Figure 1

State flow diagram for the two-strain influenza model. S denotes the susceptible state, without prior vaccination. Other susceptible individuals may receive vaccination prior to the onset of infection, or after infection has appeared, and are denoted by V. Despite vaccination, some individuals become infected and follow a similar sequence of infection states to that of the susceptibles. States (and parameters) originating from vaccination are denoted by a subscript ‘V’. States representing symptomatic infection by strain j are denoted by I _j , and correspondingly those infected asymptomatically by A _j . Double-subscripted states indicate that the individual was previously infected with one strain, and is now progressing through infected states of the other strain. P _j denotes individuals partially recovered from infection by strain j, but still susceptible to infection by the other strain. R denotes the class recovered from successive infection by both strains. In addition, infected individuals may die (at rates d or d _A ) and transfer (via the dashed arrows) to a disease-induced death class D (not shown). See text for details and explanation of the parameters.