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 t he household size. More explicit expressions are given for diseases th at are highly infectious within households, to the point that the infe ction of any member of a household results in the infection of all sus ceptible members of that household. For a variety of vaccination strat egies it is described how this approach can be used to determine the l evel of immunity required to prevent epidemics. A numerical example il lustrates the results.