Resumen: We study the dynamics of poverty and health in a model of endogenous growth and rational health behavior. Population health depends on the prevalence of infectious diseases that can be avoided through costly prevention. The incentive to do so comes from the negative effects of ill health on the quality and quantity of life. The model can generate a poverty trap where infectious diseases cycle between high and low prevalence. These cycles originate from the rationality of preventive behavior in contrast to the predator–prey dynamics of epidemiological models. We calibrate the model to reflect sub-Saharan Africa’s recent economic recovery and analyze policy alternatives. Unconditional transfers are found to improve welfare relative to conditional health-based transfers: at low income levels, income growth (quality of life) is valued more than improvements to health (quantity of life).