Stochastic agent-based modeling of tuberculosis in Canadian Indigenous communities

We developed an agent-based simulation model of Mycobacterium tuberculosis transmission in the Kivalliq Region of Nunavut, Canada (Fig. 1). The region has a population of 8952 residents and is home to seven distinct communities ranging in size from 310 to 2320 individuals [3]. This model represents individuals (agents) within a simulated environment, and their interactions, movements, decision-making, and related health states. We used an agent-based approach to account for the small population size and associated stochasticity. This approach allowed us to model the unique household and community structure in this region, and to record the health states and treatment histories of individuals over time. The model was constructed using the AnyLogic software package (http://​www.​anylogic.​com/​). Model parameters were region-specific, wherever possible, or derived from the biomedical literature (Table 1).

A brief summary of the model structure and calibration procedure is provided below, with a more complete description included in the Additional file 1.

To reflect the demographic structure of Kivalliq, individuals in the model were assigned an age, sex, household, and community. The initial age distribution of the population was based on 2001 Canadian census estimates for the Kivalliq Region [17]. Each individual was assigned to a household, which in turn was located within one of the seven communities. Average household size was based on census data [18, 19]. New households were added every year. Individuals were added to the model population by birth and left the population by death, with rates based on Nunavut data (Table 1) [20, 21]. Although we allowed for movement between communities (described in Additional file 1), we did not model migration into or out of the region.

After the initial synthetic model population was created as described above (agents assigned specific, individual attributes including an age, sex, household size, community, and specific individual household members), agents within the synthetic population were assigned a health state based on the TB natural history component of the model (Fig. 2). This aspect of the model represented each individual’s health state over time. We included the following stages of the natural history of TB: susceptible, latent TB infection (LTBI), active disease, and resusceptible. Susceptible individuals are TB naïve, having never been infected by TB before and can become infected if they come in contact with an individual with an active TB infection. Individuals who have been recently infected progress to the the latent TB classes (latent fast or latent slow). In this case, a small proportion of individuals will go on to develop active pulmonary TB within a period of 5 years (Table 1) with the remainder staying in the latent slow class where they can stay indefinitely or they can progress to the active TB state at some time in the future [22]. The active TB states are broken down into three distinct compartments: high-transmissibility, low transmissibility, and extrapulmonary active TB. Individuals in the high-transmissibility compartment are individuals who have smear-positive, pulmonary TB. These individuals are considered more infectious than individuals diagnosed with pulmonary TB but who are smear-negative (Table 1) [22]. We assume that individuals who are diagnosed with extrapulmonary TB are not infectious to others [22]. Individuals in either the LTBI states or the active TB states can transition into the ‘diagnosed and treated’ compartment based on parameters describing the rate of diagnosis and treatment of TB cases in Kivalliq, Nunavut (Table 1). Individuals in the model who have been successfully treated for TB or who spontaneously clear their TB without receiving treatment (Table 1), transition to the resusceptible compartment [12, 22]. Individuals in the resusceptible compartment can become reinfected but their risk of acquiring a new TB infection is reduced compared to a TB naïve individual (Table 1) [12]. Parameters describing all model transitions between states are presented in Table 1 and are informed by both the existing biomedical literature and data extracted from the Nunavut TB registry. To capture age-related differences in TB infection, progression, and management, we classified individuals aged <15 years as ‘children’, and those aged ≥15 as ‘adults’ based on the age cut-offs used in the Canadian Tuberculosis Standards (7^th edition) and the age groupings available from the Nunavut Department of Health [1, 22, 23]. We assumed that the majority of TB transmission occurred between individuals within a household (representing close contacts) [22]. However, we also included a community network (encompassing all agents living within an individual’s community) to allow us to investigate the contribution of community and casual contacts to TB transmission.

We assumed that susceptible individuals, as well as individuals with LTBI or undiagnosed active disease who had no prior history of treatment for LTBI or active disease, could undergo screening. Those diagnosed with LTBI and aged between 6 months and 65 years could receive treatment, with a proportion of these individuals completing treatment [5, 24]. Those diagnosed with active disease received appropriate treatment. All parameters describing baseline contact tracing and screening assumptions are found in Table 1.

We assumed that contact tracing was only done for household contacts of diagnosed index cases. Identified household contacts with LTBI (meeting age and treatment history criteria) were offered treatment, with a proportion completing treatment based on Nunavut treatment completion data (Table 1).

We used model calibration to estimate the number of individuals with latent, undiagnosed, or previously treated TB upon model initiation, as well as the annual number of respiratory contacts sufficient to transmit infection. To account for the fact that the risk of transmission is concentrated among close contacts (household contacts in our model), we assumed that the majority of respiratory contacts occurring between cases and their contacts occurred in the household. In our base case, we assumed that 5% of respiratory contacts sufficient for transmitting TB occurred within the community (with the remaining 95% of transmission-sufficient contacts occurring with household members). We also repeated the calibration process assuming that 1% or 15% of respiratory contacts occurred within the community. A total of 10 best-fit parameter sets were obtained for each value of community transmission.

We considered different interventions to reduce the burden of TB in Kivalliq (Table 2). For each intervention, changes made for that specific intervention were layered on top of the existing TB control activities that were assumed in our base case. For instance, there was a base case level of population LTBI screening in all interventions, which was increased in our population screening intervention. We included interventions that reduced TB transmission by active cases (interventions a and b), as well as those that prevented progression to active disease in LTBI cases (interventions c, d, and e):

We considered alternate approaches to evaluating intervention impact and to performing model calibration. A description of these approaches and results of these analyses are presented in the Additional file 1.

The best-fit model realizations captured the variability in diagnosed pulmonary TB cases in Kivalliq over the 14-year time period (Fig. 3). Although our base case assumed 5% of contacts occurred within the community, we present the results of calibration for all three levels of community transmission for the sake of comparison. The proportion of incident cases in community contacts ranged from less than 1% to greater than 50%, depending on the assumed intensity of respiratory contacts occurring within the community (Fig. 4). For the 5% community contacts scenario, we estimated that the contact tracing process would identify a median of 22% of household contacts with LTBI and 1.3% of contacts with active TB infection. We observed similar estimates with lower or higher amounts of community transmission (Fig. 5).

For each of the best-fit model realizations, we used the model to examine the projected dynamics of TB in Kivalliq over a 10-year period, in the absence of any additional interventions (Fig. 6). The ten best-fit parameter sets resulted in a high degree of variability between model runs (due to stochasticity and a small population size), with cumulative TB incidence estimates ranging from 33–369 cases over the ten year time period. Compared to the base case, decreasing the time to treatment initiation for active cases was projected to reduce the number of incident TB infections in the population and have an impact on reducing diagnosed active TB (Fig. 7). This finding was consistent across the ten best-fit parameter set experiments. In addition, expanded population screening was projected to reduce the number of incident TB infections in the population and have an impact on reducing diagnosed active TB (Fig. 7). Increased housing at the level implemented in the model trended toward reducing TB incidence, but there was variability between model runs.

As expected, compared to the base case, the two interventions that expanded LTBI screening (either at the population level or targeted to school aged children) resulted in more LTBI cases being detected (Fig. 8). However, greater LTBI detection and treatment did not necessarily translate into reduced TB burden: for the school-screening program, we did not observe a corresponding impact on incident or active TB diagnoses in the population. Reducing the time to identify, test, and where appropriate, treat contacts of infectious cases was not projected to have an impact on TB incidence or diagnoses.

Our findings were sensitive to assumptions around the relative fraction of TB transmission occurring in communities versus households (Fig. 9). When the contribution of community transmission was relatively low (1% of contacts sufficient to transmit TB occurred outside of the household), expected TB incidence was low (17–66 cases in the base case over a 10-year period). None of the proposed interventions were expected to have a dramatic impact on TB burden in Kivalliq, although the trend of lower incident infections and diagnosed active TB disease cases remained with the rapid treatment scenario (Fig. 9a). With higher transmission occurring outside of the household (15% of respiratory contacts sufficient to transmit TB occurring in the community), expected TB incidence in the base case ranged from 44 to 562 over the 10-year period. Rapid treatment was projected to decrease TB incidence, and to a lesser extent, diagnoses of active TB disease (Fig. 9b). Expanded population screening showed a trend toward lower TB incidence and diagnoses, but there was a fair amount of variability in these findings.

Given the slow progression of TB and the possible subsequent delay in observing impact of interventions on changes in disease dynamics, we repeated our analyses using a 25-year time horizon (Fig. 10). Rapid initiation of treatment for active TB cases remained the most attractive intervention option when considering the 25-year time horizon for all scenarios (1%, 5%, and 15% community transmission). With a longer time horizon, population screening, school screening programs, and increased housing were projected to have an overall minimal effect on reducing TB burden in the population. Under the assumption of a greater number of transmission events occurring among community contacts (15%) (Fig. 10), the rapid contact tracing intervention began to appear more attractive as an intervention, with all simulation runs resulting in a reduction in both incident and diagnosed active TB.