Models for the spread of infectious diseases can give insight into the ability of pathogens to invade a population. The possibility of invasion leading to an epidemic, or fadeout of the disease is governed by a threshold parameter called the basic reproduction number Ro. The basic reproduction number depends on the transmission pathways of the disease and on demographic and epidemiological parameters. In this talk we will consider models based on systems of ordinary differential equations for the spread of infectious diseases in heterogeneous populations. We define the threshold parameter Ro for such models and discuss how to compute this parameter using several examples.