In this paper we adapt a discrete time version of the Lucas model with social protection where part of the total production is devoted to the health expenditures. The output is produced by labor and the technomogy exhibits externalities. The rate of growth of human capital depends on the ratio of health expenditures over GDP. We give conditions for which the optimal human capital sequences are increasing. When the instantaneous utility function is isoelastic and the production function is COBB-DOUGLAS, we prove that the optimal human capital sequences grow at constant rate. Moreover, we prove there exists a unuique equilibrium in the sense of LUCAS [1988] or ROMER [1986]