Immunization levels for preventing epidemics in a community of households made up of individuals of various types

A method is proposed for computing an epidemic threshold parameter for the spread of a communicable disease in a community of households in which individuals are of p different types. The threshold parameter is the largest eigenvalue of a p x p matrix whose elements depend on the rates of disease transmission between types and the distribution of the household size. More explicit expressions are given for diseases that are highly infectious within households, to the point that the infection of any member of a household results in the infection of all susceptible members of that household. For a variety of vaccination strategies it is described how this approach can be used to determine the level of immunity required to prevent epidemics. A numerical example illustrates the results.