Stylized facts show there is a clustering of countries in three balanced growth paths characterized by differing income/growth, human capital and incidence of infectious diseases. To explain this, we develop a dynamic general equilibrium model incorporating S I S epidemiology dynamics, where households choose how much to invest in human and physical capital, as well as in controlling the risk of infection. In the decentralized economy, households do not internalize the externality of controlling infection. There are multiple balanced growth paths where the endogenous prevalence of the disease determines whether human capital is accumulated or not, i.e., whether there is sustained economic growth or a poverty trap. We characterize the optimal public health policy that internalizes the disease externality and the subsidy that decentralizes it. Perversely, for countries in a poverty trap and most afflicted with diseases, the optimal subsidy is lower than for growing economies. We also study the quantitative effects of better control of diseases, and of increasing life expectancy on countries in a poverty trap. Keywords Endogenous growth • Infectious diseases • Epidemiology • Poverty trap • Public health policy • Human capital JEL Classification E19 • I10 • D90 • O11 Goenka would like to acknowledge research support from FASS Research Grant R-122-000-131-112.