The world's rural poor rely heavily on their immediate natural environment for subsistence and suffer high rates of morbidity and mortality from infectious diseases. We present a general framework for modelling subsistence and health of the rural poor by coupling simple dynamic models of population ecology with those for economic growth. The models show that feedbacks between the biological and economic systems can lead to a state of persistent poverty. Analyses of a wide range of specific systems under alternative assumptions show the existence of three possible regimes corresponding to a globally stable development equilibrium, a globally stable poverty equilibrium and bistability. Bistability consistently emerges as a property of generalized disease-economic systems for about a fifth of the feasible parameter space. The overall proportion of parameters leading to poverty is larger than that resulting in healthy/wealthy development. All the systems are found to be most sensitive to human disease parameters. The framework highlights feedbacks, processes and parameters that are important to measure in studies of rural poverty to identify effective pathways towards sustainable development.