Irrigation schemes are one of the most important policy responses designed to reduce poverty, particularly in sub-Saharan Africa. Concomitantly, they facilitate the propagation of schistosomiasis, a water-based debilitating disease that is endemic in many developing countries. We study the economic impact of schistosomiasis in Burkina Faso via its burden on agricultural production. We use new data and new methods, merging high-resolution disease maps with agricultural survey data and using spatial densities of the intermediate vector of the disease, freshwater snails, as instrumental variables. We estimate a substantial negative effect of the disease. Poorer households engaged in subsistence agriculture bear a far heavier disease burden than do richer ones, showing that schistosomiasis is both a driver and a consequence of poverty. We show that the returns to water resources development are significantly reduced once its health effects are taken into account. We reconcile these results with a theoretical framework which shows how the joint dynamics of disease and the production decisions of farmers create Pareto-inferior endemic Nash equilibria. The wealth-dependent disease reproduction rate is the key determinant of the stability of the equilibria, and can generate poverty traps. A stochastic extension of the model shows how this rate controls the probability flow between the system attractors. We show how social optima require deviations from separability proportional to the disease burden on the maximized utility paths, and how complete information on the feedback between wealth and disease can potentially allow farmers to escape the poverty trap.