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Supplementary File 1: Supplementary Methods Supplementary file 1: Supplementary Methods Belonging to the manuscript: Cost-effectiveness of paediatric influenza vaccination in the Netherlands Pieter T. de Boer1,*, Franklin C.K. Dolk1*, Lisa Nagy2,*, Jan C. Wilschut3, Richard Pitman2, Maarten J. Postma1,3,4 1 Unit of PharmacoTherapy, -Epidemiology & -Economics (PTE2), Department of Pharmacy, University of Groningen, Groningen, the Netherlands 2 ICON Health Economics and Epidemiology, Oxfordshire, United Kingdom 3 Department of Health Sciences, University Medical Center Groningen, Groningen, the Netherlands 4 Department of Economics, Econometrics & Finance, Faculty of Economics & Business, University of Groningen, Groningen, the Netherlands *: These three authors have contributed equally to this manuscript 1 1. Transmission model (deterministic) 1.1. Transmission model data sources Data were obtained from the following sources. From Statistics Netherlands (CBS): • Population and birth data 1,2 • Life tables and mortality data 3 From the World Health Organization (WHO) • Vaccine composition from 2010/2011 to 2013/14 4 • Flunet influenza surveillance reports 5 From the National Institute for Public Health and the Environment (RIVM) • Vaccination uptake rates from 2010/2011 to 2013/14 6 • Recommendations 7 From the literature: • Netherlands-specific age stratified contact (WAIFW) matrix 8 • Transmission model parameter estimates 9,10 • Live attenuated and inactivated vaccine efficacy estimates 11 1.2. Demographics The model used a realistic age structure, stratified by age in months. The original model population used Dutch population data 1 by single year of age for 2010, separated into monthly age bands by fitting a cubic spline to the cumulative population size by age. Aging was simulated on a monthly basis, with an upper age limit in the model of 100 years. Net immigration into the Dutch population was not modelled. A birth rate of 15,366.4 live births per month was used, calculated as the average monthly birth rate over 2010 2. A background mortality was applied by converting annual lifetable surviving proportions 3 by year of age to a daily (1/365) mortality probability using: 푃(푑푒)푑푎푦 = 1 − 푃(푠푢푟푣푣푒)푦푒푎푟 . As these values were very small the daily probabilities for each year of age were used as daily rates in the transmission model. 2 1.3. R0 The basic reproductive number (R0) is defined as the number of secondary infections arising from one average 12,13 primary infection in a totally susceptible population . Using data from past pandemics, R0 for influenza has been estimated to range from 1.6 to 3.9 10. 1.4. Transmission model compartmental structure and equations SEIRRS(V) structure Each age band in the model was divided into compartments based on the natural history of infection and immunity status. For each virus the possible immunity statuses were: susceptible, exposed and latently infected, infectious, recovered (with initial immunity or with long-term immunity), and vaccinated (Table S1.1). Table S1.1: Abbreviations for compartment status with respect to a single influenza strain. Status Abbreviation Susceptible S Exposed (latently infected) E Infectious I Recovered (first immunity stage) RF Recovered (long-term immunity) RL Vaccinated V For a given influenza strain patients began as susceptible, moved to the exposed class upon infection and then the infectious class, before recovering with immunity that gradually waned until they were susceptible again. A proportion p of those who first gained naturally-acquired immunity to the strain would go on to develop long-term immunity, for which the duration was much longer than the first immunity stage. The other 1-p proportion of those leaving the first immunity stage lost their immunity altogether and returned to the susceptible class. Alternatively susceptible individuals could be vaccinated, for which the immunity also waned until they were again susceptible. The structure is therefore called SEIRRS(V) for brevity. A diagram of the model structure for a single virus is presented in Figure S1.1. The subscript ‘F’ denotes the first recovered class and the subscript ‘L’ describes the recovered class for individuals who develop long-term immunity. The flow parameters are explained in Table S1.2. 3 δ L (1-p) δF pδF λ γ r S E I RF RL μ μ μ μ μ V μ Figure S1.1: Conceptual transmission model structure for a single virus. This diagram does not represent the full model, in which two influenza strains were modelled simultaneously. Flow parameters are explained in Table S1.2. Table S1.2: Transmission model flow parameters Parameter Description λ Force of infection on susceptible individual (Equation 2) γ Rate of acquiring infectiousness given exposure (infection): reciprocal of average latent period r Rate of recovery: reciprocal of average infectious period δF Rate of waning of the First stage of naturally-acquired immunity δL Rate of waning of the Long-term naturally-acquired immunity p Probability of developing long-term natural immunity μ Mortality rate (natural) In the transmission model two influenza strains were modelled simultaneously. Figure S1.1 is not the full model structure: it is meant only as a conceptual diagram of the stages for a single virus, with the other virus held constant. Two-strain model Influenza A and influenza B were simulated independently. Within an influenza type two strains were assumed to be modelled: a strain from each of the A (H1N1) and A (H3N2) subtypes for influenza A, and a strain from each of the B (Victoria) and B (Yamagata) lineages for influenza B. Both strains were modelled simultaneously so the model compartmental structure combined the SEIRRS(V) structure of each. The combined SEIRRS(V) structure, except for vaccination, is shown in Figure S1.2. Model flows due to mortality are also left out of the diagram for simplicity. Of the two non-subscript letters in the compartment names, the left letter represents the status with respect to the first virus as in Table S1.1, and the right letter with respect to the second. 4 It can be seen that each horizontal (or vertical) line of compartments in the model corresponds to movement in the first (or second) virus only, as in Figure S1.1, with individuals maintaining the same immunity status for the second (or first) virus. Compartments in which individuals are exposed or infectious with either virus are shaded to highlight the fact that the only flows out of these compartments are due to a change of status in the infected virus; patients cannot also change their status with respect to the other virus while in these compartments, i.e., they cannot be infected with both viruses at once. Action in first virus Action in second virus SS ES IS RFS RLS SE RFE RLE SI RFI RLI SRF ERF IRF RFRF RLRF SRL ERL IRL RFRL RLRL 1-p p 5 Figure S1.2: Combined two-strain model structure, neglecting vaccinated classes. Model flow parameters and details of model flows due to mortality are left out for simplicity as they are detailed in Figure S1.1. Note that movement along a horizontal or vertical axis only equates to the single-virus compartment structure of Figure S1.1. The combined SEIRRS(V) structure, including vaccination, is shown in Figure S1.3. Model flows due to mortality are left out of the diagram for simplicity, as are the flows between unvaccinated compartments which were detailed in Figure S1.2. Overall there were 32 states in the model structure. Action in first virus Action in second virus * VV SV EV IV RFV RLV VS SS ES IS RFS RLS VE SE RFE RLE VI SI RFI RLI VRF SRF ERF IRF RFRF RLRF VRL SRL ERL IRL RFRL RLRL 1-p p Figure S1.3: Combined model structure including vaccination. Details of model flows between compartments with no vaccinated individuals are left out for simplicity as they are detailed in Figure S1.2. Model equations The model equations are an adaptation of a previously-published model to allow for two virus strains circulating simultaneously. Additionally, these equations were updated to stratify age by month of age, not year. 6 The flows of individuals between compartments are described by the following set (Equation 1) of linked differential equations for m = 0, 1, 2, … , 1199 months of age. The choice of compartment naming based on two letters, while it conceptually streamlines the flow diagram (Figure S1.3), becomes somewhat cumbersome for the differential equations (Equation 1) as it appears there are compartment populations being multiplied. With the exception of the transmission terms, in which the λi factor is dependent on the population infectious with strain i, there is no such multiplication. Each term in square brackets (‘[ ]’) is a single compartment population. 7 (1) The coefficients of the flow terms in the equations in Equation 1 are described in Table S1.2. 1/γ is the duration of the latent period and 1/휌 is the duration of the infectious period. μ is the natural death rate, applied by month of age 8 but constant for all individuals of the same year of age. The subscript i represents the virus to which the parameter refers. Vaccination was modelled continuously as part of the differential equations for the system. The vaccination campaign was assumed to start on in mid-October (day 288) and last between 30 to 40 days. By the end of the vaccination campaign, a proportion of the susceptible population equal to the effective vaccine coverage for that strain in that age group (product of uptake and efficacy) was transferred to the vaccinated category. (These individuals did not necessarily remain in the vaccinated category, due to mortality and other model flows.) When individuals were vaccinated to two strains at once, with strain-specific efficacies it was necessary but non-trivial to determine the shared rate of vaccination.
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