Data-driven models to predict the elimination of sleeping sickness in former Equateur province of DRC.

Approaching disease elimination, it is crucial to be able to assess progress towards key objectives using quantitative tools. For Gambian human African trypanosomiasis (HAT), the ultimate goal is to stop transmission by 2030, while intermediary targets include elimination as a public health problem - defined as <1 new case per 10,000 inhabitants in 90% of foci, and <2000 reported cases by 2020. Using two independent mathematical models, this study assessed the achievability of these goals in the former Equateur province of the Democratic Republic of Congo, which historically had endemic levels of disease. The two deterministic models used different assumptions on disease progression, risk of infection and non-participation in screening, reflecting biological uncertainty. To validate the models a censor-fit-uncensor procedure was used to fit to health-zone level data from 2000 to 2012; initially the last six years were censored, then three and the final step utilised all data. The different model projections were used to evaluate the expected transmission and reporting for each health zone within each province under six intervention strategies using currently available tools. In 2012 there were 197 reported HAT cases in former Equateur reduced from 6828 in 2000, however this reflects lower active testing for HAT (1.3% of the population compared to 7.2%). Modelling results indicate that there are likely to be <300 reported cases in former Equateur in 2020 if screening continues at the mean level for 2000-2012 (6.2%), and <120 cases if vector control is introduced. Some health zones may fail to achieve <1 new case per 10,000 by 2020 without vector control, although most appear on track for this target using medical interventions alone. The full elimination goal will be harder to reach; between 39 and 54% of health zones analysed may have to improve their current medical-only strategy to stop transmission completely by 2030.

Progress in the Mathematical Modelling of Visceral Leishmaniasis.

The leishmaniases comprise a complex of diseases characterized by clinical outcomes that range from self-limiting to chronic, and disfiguring and stigmatizing to life threatening. Diagnostic methods, treatments, and vector and reservoir control options exist, but deciding the most effective interventions requires a quantitative understanding of the population level infection and disease dynamics. The effectiveness of any set of interventions has to be determined within the context of operational conditions, including economic and political commitment. Mathematical models are the best available tools for studying quantitative systems crossing disciplinary spheres (biology, medicine, economics) within environmental and societal constraints. In 2005, the World Health Assembly and government health ministers of India, Nepal, and Bangladesh signed a Memorandum of Understanding to eliminate the life threatening form of leishmaniasis, visceral leishmaniasis (VL), on the Indian subcontinent by 2015 through a combination of early case detection, improved treatments, and vector control. The elimination target is <1 case/10,000 population at the district or subdistrict level compared to the current 20/10,000 in the regions of highest transmission. Towards this goal, this chapter focuses on mathematical models of VL, and the biology driving those models, to enable realistic predictions of the best combination of interventions. Several key issues will be discussed which have affected previous modelling of VL and the direction future modelling may take. Current understanding of the natural history of disease, immunity (and loss of immunity), and stages of infection and their durations are considered particularly for humans, and also for dogs. Asymptomatic and clinical infection are discussed in the context of their relative roles in Leishmania transmission, as well as key components of the parasite-sandfly-vector interaction and intervention strategies including diagnosis, treatment and vector control. Gaps in current biological knowledge and potential avenues to improve model structures and mathematical predictions are identified. Underpinning the marriage between biology and mathematical modelling, the content of this chapter represents the first step towards developing the next generation of models for VL.

Age- and bite-structured models for vector-borne diseases.

The biology and behaviour of biting insects is a vitally important aspect in the spread of vector-borne diseases. This paper aims to determine, through the use of mathematical models, what effect incorporating vector senescence and realistic feeding patterns has on disease. A novel model is developed to enable the effects of age- and bite-structure to be examined in detail. This original PDE framework extends previous age-structured models into a further dimension to give a new insight into the role of vector biting and its interaction with vector mortality and spread of disease. Through the PDE model, the roles of the vector death and bite rates are examined in a way which is impossible under the traditional ODE formulation. It is demonstrated that incorporating more realistic functions for vector biting and mortality in a model may give rise to different dynamics than those seen under a more simple ODE formulation. The numerical results indicate that the efficacy of control methods that increase vector mortality may not be as great as predicted under a standard host-vector model, whereas other controls including treatment of humans may be more effective than previously thought.