Inferring Patterns, Dynamics, and Model-Based Metrics of Epidemiological Risks of Neglected Tropical Diseases

Data scarcity and ecological complexity: the cutaneous leishmaniasis dynamics in Ecuador

Cutaneous leishmaniasis (CL) is a neglected tropical disease transmitted by species of Phlebotominae sand flies. CL is responsible for more than 1000 reported cases per year in Ecuador. Vector collection studies in Ecuador suggest that there is a strong association between the ecological diversity of an ecosystem, the presence of potential alternative or reservoir hosts and the abundance of sand fly species. Data collected from a coastal community in Ecuador showed that Leishmania parasites may be circulating in diverse hosts, including mammalian and potentially avian species, and these hosts may serve as potential hosts for the parasite. There has been limited reporting of CL cases in Ecuador because the disease is non-fatal and its surveillance system is passive. Hence, the actual incidence of CL is unknown. In this study, an epidemic model was developed and analysed to understand the complexity of CL transmission dynamics with potential non-human hosts in the coastal ecosystem and to estimate critical epidemiological quantities for Ecuador. The model is fitted to the 2010 CL outbreak in the town of Valle Hermoso in the Santo Domingo de los Tsachilas province of Ecuador and parameters such as CL transmission rates in different types of hosts (primary and alternative), and levels of case reporting in the town are estimated. The results suggest that the current surveillance in this region fails to capture 38% (with 95% CI (29%, 47%)) of the actual number of cases under the assumption that alternative hosts are dead-end hosts and that the mean CL reproduction number in the town is 3.9. This means that on the average 3.9 new human CL cases were generated by a single infectious human in the town during the initial period of the 2010 outbreak. Moreover, major outbreaks of CL in Ecuador in coastal settings are unavoidable until reporting through the surveillance system is improved and alternative hosts are managed properly. The estimated infection transmission probabilities from alternative hosts to sand flies, and sand flies to alternative hosts are 27% and 32%, respectively. The analysis highlights that vector control and alternative host management are two effective programmes for Ecuador but need to be implemented concurrently to avoid future major outbreaks.

Approximation methods for analyzing multiscale stochastic vector-borne epidemic models

Stochastic epidemic models, generally more realistic than deterministic counterparts, have often been seen too complex for rigorous mathematical analysis because of level of details it requires to comprehensively capture the dynamics of diseases. This problem further becomes intense when complexity of diseases increases as in the case of vector-borne diseases (VBD). The VBDs are human illnesses caused by pathogens transmitted among humans by intermediate species, which are primarily arthropods. In this study, a stochastic VBD model is developed and novel mathematical methods are described and evaluated to systematically analyze the model and understand its complex dynamics. The VBD model incorporates some relevant features of the VBD transmission process including demographical, ecological and social mechanisms, and different host and vector dynamic scales. The analysis is based on dimensional reductions and model simplifications via scaling limit theorems. The results suggest that the dynamics of the stochastic VBD depends on a threshold quantity R₀, the initial size of infectives, and the type of scaling in terms of host population size. The quantity R₀ for deterministic counterpart of the model is interpreted as a threshold condition for infection persistence as is mentioned in the literature for many infectious disease models. Different scalings yield different approximations of the model, and in particular, if vectors have much faster dynamics, the effect of the vector dynamics on the host population averages out, which largely reduces the dimension of the model. Specific scenarios are also studied using simulations for some fixed sets of parameters to draw conclusions on dynamics.