Mathematical Models of the Transmission Dynamics of Human Immunodeficiency Virus in England and Wales: Mixing between Different Risk Groups

A mathematical model of the transmission dynamics of the human immunodeficiency virus, type 1, in England and Wales is described. The model mimics transmission within and between different sexual activity classes (or needle sharing classes in the case of intravenous drug users) and within and between different risk groups such as male homosexuals, intravenous drug users and heterosexuals. Patterns of mixing and sexual contact are described by mixing matrices whose elements define the degree of assortative (like with like) or disassortative (like with unlike) contact between different stratifications of the sexually active population. Wherever possible parameter assignments are based on published data but likely patterns of mixing are crudely estimated by fitting model projections to past temporal trends in the incidence of acquired immune deficiency syndrome (AIDS) in the different at‐risk groups in England and Wales. Many different parameter combinations are shown to fit past trends, and each has different implications for projections into the future. The importance of mixing patterns to future trends is highlighted. It is concluded that future trends are uncertain (on the basis of current information) particularly within the heterosexual population. Small changes in the values of key parameters induce significant changes in projected trends. Transmission models are shown to be of greatest value as tools to highlight needs for data for accurate projection and as a template for assessing the relative contribution of various factors to future trends in the incidence of AIDS.