Mortality from causes other

than influenza starts from age 65 and thereafter is assumed to be a constant risk, corresponding to a mean life expectancy of 25 years for individuals aged 65 (Table 1). Individuals in different age groups mix with one another as defined in a UK specific age stratified contact matrix developed by the POLYMOD study [16]. Such matrices are usually referred to as ‘Who Acquires Infection from Whom’ (WAIFW) contact matrices (Fig. 1) and provide a relative measure of the frequency GSK 3 inhibitor of contact between individuals of different or similar ages. An influenza transmission model was developed, building on an approach set out previously [17]. For the purposes of this model, influenza is assumed to occur as two sub-types of influenza A (e.g. H1N1 and H3N2) and as influenza B. All subtypes are assumed to be immunologically distinct and to occur every two years, with the A subtypes alternating to give an annual peak in incidence between week 40 and week 20 of the following year. The dynamic transmission model subdivides the population into 5 subgroups, the Susceptible, Exposed, Infectious, Recovered and Vaccinated populations (Fig. 2). This stratification is based on the influenza virus infection status of members of the population

and not on clinical presentation. A set of linked differential equations (see Appendix A) describes the flow of individuals between these subgroups and the system is solved numerically using a fourth order Runge–Kutta method with adaptive step control [18]. Exposed (latently infected) individuals are assumed to be infected for an average of 2 days before becoming infectious Enzalutamide solubility dmso [19]. They remain infectious on average for a further 2 days [19], during which time the intensity and duration of viral shedding is assumed to be uniform across the age bands. ALOX15 Once an individual has recovered from infection, they are assumed to be immune to reinfection with the same subtype. This immunity wanes over time as a result of the combined effects of a gradual decline in immunological memory and antigenic drift on the part of the virus. The resulting duration

of protection was assumed to last for 6 and 12 years for influenza A and influenza B, respectively [17]. The basic reproductive rate (R0) is defined as the number of secondary infections arising from one primary infection in a totally susceptible population [20] and [21]. Using data from past pandemics, R0 for influenza has been estimated to range from 1.6 to 3.9 [22] and [23]. A value for the transmission coefficient was chosen, corresponding to a conservative R0 of 1.8, calculated using the dominant eigenvalue of the next generation matrix [24] and [25]. The incidence of influenza follows a marked seasonal pattern. Peak incidence was assumed to occur on December 22 and to reach a minimum on June 23. The magnitude of the basic reproduction number at the peak of influenza incidence compared to baseline was set to 1.43 [17].