Here, we present a method for incidence estimation of a curable, non-recurring disease when data from a single cross-sectional survey are used together with population-level mortality rates and an assumption of differential mortality of diseased versus non-diseased individuals. The motivating example is cataract, and the VISION2020 goal to eliminate avoidable blindness globally by 2020. Reliable estimates of current and future cataract disease burden are required to predict how many surgeries would need to be performed to meet the VISION2020 goals. However, incidence estimates, needed to derive future burden, are not as easily available, due to the cost of conducting cohort studies. Disease is defined at the person-level in accordance with the WHO person-level definition of blindness. An extension of the standard time homogeneous illness-death model to a four-state model is described, which allows the disease to be cured, whereby surgery is performed on at least one diseased eye. Incidence is estimated, and the four-state model is used to predict disease burden assuming different surgical strategies whilst accounting for the competing risk of death. The method is applied to data from approximately 10,000 people from a survey of visual impairment in Nigeria.