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Modelling Methods

Simulating elimination dynamics in connected villages

By simplifying the infection structure of the Warwick gHAT model, we reduce the dimensionality of our The risk distribution of infection in selected villages of Kwamouth at different time points (the years 2000, 2010, 2020 and 2030); the first possible active screening of each village was in 1998. There are 418 villages with populations ranging between 3 and 20,697 of which we present the probability distribution of infected people in four villages ($N_H=100$, $971$, $5,628$ and $20,697$). On each subplot the $x$-axis represents the number of high-risk people infected, and the $y$-axis, the number of low-risk people infected. The risk distribution of infection for the alternative health zone of Mosango are presented in the supplementary material.infection system such that we can utilise the powerful method of Kolmogorov forward equations. This newly developed model variant captures the infection dynamics within the groups of spatially-connected villages that make up a health zone. Using this model, the probability of elimination of infection can be calculated on different spatial scales in a consistent manner and scaled between them. We see comparable results at the health zone level to the higher-dimensional models. However, the novel flexibility of the new model allows interventions to be modelled specific to each village, which introduces the modelling framework that we can use to consider the possible future strategies: test-and-treat or direct treatment of individuals living in villages where cases have been found, using new drug, acoziborale.

Forthcoming paper: Davis, CN, Keeling, MJ, Rock KS (2021). Modelling gambiense human African trypanosomiasis infection in villages of the Democratic Republic of Congo using Kolmogorov forward equations. M[pre-print, not peer-reviewed]. Paper summaries: English, French

Potential impact of asymptomatic human infections on gHAT transmission

Sensitivity analysis in terms of model parameters.
There is evidence of asymptomatic human gHAT infection but there is uncertainty around the role it plays in overall transmission and maintenance. To study this challenge, we developed a novel model by extending our established baseline framework for gHAT to account for asymptomatic infections including those in people with blood-dwelling trypanosomes, without discernible symptoms, and those with parasites only detectable in skin. Our new model adds extra parameters to the baseline model including different self-cure, recovery, transmission rate from skin-only infections, and the proportion of exposures resulting in initial skin or blood infection. Performing sensitivity analysis suggests the new parameters introduced in the asymptomatic model can impact the infection dynamics substantially. For some plausible parameterisations, an initial fall in infection prevalence - due to screening and treatment interventions - could subsequently stagnate even under continued screening due to the formation of a new, lower endemic equilibrium. Excluding this scenario, our results still highlight the possibility for asymptomatic infection to slow down progress towards elimination of transmission. Location-specific model fitting will be needed to determine if and where this could pose a threat.

Forthcoming paper: Aliee, M, Keeling, MJ, Rock, KS (2021). Modelling to explore the potential impact of asymptomatic human infections on transmission and dynamics of African sleeping sickness. M[pre-print, not peer-reviewed]. Paper summaries: English, French

Extending a cost-effectiveness framework to account for elimination goalsCost-effectiveness acceptability curves and cost breakdown for Region 1. A) the probability of EOT by 2030 for each strategy. B) The traditional cost-effectiveness acceptability frontiers (CEAFs). C) The total cost for a strategy that reaches elimination with 100% probability and the breakdown between minimum cost strategy, and justifiably additional costs and premium of elimination across willingness to pay to avert DALY values.

Various diseases are earmarked for elimination by the global health community. While the health economic implications of elimination have been discussed before, the combination of uncertainty, cost-effectiveness in terms of cases averted, and elimination in the face of rising per-case costs has not been tackled before.

We propose an approach that considers the tension between the dual objectives of cost-effectiveness and elimination while incorporating uncertainty in these objectives. This framework enables us to compute the additional costs of implementing a strategy which is more likely to achieve elimination beyond what would normally be considered cost-effective - which we call the premium of elimination.

We apply our method to strategies against human African trypanosomiasis in three settings, but this method could be directly applied to simulation-based studies of the cost-effectiveness of other disease elimination efforts. The method yields common metrics of efficiency for stakeholders who have different objectives.

Forthcoming paper: Antillon, M, Huang, C, Rock, K and Tediosi, F (2021). Economic evaluation of disease elimination: an extension to the net-benefit framework and application to human African trypanosomiasis [pre-print, not peer reviewed]. Paper summaries:  English


Elimination thresholds for the gHAT model

(A-D) Probability distribution of extinction time in the model of birth-death process for different values of birth rate b, when d=1 per unit time for all. Gray bars represent the solutions of Kolmogorov forward equation. The coloured lines show the F distribution estimated from the first four moments of birth-death process. (E) Comparing the estimated F distribution functions plotted for all values of birth rate b.Predicting the time to elimination of gHAT transmission in different circumstances is pivotal to our research. Analysis has been undertaken to identify a threshold value for the deterministic model that equates to the mean extinction time of the associated stochastic model.


We study this problem with the help of an effective "birth-death" description of infection and recovery processes and present a practical method to estimate the distribution of extinction times.
This work can be used in the future to enable more robust predictions for time to local elimination of transmission when using deterministic models. 


Peer-reviewed paper: Aliee, M, Rock, KS, Keeling, MJ (2020). Estimating the time to extinction of infectious diseases in mean-field approaches. Journal of the Royal Society Interface. Paper summaries: English, French