miliary TB was estimated at 14% in one case series [17], which is considerably greater than the estimate of 3.5% for all cases from one meta-analysis [18]. However, this is clearly not a direct comparison, as this higher rate was observed only in a subgroup of paediatric cases, and may well be offset by lower case fatality rates in the other subgroups, such as tuberculous lymphadenitis. Moreover, these estimates primarily consider patients under treatment, and so cannot be used to estimate the case fatality of untreated TB (which is of greater relevance to our model parameters).

Conclusions and model implementation
We use the age-specific progression proportions reported by Trauer et al. and are currently undertaking further work to refine these parameters. Although difficult to quantify, the infectiousness of persons aged under 10 is lower than those of older ages, and we apply a 10fold reduction as described above. Case fatality rates are not currently modified for age, although we continue to seek evidence to quantify this.

Implementation
We estimate the relative risk or odds ratio for developing TB in patients with diabetes by comparing the risk of disease in affected patients to the risk for patients without diabetes. Ideally, a relative risk or hazard would be applied to the rate of late progression from late latency to active disease, while an odds ratio would be applied to the proportion of patients in early latency who progress to active disease rather than stabilising to late latency. For individuals in early latency, we do not adjust the duration of early latency for persons with comorbidities. Instead, we only adjust the duration of early latency for the proportion of patients undergoing early progression to active TB. We apply an estimate of the odds ratio for progression to active disease associated with the comorbidity to the original estimate for the proportion progressing, which is age-specific in the age-stratified models. We term the proportion of persons in early latency progressing to active TB in the absence of comorbidities "pn", such that the odds of progressing is equal to pn / (1 -pn). Similarly, the proportion progressing in the presence of the comorbidity is termed "pc", with associated odds pc / (1 -pc). Therefore, if the odds ratio associated with the comorbidity is termed "OR": 1 − = × 1 − Solving for pc gives: This formula is used to calculate the rate of progression in the presence of diabetes. It has the advantages of producing a similar modification in pc to that achieved with a relative risk calculation if the odds ratio (OR) is relatively small, but having a ceiling value at one for large ORs. As this is a proportion that is used to determine the rates of flows from early latency, the rate of progression from early latency to active disease and to late latency are:

Quantification of effect
Several epidemiological studies have found a greater rate of incident TB in patients with diabetes across a range of contexts [19,20]. Observations from such individual studies include a generally similar or greater rate of bacteriologically-confirmed disease than for all forms [21] and similar increases in risk associated with recent and reactivation disease [22]. One study reported a slightly lower strength of association, but recruited controls with medical conditions that are potentially weakly associated with TB [23]. A limitation of several of these studies is that TB itself is known to be associated with transient impairment to glucose metabolism [24,25], although the above studies varied as to whether they considered previously diagnosed diabetes or performed glucose metabolism testing at the time of diagnosis. Several of the above-mentioned studies were included in a meta-analysis of the association of diabetes on TB published by Jeon et al. in 2008 [26]. This study found a relative risk for diabetes of 3.11 (95% CI 2.27 to 4.26) from a random effects meta-analysis of three cohort studies. To apply the modification in the rates of progression to active disease due to diabetes, we adopt the approach outlined above, estimating both the odds ratio for early progression and the relative risk for late progression at 3.11.

Impact of diabetes on TB epidemic
The following figure presents the scale-up functions that were used to simulate different levels of diabetes prevalence in the future population of Fiji.  Disease burden estimates by age groups Figure S16. Estimated distribution of TB incidence by age group over time. Figure S17. Estimated distribution of TB notifications by age group over time. Figure S18. Estimated distribution of the number of TB deaths by age group over time. Figure S19. Percentage of incident TB that is due to fast progression rather than late reactivation.

Profile of incident TB: fast progression versus late reactivation
Although evidence is variable and past research has been inconsistent, it is likely that carefully constructed, context-specific, multifactorial interventions to support patients in treatment are effective in improving patient adherence and treatment outcomes. For model implementation, unfavourable treatment outcomes are reduced to 0.43 (95% CI 0.21 to 0.89), multiplied by the coverage of the intervention times the pre-intervention values, which are consistent with findings from a study in Senegal [27]. This is intended to reflect a comprehensive change to how patients are supported during their treatment across the country. Figure S20. Effects of treatment support with intervention uncertainty.

Results
In the context of Fiji, the decentralisation of clinical care for patients with active TB represents a comprehensive intervention to bring high-quality TB care to patients in their local communities. The effect of this intervention, when fully implemented, is to entirely eliminate all the geographical barriers to accessing curative care for any patient with TB in any geographical location in the country. Conceptually, this means that patient-related delays to starting treatment are considerably reduced, such that case detection is faster and more consistent across the country.
Given the logistical difficulties, few or no studies have considered an intervention consisting of the expansion of health facilities in the context of medical research or a randomised controlled trial. Ecological studies give some sense that the decentralisation of TB treatment facilities is likely to improve case detection rates. For example, observations from Armenia indicate that TB clinics located near urban centres and examining more presumptive cases of TB are likely to have greater TB notification rates [28]. Similarly, geospatial modelling from a remote zone of Ethiopia indicates that notification rates are higher in areas with closer proximity to TB health care [29]. Studies from various contexts have found that treatment from decentralised, community-based, or patient-centred care centres, potentially involving outreach visits by health extension workers, is as effective as clinic-based management [30,31]. Together, this evidence implies that support for community-based TB treatment, along with an increase in the number of health facilities available, could improve case detection rates.
As passive case finding remains the basis for TB detection in most countries worldwide, we consider an "idealised" case detection rate to be equal to that estimated by the best performing TB programs reported in the WHO's Global TB Report. Low-burden, highresource countries, along with the best-performing high-burden countries, are able to consistently achieve case detection rates of 80% to 90% for periods of several years, suggesting that this may be an upper limit for case detection through passive strategies alone. Therefore, this intervention is implemented in the model by increasing the case detection ratio from its baseline value towards an idealised case detection ratio, which by default is set to 85%. To estimate the adjusted case detection rate, the gap between the current case detection ratio and the ideal is decreased by the coverage of the intervention. That is: If the current case detection ratio is greater than the ideal case detection ratio at any time point during integration, the intervention is applicable at that time and is not applied. Note that this intervention is applied before adjustments are made for active case finding, which may further modify the effective case detection rate modelled if both are implemented together. Figure S21. Effects of decentralisation on TB epidemic with intervention uncertainty.

Implementation Background
Sputum smear microscopy has been the mainstay of TB diagnostics since the 1850s, although the test is known to have sub-optimal sensitivity, particularly for paucibacillary cases (such as HIV-associated TB, paediatric TB, and extrapulmonary TB). Meanwhile, mycobacterial culture techniques have the disadvantage of a substantial delay in results that could influence the availability of clinical decisions [32] and the technical complexity of maintaining a functioning laboratory service.
GeneXpert (Cepheid Inc, Sunnyvale, California, USA) is the current leading technology in the molecular diagnosis of TB. It was endorsed by the WHO with unprecedented speed in December 2010 as the initial diagnostic for HIV-associated TB and where high rates of drugresistant TB are present [33]. Despite uncertainties as to the ideal approach to implementation, South Africa has led the way in deploying GeneXpert devices from 2011 to 2013, deploying 314 such devices by 2017 and being responsible for over half the global cartridge utilization [34].

Time to treatment initiation
Although GeneXpert has the potential to provide results within two hours of specimen submission, it remains important to assess the real effect on accelerating patients' progression through the treatment cascade. Reasons for a longer actual time to diagnosis or change in clinical decisions may include a preference for delaying specimen processing until a sufficient number of samples are received at a clinic.
A 2013 Cochrane review found a significantly shorter time to detection for GeneXpert compared to culture methods [35]. Moreover, there is evidence of decreased time to treatment initiation for patients with drug-susceptible TB compared to other approaches. The large multi-centre study considering the implementation of GeneXpert across six countries in three continents found a median time to detection of Mtb of zero days for GeneXpert, one day for smear microscopy, 16 days for liquid culture, and 30 days for solid culture [36]. However, time to treatment commencement for smear-negative, culture-positive patients decreased from a median 56 days to five days, while for smear-positive patients, a non-significant reduction from four to two days occurred. A study in Johannesburg (641 presentations with possible TB, 69% HIV-infected) found delays to treatment initiation of zero days for GeneXpert, 14 days for clinical or radiological diagnoses, and 144 days for culture-based diagnoses [37]. Similarly, a study from Saudi Arabia found results for both GeneXpert and smear microscopy were available on the same day, while cultures took a median of 22 days for results to be available [38].
The roll-out of GeneXpert technology has also been demonstrated to reduce the time taken for patients to begin treatment for MDR-TB. For example, the time to commence treatment decreased from a median of 40 days to seven days in Latvia [39]. Similarly, in Cape Town, GeneXpert also decreased time to treatment commencement for MDR-TB by around a month, with the median time to commencement falling from 42 to 17 days [40].
A 2017 systematic review of the programmatic effect of GeneXpert included 18 studies finding a significant reduction in time to treatment, while only four did not [34].

Diagnostic accuracy for the presence of TB
In the large multi-centre study introduced above, pooled results across all the centres gave a 98.3% sensitivity for smear-positive TB, 76.9% for smear-negative (ranging from 56.3% to 100.0% by a study site) and culture-positive TB, and a specificity of 99.0% [36]. This was associated with a reduction from 39.3% to 14.7% in the proportion of patients with smearnegative, culture-positive disease who remained untreated. These estimates are close to those derived from a 2014 Cochrane review of 27 studies (including the study described above), which reported a pooled sensitivity of 98% for smear-positive TB, 67% for smear-negative, culture-positive TB, and a specificity of 99% [35,41].
However, a critical consideration is the extent of empiric treatment undertaken prior to the implementation of GeneXpert or the sensitivity of clinical assessments for TB. That is, in a setting in which the threshold for initiating empiric treatment for TB is low, implementation of a highly sensitive diagnostic may do little to increase the number of patients commenced on treatment, and so have little programmatic effect [42]. Although this is an important concern, estimating the underlying sensitivity of clinical diagnosis across a country is challenging. Several factors may influence the threshold for clinical diagnosis, with one being the underlying prevalence of TB in the population, such that rates of empiric diagnosis may be higher in high-burden countries. A 2013 meta-analysis pooled five studies that estimated the sensitivity and specificity of the clinical WHO algorithm for the diagnosis of smearnegative TB found a pooled sensitivity of 0.61 (0.55 to 0.67), but with substantial heterogeneity [43]. Clinicians in real-world settings may conceivably do better [44] or worse than such standardised diagnostic algorithms. By default, this parameter is set to 0.61.
The sensitivity of GeneXpert-based platforms may improve in the near future through the release of the GeneXpert MTB/RIF Ultra. This test is currently under evaluation [45], but is anticipated to significantly improve the sensitivity of GeneXpert for paucibacillary forms of TB (including children, HIV-positive, and smear-negative culture-positive cases) with the manufacturer claiming levels of sensitivity that approach those for liquid culture [46].

Implementation
The WHO strongly recommends the systematic evaluation of contacts of potentially infectious cases of active TB as a form of intensified case finding for further cases of active disease. The investigation of close/household contacts of higher risk index cases (e.g. smearpositive pulmonary TB) is strongly recommended, while the investigation of all close/household contacts is conditionally recommended. Following such screening for active TB, preventive therapy is then recommended for contacts at the highest risk of progression to active disease following infection. However, the groups for which treatment is recommended has been highly restricted, focusing on PLHIV and children aged under five years [47]. Moreover, screening policies vary substantially between countries, and recommendations are inconsistently implemented [48]. At least seven meta-analyses have estimated the sensitivity of TST in diagnosing LTBI, with results ranging from 0.70 to 0.82 [49]. Meanwhile, metaanalytic estimates for the sensitivity of QuantiFERON range from 0.66 to 0.83, and of T-SPOT range from 0.62 to 0.90. Therefore, there is no evidence that any one of these tests has superior sensitivity to the others, and all the tests have a sensitivity of approximately 0.7 to 0.8. A Cochrane review of IPT was undertaken in 1994, with the 2003 update to this review finding no further citations, such that the authors do not plan any further updates. The review was limited to randomised trials of appropriately dosed IPT provided for at least six months with follow-up for at least two years. It found IPT to be associated with a risk ratio for active TB of 0.40 (95% CI 0.31 to 0.52) [50]. This estimate is very similar to the results of a recent meta-analysis, which found a risk ratio of 0.41 (95% CI 0.19 to 0.80) [51]. When six-month and 12-month courses were considered separately, the respective risk ratios were 0.44 and 0.38, although this difference was not statistically significant. Rates of hepatotoxicity for these two regimen durations were 0.36% and 0.52%, respectively. For model implementation, it should be noted that all but one of the studies included in this review were analysed by intention-to-treat. Therefore, this estimate does not need to be reduced to reflect patient compliance.
Concerns regarding the relatively low efficacy of six-month isoniazid treatment and poor completion of twelve-month isoniazid treatment have resulted in a re-analysis of data from several clinical trials [52]. This re-analysis suggests that the optimal duration of isoniazid is nine months, and that this is associated with a 90% reduction in the risk of progression to active TB in fully compliant patients. Extending to 12 months is unlikely to improve efficacy any further. The findings of this re-analysis have resulted in the recommendations for nine months of INH by the American Thoracic Society in 2000, followed by health authorities of other countries soon after.
Recently, a randomised control trial (RCT) compared treatment efficacy of three-month weekly INH plus rifapentine and nine-month INH alone [53]. The combination therapy was found to be as effective as INH alone, but associated with less hepatotoxicity.
As this intervention is considered to target household contacts specifically, the first step in model implementation is to estimate the proportion of infections that occur at the household level; we estimate this at 60% by default, but encourage users to modify this value. Since only contacts of detected cases are detectable, this value is next multiplied by the proportion of active cases that are detected by the health system, which is modelled explicitly through the case detection rate. Last, this product is multiplied by the sensitivity of the diagnostic test employed for LTBI. All of the age and age group-specific IPT programs can each be implemented. If these programs are implemented together, the sum of the coverage of the two programs is used to determine the aggregate coverage for each age group that is specifically targeted. The resulting proportion of infections effectively targeted by IPT are subtracted from the force of infection and moved instead to IPT compartments, where patients remain for the duration of treatment (set by default to nine months through) before moving to the partially immune susceptible compartments applicable to their age group, treatment history, and risk group status. Figure S23. Effects of IPT on TB epidemic with intervention uncertainty.

Rationale
To effectively decrease the transmission of Mtb, the duration of infectiousness should be kept to a minimum, although there are no specific targets for what an acceptable time to diagnosis is, nor is this time period required reporting for national TB control programs (NTPs) [54]. The delay to treatment initiation has been found to be significantly associated with the proportion of household contacts infected, with one study finding a delay of greater than 30 days to be an important threshold [55]. A systematic review found that a variety of features of the disease, patient, health system, culture, and environment may be important in influencing the time to presentation [56]. However, detecting patients early can be challenging, given that a small but significant proportion of patients report no symptoms at all, while a sizeable proportion (as many as half) do not report symptoms that are consistent with the commonly utilised criteria [57]. A substantial proportion of all cases of TB are still missed entirely [58], while both patient and health system-related delays to treatment initiation are substantial in a range of settings [59].

Historical background
Active case finding (ACF) through the chest radiography of asymptomatic persons was implemented extensively in developed country settings from the 1930s to the 1960s. Although this strategy was successful in detecting a significant number of previously undiagnosed cases, the financial expense and logistics were considerable. From the early 1960s, the paradigm began to change in the light of studies, finding that most patients with undiagnosed TB had symptoms for some time, and had often sought care previously. These studies suggested that few patients would be missed by restricting ACF to those with symptoms, such as having a cough for two weeks or more. Therefore, the focus shifted to health system strengthening with ACF considered unnecessary, particularly at a time when TB was thought to be becoming a relatively minor problem in global health. Since then, a range of ACF strategies have been studied, although few have been linked to prevalence surveys that could shed light on the proportion of undiagnosed cases detected [60].

DETECTB
One of the most important studies in ACF was DECECTB, which was a cluster randomised study of two alternative approaches to ACF undertaken in Harare from 2006 to 2008 [61]. This study compared six rounds of ACF at six-monthly intervals, either through the presence of a mobile van in the community for five days (manned by three lay workers equipped with a loudspeaker and leaflets) or through door-to-door enquiry at the household level (with each household approached once per ACF round by two teams of three lay workers). Two sputum specimens were collected from individuals with a history of cough for two weeks or longer and analysed with smear microscopy (but not culture). The primary outcome was the relative yield of smear-positive TB between the two screening methods, while the secondary outcome was the change in culture-positive TB through prevalence surveys performed with the first and last ACF round. Consistent with evidence from elsewhere (Thailand), the door-to-door approach did not lead to a marked increase in the number of cases diagnosed [62]. In fact, the mobile van intervention detected considerably more cases (255) than did the door-to-door intervention (137), for a cumulative yield of 4.27 and 2.38 smear-positive cases per 1000 population over the six rounds of intervention (or 0.71 and 0.40 per round). Given that the prevalence was 4.0 smear-positive cases per 1000 population at the start of the intervention and 2.3 smearpositive cases per 1000 per population before the fifth round and assuming a linear decrease in burden over the study period (as the authors did), the average prevalence of smear-positive disease over the course of the study would have been 3.1 per 1000. Therefore, the 0.71 smear-positive cases diagnosed in each round of van-based ACF and 0.40 cases in each round of door-to-door based ACF represent 23.2% and 12.8% of all the undiagnosed cases respectively.

Other recent studies
Sekandi et al. reported on a single round of ACF undertaken in a peri-urban setting of around 10,000 persons, finding 33 additional cases of smear-positive TB through an algorithm of symptom screening for chronic cough and smear microscopy [63]. This study was limited by comparison to DETECTB, in that no prevalence surveys were undertaken, such that the proportion of all undiagnosed cases that this represents is difficult to estimate. Given Uganda's prevalence of TB of around 150 to 200 per 100,000 with around 60% of notified cases smear-positive, the smear-positive prevalence may be around 100 per 100,000. Therefore, it could be estimated that around 10 undiagnosed such cases should be present in a population of 10,000. Clearly, the study results refute this estimate, and indicate that the true prevalence was much higher in this slum setting, as the authors acknowledge. A study of free workplace TB diagnostics included a prevalence survey at study completion, but not at the outset, and did not constitute active case finding in the sense reviewed here [64]. A comparison of cohorts of patients diagnosed by ACF and passive case finding in Cambodia found that the patients diagnosed through ACF were generally older (55 versus 48 years) and were considerably more likely to be smear-negative (71.4% versus 40.5%). Reassuringly for this intervention, treatment outcomes were comparable between the two groups, with treatment success rates of 96.4% and 95.2% for patients diagnosed through ACF and passive case finding, respectively [65]. Another study in the same country found that 810 cases of active TB were diagnosed through an ACF intervention, after the screening of 35,005 patients with chest x-ray and symptoms and testing of 3649 of these with GeneXpert. The intervention covered 30 operational districts with a population of approximately 100,000 to 200,000 each, and a TB incidence of around 176 cases per 100,000 per year [66,67]. The authors estimated that an additional 9.8% of cases had been found compared to the baseline case detection rate, but if the expected decline in burden is allowed for, an additional 18.5% of cases were detected. As the total population in the intervention area was around 2.9 million, the proportion of the population screened was around 1.21%, and the proportion of the population definitively tested was 0.126%.

Conclusions and model implementation
For smear-based ACF, we estimate that van-based ACF implemented with screening rounds at six-monthly intervals can be expected to diagnose around 23.2% of smear-positive cases not previously diagnosed at each round. For GeneXpert-based strategies, the intervention can also be reasonably applied to the undiagnosed smear-negative population, but is multiplied by the sensitivity of GeneXpert for smear-negative disease (i.e. 67%, to give an overall proportion diagnosed of 15.6%). As these strategies generally commence with enquiry as to the presence of cough, no effect on extrapulmonary disease is expected. In this analysis, we consider the intervention to be directed at the general community.

Implementation Background
Cultural, environmental, and politico-economic factors are known to be important in driving the TB epidemic, which is more often conceptualised from a biological perspective [68]. Therefore, communication interventions for TB control have the potential to markedly improve rates of presentation for care through reduction in stigma, improved understanding of the condition, and greater community awareness. Countries such as Peru and Vietnam have used improved awareness as a cornerstone of their control efforts [69][70][71]. Although a systematic review was registered in 2014 to consider the effect of mass media interventions on TB knowledge, attitudes, awareness, health care seeking behaviour, and health service utilisation, no results are yet available from this study. Moreover, there are a number of critical considerations to bear in mind in estimating the likely effectiveness of such interventions, including tailoring messages to the context and culture in which they are provided, and ensuring that curative care of a sufficient standard is available to the additional persons who may present for care as a result of the intervention.

TB-specific studies
Studies investigating the impact of awareness programs on TB have reported variable results, but have consistently found increased rates of presentation for care, increased detection of new active and latent cases, and reduced rates of treatment abandonment [72]. In a study conducted in an indigenous community with high TB burden in Canada in the context of passive case finding, Alvarez et al. found that the number of people presenting themselves to clinics increased by 92% during the four-month community-wide awareness campaigns, compared to the previous periods without the campaign (increased from an average of 26 people per month to 50 per month) [73]. This study also found that a door-to-door campaign increased the number of new LTBI cases by 34%, and increased the number of newly diagnosed active TB cases by 29.5%. In Columbia, Jaramillo reported that a six-week mass media-based health education campaign (radio, television, and newspaper) increased the number of smears processed by laboratories by 64%, and increased the number of smearpositive pulmonary TB cases detected and notified by 52% [74]. However, this increase only accrued in the study area and for the quarter during which the intervention was implemented, with programmatic effects not sustained after the intervention for either study. Awareness programs have also been found to enhance treatment retention. A report using nationwide data in Peru found that health communication steadily reduced the rate of TB treatment abandonment from 12.1% prior to the start of the program to 2.8% over a period of 10 years. A brief report of an intervention in Odisha (India) involving health worker education, van-mounted loudspeakers, and community-based health camps found an increase in the number of detections [75]. Although the increase in the total number of TB diagnoses made was not reported, the number of persons screened increased by 87.8% and the number of smear-positive diagnoses made increased by 10.8% (figures that seem consistent with those reported by the studies discussed above).

Conclusions and model implementation
Implementation of this intervention acts to accelerate the rate of case detection from baseline, and similarly the rate at which missed cases accrue through incorrect diagnosis, reflecting a decrease in pre-presentation delays to treatment. The applied value for the relative increase in presentation rate is 1.52-fold the baseline rate, using the results of the study by Jaramillo et al. above. This is intended to reflect intensive, periodic advertising and awareness raising through the mass media, but without the extensive community mobilisation described in Alvarez et al. above. An even more extensive intervention could be captured by implementing a relative increase parameter of 1.92 or similar. However, we believe that the value of 1.52 better reflects the interventions considered in Fiji. An important caveat is that we aim to simulate repeated media-based interventions in order to maintain the effectiveness of this intervention over time, assuming interventions of six weeks in duration implemented quarterly or similar. We also assume that the effect of the intervention is maintained over time, ignoring the potential for loss of effectiveness with time, which is impossible to quantify. Figure S25. Effects of awareness raising on TB epidemic with intervention uncertainty. Figure S26. Effects of interventions on true mortality. This includes all the modelled mortality occurring outside of the health system.

Support for patients under treatment
In Fiji, this intervention involves getting a person trained in directly observed therapy short course (DOTS) to administer daily treatment and being given USD 10 per day while they are a DOTS trained-treatment administering person. The Fiji NTP estimates that the total cost of the program in 2015 is about USD 150,000 with a total annual number of patients to be treated of 305, giving a unit program cost of USD 500 (USD 534 in 2017 values). The yearly cost of treatment support is projected by the NTP to be USD 3469 for the next three years (USD 10,407 for a total of three years) to scale up the program; however, cost components of this amount are not available.

Decentralisation
Fiji-specific cost data for the decentralisation of TB care are lacking, nor are such data available in the literature. In consultation with the Fiji NTP, we assumed a unit cost of USD 1000 per patient for decentralization. An arbitrary value of USD 700,000 for start-up cost for three years was used.

GeneXpert
Using an ingredient costing approach of identifying all the inputs and quantities required to perform the test such as cartridge, equipment, and salaries, Vassall et al. [81] estimated that the cost for the GeneXpert test ranged from USD 23 in India to USD 39 in South Africa and USD 47 in Uganda. These estimates are consistent with those from Dowdy et al. [82] and Menzies et al. [83]. Although the WHO recommends the rapid implementation of GeneXpert because of its proven benefits for the diagnosis of TB, implementation among resourceconstrained countries has been slow due to the substantial start-up costs of GeneXpert, which is estimated to be $103,679. 5   Procure and distribute consumables for GeneXpert (USD 3620)

Isoniazid preventive therapy
As with most TB programs in Fiji, country-specific cost data for IPT are not available. As such, we performed a literature search to inform the cost inputs for the program. Although a few studies that investigated the economics of six-month IPT exist, most of these studies focused on IPT in HIV-infected adult patients [76][77][78][79]. To date, there is only one study that investigated the cost and cost-effectiveness of IPT in children contacts (<5 years of age), which are the target population group of the IPT program in Fiji [80]. Mandalakas et al. [80] estimated that the unit costs of IPT in this setting were USD 179 for health providers. These estimates included costs of screening using TST, medications, clinic visits, and liver function tests. In Fiji, the current coverage of IPT in children under five years old is only 23.6%, and the country aspires to scale up the program to achieve a high level of coverage of 80% in the next few years. Sutton et al. [78] estimated the cost required for starting an IPT program to be USD 105.35 per patient, which includes costs of personnel, laboratory use, supplies, capital, and infrastructure. Under most simulations, our model projected that the total number of children over the next three years who are eligible for the program is around 672, such that the total start-up cost was estimated to be USD 70,800.

Active case finding
Evidence on the cost of active case finding is limited. The total per patient cost is estimated to be USD 74 in urban Africa from a health provider perspective [63]. These costs include program costs (administration, transportation, communication, health personnel), direct medical costs (smear tests, culture tests, chest X-ray, consumable supplies), and patient and caregiver costs (for analysis from societal perspective). Of note, sputum smear microscopy is used for TB screening and diagnosis in this study. Then, the unit cost of GeneXpert-based ACF is calculated as follows: unit cost of GeneXpert-based ACF = unit cost of smear-based ACF (USD 74.  Consumables for GeneXpert (USD 3620) Based on the above activities and costs, the yearly start-up costs for GeneXpert-based active case finding are estimated to be USD 266,651. We assume that the start-up cost is applied for three years, with the cost of purchasing mobile caravans (USD 116,402.68) excluded from year 2 and year 3.