Comparison of stochastic and deterministic models forgambiensesleeping sickness at different spatial scales: A health area analysis in the DRC
Authors: Davis Christopher N , Crump Ronald E , Sutherland Samuel A , Spencer Simon E F , Corbella Alice , Chansy Shampa , Lebuki Junior , Miaka Erick Mwamba , Rock Kat S 
Published: August 2023

The intensification of intervention activities against the fatal vector-borne diseasegambiensehuman African trypanosomiasis (gHAT, sleeping sickness) in the last two decades has led to a large decline in the number of annually reported cases. However, while we move closer to achieving the ambitious target of elimination of transmission (EoT) to humans, pockets of infection remain, and it becomes increasingly important to quantitatively assess if different regions are on track for elimination, and where intervention efforts should be focused.

We present a previously developed stochastic mathematical model for gHAT in the Democratic Republic of Congo (DRC), and show that this same formulation is able to capture the dynamics of gHAT observed at the health area level (approximately 10,000 people). This analysis was the first time any stochastic gHAT model has been fitted directly to case data, and allows us to better quantify the uncertainty in our results. The analysis focuses on utilising a particle filter Markov chain Monte Carlo (MCMC) methodology to fit the model to the data from 16 health areas of Mosango health zone in Kwilu province as a case study.

The spatial heterogeneity in cases is reflected in modelling results, where we predict that under the current intervention strategies, the health area of Kinzamba II, which has approximately one third of the health zone’s cases, will have the latest expected year for EoT. We find that fitting the analogous deterministic version of the gHAT model using MCMC has substantially faster computation times than fitting the stochastic model using pMCMC, but produces virtually indistinguishable posterior parameterisation. This suggests that expanding health area fitting, to cover more of the DRC, should be done with deterministic fits for efficiency, but with stochastic projections used to capture both the parameter and stochastic variation in case reporting and elimination year estimations.

Author summary

Gambiensehuman African trypanosomiasis (gHAT, sleeping sickness) is a parasitic infection transmitted by tsetse in sub-Saharan Africa. The distribution of infections is patchy and highly correlated to the regions where humans and tsetse interact. This presents the need for mathematical models trained to the particular regions where cases occur.

We show how a stochastic model for gHAT, which captures chance events particularly prominent in small populations or with extremely low infection levels, can be directly calibrated to data from health areas of the Democratic Republic of Congo (DRC) (regions of approximately 10,000 people). This stochastic model fitting approach allows us to understand drivers of transmission in different health areas and subsequently model targeted control interventions within these different health areas.

Results for the health areas within the Mosango health zone show that this modelling approach corresponds to results for larger scale modelling, but provides greater detail in the locations where cases occur. By better reflecting the real-world situation in the model, we aim to achieve improved recommendations in how and where to focus efforts and achieve elimination of gHAT transmission.