Quantitative evaluation of the strategy to eliminate human African trypanosomiasis in the Democratic Republic of Congo

Background The virulent vector-borne disease, Gambian human African trypanosomiasis (HAT), is one of several diseases targeted for elimination by the World Health Organization. This article utilises human case data from a high-endemicity region of the Democratic Republic of Congo in conjunction with a suite of novel mechanistic mathematical models to address the effectiveness of on-going active screening and treatment programmes and compute the likely time to elimination as a public health problem (i.e. <1 case per 10,000 per year). Methods The model variants address uncertainties surrounding transmission of HAT infection including heterogeneous risk of exposure to tsetse bites, non-participation of certain groups during active screening campaigns and potential animal reservoirs of infection. Results Model fitting indicates that variation in human risk of tsetse bites and participation in active screening play a key role in transmission of this disease, whilst the existence of animal reservoirs remains unclear. Active screening campaigns in this region are calculated to have been effective, reducing the incidence of new human infections by 52–53 % over a 15-year period (1998–2012). However, projections of disease dynamics in this region indicate that the elimination goal may not be met until later this century (2059–2092) under the current intervention strategy. Conclusions Improvements to active detection, such as screening those who have not previously participated and raising overall screening levels, as well as beginning widespread vector control in the area have the potential to ensure successful and timely elimination. Electronic supplementary material The online version of this article (doi:10.1186/s13071-015-1131-8) contains supplementary material, which is available to authorized users.


S1 Model formulation
The HAT model equations are given below and correspond with Figure 2 (main text).
Human hosts are assumed to be in one of four distinct classes: either low-risk and randomly participant in screening (subscript H1), high-risk and random participants (H2), low-risk and never participate in screening (H3) or high-risk and never participate. Tsetse bites are assumed to be taken on humans or animals. The model incorporates reservoir animals which can become infected and assumes that the remainder of the bites are taken on non-reservoir animal species which do not need to be explicitly modelled.
Here the N H = i N Hi and the actual number of vectors is S V , E 1V , E 2V , E 3V and I V multiplied by N V /N H .
i f i = f H i.e. the total proportion of tsetse bites taken on humans. s i is the relative availability/attractiveness of different host types, so for the 4 different humans types (low/random participant, high/random, low/non-participant, high/non), where high risk humans are r-fold more likely to receive bites, s = (1, r, 1, r). The f i 's are calculated using f i = s i N Hi j s j N Hj .

S1.1 Basic reproductive ratio
The next generation matrix (NGM) (see [S2]) is used to compute R 0 before active case detection and treatment began (but includes passive case detection and treatment). Transmissions: The NGM, K, is given by: and the R 0 is the spectral radius of K: In all further discussion, R 2 0 is used as a measure of the reproductive ratio, due to its biological representation of full cycle or host-to-vector-to-host transmission.

S2 Model output
The compartmental ODE model is simulated to compute the disease dynamics in humans, animals and tsetse (see Figure S1). The total annual passive reported cases for year, T is calculated by integrating over the new hospitalisations from self-presentation multiplied by the reporting parameter, u, to compensate for underreporting of passive cases: where i ∈ all human types), whereas the active number of reported cases is given as: where j ∈ random participants. The number of reported cases seen under the model is also shown in Figure S1. 1996 1997 1998 1999 2000 2001 2002 2003 2004 % Hosts  1996 1997 1998 1999 2000 2001 2002 2003 2004 Incidence per year per 10 000 0 20 40 Active Passive Total New infections Figure S1: Example disease dynamics of the human, animal, tsetse model. The top 3 graphs show the continuous disease dynamics generated by the ODE model, with active, pulsed screening taking place annually from 1998 and a passive reporting level of u = 0.32. The bottom graph shows the incidence per year per 10,000 which is computed after obtaining the solutions to the ODE (see (S2.1) and (S2.2)).

S3 The homogeneous case
In the simple case with homogeneous human risk/behaviour and no animal reservoirs, the relationship between the R 0 and p V , ε and m ef f is given by: where A = 0.7668 and B = 11.1 for the given parameters in Table 1 with u = 0.32 (see main article).
Consequently, there are whole regions, rather than points in parameter space which yield the maximum likelihood due to the strong correlation of vector-related parameters. In particular, the effects of m eff and p V are indistinguishable (for the same R 2 0 it does not matter how m eff and p V are chosen, the log-likelihood will be the same), whereas ε impacts the force of infection term (a rate) and so the same R 2 0 value may give a different likelihood (see Figure S2).  Figure S2: Scatter plot of the log-likelihood function against R 2 0 under Model 1 for fixed u = 0.32. Whilst the same R 2 0 generates slight variation in the value of the likelihood with varying ε, the maximum likelihood is still achieved at the same R 2 0 (≈ 1.03)

S4 Parameters and credible intervals
Imputation was performed using the standard Metropolis-Hastings MCMC algorithm with a Gaussian random walk generating sample proposals. The chain was thinned (keeping 1 out of every 100 steps) to reduce autocorrelation between samples. As there is little existing information in the literature for many of the target parameters, uniform priors were taken for all but one of the parameters (see Table S1). Posterior distributions of the fitted parameters for Models 1, 4 and 7 are shown in Figure  S3. Mean acceptance rates varied between Model variants and lay between 30-75%. Table S2 gives the mean and 95% credible interval for the fitted model parameters for Models 1, 4, 6 and 7.
Model selection was performed using the popular deviance information criterion (DIC), which assigns a lower score to models with high posterior mean log-likelihood whilst penalising models with a larger number of parameters [S3]. The relative likelihood of model i was computed using, and was used to compare models (see Table 3 in main text). It was found that there is statistical support for both Models 4 (Relative DIC = 0.83) and 7 (Relative DIC = 1). Since DIC is known to favour over-fitted models [S1], both models were considered to be similarly supported by the data despite the marginally lower DIC score for Model 7. All other models were found to be less well supported by current data.