A multigroup model for a heterosexually transmitted disease

A multigroup model is considered for a disease transmitted heterosexually in which there is a core group that has higher sexual activity than other groups. In order to develop control strategies to eradicate the disease, type reproduction numbers are determined. A graph-theoretic interpretation of type reproduction numbers for a star network with a core group at the center is established. Using these general formulas for the star network, a two-group model consisting of a core and a non-core group is considered. If disease can persist in the core group in isolation, then the amount of increase of treatment or decrease of the contact rate of infectious males (or females) in the core group that is required to eradicate the disease is expressed in terms of model parameters. If disease can persist but not in either group in isolation, then the amount of reduction of the connection between the two groups needed to eradicate the disease is determined. These two cases are illustrated with parameters applicable to gonorrhea in the US.