We build an economico-epidemiological Solow-Swan model. Mortality and morbidity effects on effective labor are taken into account. A Ben-Porath-like mechanism affects the dynamics of the saving rate and reduces labor productivity. Based on optimal projections of the demographic and economic South African series on the period 2000-2050, we identify a delayed effect of HIV/AIDS on economic growth: the growth rate gap between the AIDS and no-AIDS scenarios is rather stable between 2010 and 2020, but then it increases sharply between 2020 and 2030, keeps increasing at a much lower pace between 2030 and 2040, and finally stabilizes after 2040. The fall in active population is the main factor behind AIDS impact on economic growth during the decade 2020-2030 while the Ben-Porath mechanism on labor productivity is more relevant in the last decade. Physical capital accumulation plays a minor role.