Model for unobserved processes. Before wave 1, people are either susceptible (S1) or resistant (R1) because of prior immunity. Persons exposed to the virus either express symptoms (E1), or have an asymptomatic infection (A1). Others are unexposed (U1). After exposure, persons become immune (E1R or A1R), and a proportion become susceptible again prior to wave 2 (E1S2, A1S2 and R1S2, plus the susceptible persons who escaped exposure in wave 1 (U1S2). All susceptible persons are at risk of exposure in wave 2 (see figure), and either express symptoms, have an asymptomatic infection, or remain unexposed. The extension to wave 3 adds an additional layer of complexity, but there are no new principles invoked.
Mathews et al. BMC Infectious Diseases 2010 10:128 doi:10.1186/1471-2334-10-128