State and parameter estimation for a class of schistosomiasis models

We develop a general framework to estimate the proportion of infected snails and snail-human transmission parameter of a class of models that describes the evolution of schistosomiasis. To do so, we consider simultaneously the dynamics of schistosomiasis, captured by the homogeneous version of the classical MacDonald's model, and the measurable output: the number of female schistosomes per single host. The proposed method consists of designing an auxiliary dynamical system, called observer, whose solutions converge exponentially to those of the system capturing the schistosomiasis model. Moreover, we derive an estimation of the snail-human transmission rate, an unknown but key parameter in the dynamics of schistosomiasis. These estimations are central in two of the strategies of controlling schistosomiasis, namely the use of molluscicides and mass drug administration. To further investigate control strategies on a larger scale, we consider a heterogeneous model which consists of an arbitrary number of human groups or patches and an arbitrary number of fresh-water sources, natural habitats of snails. Provided that the data of infected humans' worm burden in each patch or group is available, we provide a method of estimating the proportion of infected snails in each snail natural habitat, thereby providing a map on where to implement control strategy to mitigate or eliminate Schistosomiasis.