Threshold parameters for a model of epidemic spread among households and workplaces

The basic reproduction number R0 is one of the most important concepts in modern infectious disease epidemiology. However, for more realistic and more complex models than those assuming homogeneous mixing in the population, other threshold quantities can be defined that are sometimes more useful and easily derived in terms of model parameters. In this paper, we present a model for the spread of a permanently immunizing infection in a population socially structured into households and workplaces/schools, and we propose and discuss a new household-to-household reproduction number RH for it. We show how RH overcomes some of the limitations of a previously proposed threshold parameter, and we highlight its relationship with the effort required to control an epidemic when interventions are targeted at randomly selected households.