Abstract Compartmental model diagrams have been used for nearly a century to depict causal relationships in infectious disease epidemiology. Causal directed acyclic graphs (DAGs) have been used more broadly in epidemiology since the 1990s to guide analyses of a variety of public health problems....

We analyze a mathematical model of the simultaneous transmission of two HIV subtypes and their control by vaccines. Two vaccines are analyzed which utilize different mechanisms, one in which the vaccine take differs for each subtype, and the other in which a different level of reduced...