Data

The Democratic Republic of Congo (DRC) has the highest burden of gHAT cases (1,110 cases out of 1,420 reported globally in 2017 [1]), and 46% of these cases are concentrated in the former Bandundu province [9]. We focus on models and data for two high-prevalence health zones in this former province (now in Kwilu province): Yasa-Bonga and Mosango. Reported case information made available by the WHO HAT Atlas [7, 13] details the locations of settlements with estimates of population size, the years that active screenings took place, the number of people screened and the resulting newly identified gHAT cases. In Yasa-Bonga and Mosango, we consider 559 settlements, which experienced 2,701 active screenings in 2000–2012, each where a full village population was targeted to be screened, resulting in 4,875 detected gHAT cases, as well as 2,496 additional cases from detected by passive surveillance. Our model utilises these recorded screening patterns to simulate interventions, while the active and passive cases detected in each settlement are stochastically generated by the model.

Population sizes for settlements are also obtained from census estimates within the WHO HAT Atlas (Fig 1B) [7, 13]; we account for an estimated yearly population growth of 2.6% [24]. Screening coverage from active surveillance is then calculated as the number of individuals screened divided by this population estimate in each year. Annual screenings larger than the estimated accessible population (yellow and red bars in Fig 1D) may indicate either multiple screenings in a year or misreporting of individuals attending from neighbouring settlements. Low annual screening coverage (at less than 20% of the population size, gray bars in Fig 1D) is assumed to represent individuals screened outside their home settlement and therefore is not considered as a complete active screening of any given village.

All relevant model data are displayed within the paper and the Supporting Information files (Table 2 in S1 Appendix). Epidemiological data for the study were provided by the WHO in the frame of the Atlas of gHAT which may be viewed at www.who.int/trypanosomiasis_african/country/risk_AFRO/en and may be requested through Jose Ramon Franco (francoj@who.int).

Modelling

The infection dynamics are described by a stochastic compartmental Ross–Macdonald-type model [25–28] extended from the previous work of Rock et al. [17] (using the formulation of Model 4 from that study) (Fig 1 in S1 Appendix). The model captures a population of humans, which is initially partitioned into those at high and low risk of being exposed to tsetse bites. Each person will transition between five different epidemiological compartments: susceptible; exposed (or latent); Stage 1 infection; Stage 2 infection; and hospitalised (and temporarily removed). We assume that there is natural mortality from all compartments, which leads to replacement of that individual as a susceptible in the population.

The risk structure is used to capture the behaviour of the small proportion of individuals that both work in the habitat of many tsetse and so have a higher biting exposure and also do not partake in active screening, thereby acting as a human reservoir of infection [16–18]. The proportion of the individuals in the high risk group is estimated through extensive model fitting to be 7.6% of the population for these health zones [17]. While the high risk group have a higher biting exposure, the probability of tsetse infection per single infective bite is the same for both risk groups. This model structure, where individuals are either high risk and non-participating in active screening or low risk and randomly participating in active screening, was selected using the deviance information criterion (DIC), which assigns low scores for models with high posterior mean log-likelihood and penalises models with more parameters.

Tsetse in the model are similarly compartmentalised into four epidemiological states: teneral (unfed); non-teneral yet uninfected; exposed (or latent); and infected. The distinction between teneral and non-teneral yet uninfected is used to capture the observation that tsetse are far more susceptible to infection at their first blood meal than at any subsequent blood meals [29]. The effect of a possible animal reservoir is not considered, since its role remains unclear [15, 17, 20, 30, 41] and its inclusion does not significantly improve the match between model outputs and currently available data in this setting [17].

Additional to the epidemiological and demographic processes, we simulate the effect of active screening and passive detection of cases. Passive detection (and disease-induced mortality) is assumed to occur at a fixed (per capita) rate for all Stage 2 infected individuals [11]. Active screening takes place annually; the proportion screened is either replayed from the historic pattern for that settlement or chosen randomly from the set of all screening coverages recorded, allowing a greater range of scenarios to be explored. Since Yasa-Bonga and Mosango are high endemicity regions, we assume that the screening coverage and frequency remains constant over time but note that these quantities are somewhat affected by population size (Fig 9 in S1 Appendix).

Individuals in the low risk group are selected randomly for screening, irrespective of epidemiological status, and those that are found to be infected are moved to the hospitalised class. We assume that screening only applies to low risk individuals, such that screening coverages greater than 92.4% (the estimated proportion in the low risk group) [17] are truncated (Fig 1D). In the field, the diagnostic process is complex and multi-stage [31]; however, in the model, we collapse this into characteristics for the whole algorithm, which is assumed to be 91% sensitive [32] but 100% specific. False negatives remain undetected in the settlement, but by assuming 100% specificity, there are no false positives as we assume confirmation by microscopy will be carried out due to the low case numbers.

For the majority of this paper, we model the dynamics as a closed population, without emigration or immigration, so that once the disease has gone extinct in a population it cannot be re-introduced. This removes a critical dependency in model formulation, and greatly simplifies the presentation of results. In reality, no population is ever completely isolated; however we show that the expected rate of infectious imports is very low and does not affect our main results or conclusions (S1 Appendix).

Parameters

Model parameters for the underlying compartmental model are taken from the previous work of Rock et al. [17]. The values of these parameters were taken from literature, where well-defined, and otherwise inferred by model fitting using a Metropolis–Hastings MCMC algorithm, which sought to match the deterministic model to observed cases and screening effort in Yasa-Bonga and Mosango. The values used in this manuscript are the median of the distributions inferred using MCMC methodology applied to the aggregate annual data from Yasa-Bonga and Mosango. Therefore, the parameter values are specific to the study region, and the model is well-matched with the incidence data from active and passive surveillance. A full list of parameters is given in Table 2 in S1 Appendix.

Comparison with data

While the underlying deterministic model has been fitted to the aggregate data from this region, it is important to assess the behaviour of the stochastic model against village-scale observations. Unfortunately, local disease extinctions cannot be directly observed; failure to discover any cases does not necessarily mean that the infection is not present, simply that it has not been detected. Thus, to validate our model, we make comparisons between the simulated predictions and WHO HAT Atlas data [7, 13] for the probability of detecting no cases on an active screening (termed zero-detections for brevity), which is a combination of failure to detect and local extinction. We compare model predictions to observations by calculating the percentage of zero-detections in aggregations of 100 active screenings with similar village population sizes (Fig 2A). We find very strong agreement between model predictions and data, with a pronounced decline in zero-detections for larger populations.

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Fig 2. Comparison of model predictions and data for active screenings with no detected cases (zero-detections).

(A) Histogram by population size of the percentage of active screenings that find no new gHAT cases for both the model and the HAT Atlas data. Each bar represents 100 screenings of simulated results (averaged over 10,000 replicates) from the model that uses the observed pattern of screenings and compares to the data. Values where the model predictions have more zero-detections than the data are in red, while the reverse is shown in yellow. Error bars represent the 95th percentile of model results. (B) Map of populations in Yasa-Bonga and Mosango showing the settlements with significant differences (at the 95% level) in the expected proportion of active screenings with no cases detected. Red circles are where the observed number of active screenings with zero-detections is below the 95th percentile of the model; yellow circles are where the data falls above the 95th percentile; small blue circles are for data that lie within the 95th percentile of predictions and therefore are well described by the model. The satellite image shown is from Landsat-8 accessed through https://earthexplorer.usgs.gov/ from the U.S. Geological Survey.

https://doi.org/10.1371/journal.pntd.0007838.g002

For individual settlements, those where the number of zero-detections lie outside the 95th percentile of model predictions are notably spatially clustered (Fig 2B). In 2.1% of settlements (red), there are significantly fewer zero-detections than predicted and hence greater persistence; these villages are generally localised around the main river through the region. In 6.3% of settlements there are significantly more zero-detections than expected (yellow), and these are clustered far from the major rivers and in upland areas. Since tsetse are most densely distributed surrounding riverine areas [33], this spatial clustering may indicate the need for spatially heterogeneous parameters that reflect the suitability of the local environment for tsetse. However, given that more than 90% of villages fall within our prediction intervals, we believe the homogeneous parameters capture the general stochastic behaviour of this region.

Local gHAT persistence

Local gHAT persistence, where human infection is maintained in a settlement, is affected by many factors (Fig 3), including the population size of the settlement; the vector-to-host (tsetse-to-human) ratio; the exposure to the tsetse; the screening procedure; and any movement of infected individuals between populations. We calculate the probability of persistence by stochastically simulating the epidemic for 16 years from the endemic (uncontrolled) disease equilibrium. If there is zero gHAT infection in the human population after a given number of years and no further human infection emerges in the following year from infected tsetse, we say in this simulation there is local disease elimination with no immediate threat of re-emergence (Fig 4A provides a justification for this criteria). This procedure is repeated for multiple population sizes; the proportion of simulations that retain infection after a given number of years determines the probability of persistence (Fig 3).

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Fig 3. Predicted probability of gHAT persistence in isolated settlements.

Simulations are started at the endemic (uncontrolled) equilibrium and iterated forwards (without infectious imports), while the persistence of infection is recorded. This is repeated 100,000 times for settlement population sizes between 50 and 2,000 individuals. The expected number of yearly new infections if the system were at equilibrium is proportional to the population size and is given by the top scale. (A) Impact of active screening on gHAT persistence; annual screening at a fixed coverage per year yields a drop in persistence with increased coverage. (B) Comparison of screening assumptions on the persistence of gHAT. The solid curve shows results where annual screening coverages were randomly sampled from all observed coverages; dots represent the individual settlements recorded in the WHO HAT Atlas for Yasa-Bonga and Mosango health zones [7, 13], where the reported coverage in each year is used. There were sufficient simulations such that confidence intervals are too small to be visible.

https://doi.org/10.1371/journal.pntd.0007838.g003

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Fig 4. Dynamics of extinction and reintroduction.

(A) Starting with no infected humans but the tsetse population at its endemic equilibrium and a settlement size of 1,000 individuals, the model predicts a dramatic decline in the infected tsetse population, depending on whether subsequent human cases are generated by the infected tsetse. (B) Extending this model further for a range of initial conditions, we examine the probability that at least one human case is generated and the infection persists for a given time, when starting with one infected human and no infected tsetse for both uncontrolled and random screening.

https://doi.org/10.1371/journal.pntd.0007838.g004

We focus on settlements with fewer than 2,000 inhabitants, typical of Yasa-Bonga and Mosango (Fig 1B), and use regionally specific parameters. In all scenarios investigated, we find that persistence increases with increasing population size (Fig 3). This echoes results from other infections [22, 23, 34, 35], where small populations with low incidence experience a greater impact of stochasticity and chains of transmission that are more likely to be broken. In addition, given that long-term persistence relies on persistence for shorter time intervals, the probability of persistence decreases with time (Fig 10B–C in S1 Appendix). The relatively long persistence times of gHAT, compared to the frequently studied persistence of childhood diseases [22, 23], are attributable to the long time-scale of gHAT infection in the absence of active interventions [36].

The addition of active screening (leading to the treatment of detected cases) decreases the probability of persistence across all population sizes, since removing infected individuals leads to a greater chance of breaking chains of transmission (Fig 3A). Increasing levels of screening, beyond the observed 21% average, leads to further reductions for persistence. We compare three assumptions for active screening (Fig 3B): that each population is screened annually at a fixed coverage equal to the regional average (21%); that each population experiences screening coverages sampled from the regional pattern including not screening in a given year; and simply replaying the recorded pattern of active screening in each village. Despite the very different distributions of screening effort, all three of these assumptions produce comparable levels of persistence.

Re-invasion probability

Following localised elimination of infection, populations remain vulnerable to re-invasion; we investigate the potential for re-establishment of sustained transmission in a settlement for different invasion scenarios. For a village of 1,000 individuals, following the elimination of infection in humans, the level of infection in tsetse falls rapidly, even when starting at the endemic level in these vectors (Fig 4A). In approximately 65% of simulations, the initially infected tsetse generate human cases, and the level of infection in vectors rapidly plateaus; otherwise, infection is eliminated from the location within six months due to short vector life expectancies in comparison to the human hosts. This validates the previous simulation assumption (Fig 3) that local disease elimination can be considered achieved after a period of one year in which there are no infected humans, as the number of infected tsetse will also become negligible.

The probability that a population of tsetse, infected at the endemic equilibrium (0.02% of tsetse exposed or infected), will lead to re-establishment of infection is predicted to be a function of settlement size (Fig 11A in S1 Appendix). Small populations are unlikely to see any new human infections, and those that are generated fail to persist. However, even for large population sizes of 2,000 individuals, the chance of continued transmission beyond one year is only 55% and is less than 10% over 15 years. For lower levels of infection in the tsetse population, the risk of successful re-establishment is proportionally reduced.

In contrast, if re-invasion of an infection-free population is due to the movement of an infected person into the settlement (in the absence of infected tsetse) the probability of re-establishment over different time-frames is largely unaffected by the population size (Fig 4B). We predict a high probability (> 70%) of short term re-invasion, but a more limited chance (< 20%) that this will generate persistent infection for 15 years or more. This is typical of stochastic dynamics of infection with low basic reproductive ratio (R₀), where, although short chains of transmission are likely, it is difficult for the infection to fully establish.

Detecting elimination

As discussed above, zero-detections may be an indication that there is no infection in a settlement; however, it may simply be that infected individuals were not screened or were false negatives. Despite this, there is a temptation to associate zero-detection with zero infection; we therefore use our simulations to tease apart this complex relationship. The model replays the observed pattern of screening in each settlement, but we perform multiple simulations to ascertain the probability that infection has been locally eliminated following one, two or three consecutive zero-detection screenings, in which at least 20% of the population are screened (Fig 5). We also insist that no passive cases were detected between the screening events. Our standard assumption, in agreement with parameter inference for this region, is that 26% of Stage 2 infections, where people either self-report or likely die of gHAT infection, are detected and reported [17], but we also investigate 0% (no passive reporting) and 100% (all passive cases and deaths are reported) for comparison.

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Fig 5. Probability of elimination in a settlement, given consecutive zero-detections with no detected passive cases.

(A) Consecutive zero-detections means consecutive in the observed years of screenings, not necessarily in consecutive years, and with no passive cases detected in between. Each point represents the average from multiple simulations of individual settlements where the reported pattern of screenings is replayed. The points and solid lines assume a reporting rate of 26% [17], while the dashed and dotted lines show reporting rates of 0% and 100%, respectively. Sufficient simulations are used such that the confidence intervals are small (unobservable on the scale of this graph). Lines represent a weighted local regression fit. Active screenings where fewer than 20% of the population are assessed are excluded from our analysis due to the small sample sizes (alternative cut-offs of less than 10% and less than 50% are presented in Fig 13 in S1 Appendix).

https://doi.org/10.1371/journal.pntd.0007838.g005

For small settlements, given that long-term persistence is unlikely (Fig 3), even a single zero-detection screen (Fig 5, blue) is frequently associated with local elimination. For larger populations, a single zero-detection has limited predictive power and three consecutive zero-detections are needed to have any degree of confidence, in which case the reporting of passive cases plays a noticeable role. There is, however, significant variation between settlements, reflecting very different patterns of reported screening. Moderate population sizes of between 200 and 1,000 individuals show extreme variation in the ability to predict local elimination, while smaller villages have less variation, in part due to rarely being screened before 2009 (Fig 9C in S1 Appendix).

Importation rates

Regional persistence relies on more than independent persistence in individual settlements. It is likely that the occasional movements of infected people lead to a stochastic meta-population paradigm [40], where rare local extinctions of infection are balanced by external imports. However, the agreement between model and data (Fig 2), together with the low prevalence of infection, indicates that imports are likely to be rare.

We make this more quantitative by fitting an importation rate of infection, proportional to the size of the population. Before interventions, the presence/absence of infection in a population reflects the equilibrium balance between extinction and re-colonisation; we can therefore use the presence of infection at the first recorded active screening within a village as measure of the equilibrium state. Fitting the external importation rate to the probability of detecting infection in a village at the first active screen gives the best fit when the rate is small at just 3.4 × 10⁻⁶ per person per day (Fig 6A). Moreover, it is assumed that the importation rate declines over time as the overall prevalence in DRC reduces.

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Fig 6. Simulating external importations of infection into village populations.

(A) By running simulations with different values for the external infection parameter, we find the best fit—to data binned by population size from the WHO HAT Atlas on whether there are any detected cases on the first active screening—is when imports per susceptible individual are equal to 3.4 × 10⁻⁶ days⁻¹ (solid line). (B) Curves of the expected time for an external importation into a village population using the fitted importation parameter. The importation parameter is assumed to decay at the same rate as total number of cases in time in the DRC (see Fig 5 in S1 Appendix).

https://doi.org/10.1371/journal.pntd.0007838.g006

For most population sizes in the region, the expected time to importation is therefore relatively long (Fig 6B), and in many cases a single importation will not cause further transmission events (Fig 4), leading us to conclude that in general the level of importation will not qualitatively change our results. This is made more explicit in the supporting information (Fig 6 in S1 Appendix), where it is shown that the model with the fitted level of infectious imports generates comparable results to those described in the main paper. This justifies our modelling assumptions that villages act as isolated populations and that importation of infection is unlikely to perturb the dynamics; instead, we are able to separate the processes of local elimination and re-invasion.

Conclusion

The ability to capture the stochastic dynamics and persistence of gambiense gHAT infection at the village-scale is a major advance in public health modelling, with far-reaching consequences for informing policy decisions. This is particularly pertinent as our models operate at the same spatial scale as controls and can capture the local elimination of infection that is a prerequisite of achieving the 2030 goal of zero transmission globally.