We present a mathematical model of the activation and proliferation of a clone of T helper cells in response to a replicating antigen. This is able to show types of behaviour akin to persistent infection and to immune memory. This model is expanded to include the infection and destruction of activated T helper cells by human immunodeficiency virus and the growth of a population of circulating human immunodeficiency virus. The resulting model is used to investigate the circumstances under which the human immunodeficiency virus can destabilize persistent infections and destroy immune memory, and to illustrate the impact of antigenic stimulation of infected T helper cell clones upon human immunodeficiency virus replication rates.