Model-based reconstruction of an epidemic using multiple datasets: understanding influenza A/H1N1 pandemic dynamics in Israel

Abstract

Intensified surveillance during the 2009 A/H1N1 influenza pandemic in Israel resulted in large virological and serological datasets, presenting a unique opportunity for investigating the pandemic dynamics. We employ a conditional likelihood approach for fitting a disease transmission model to virological and serological data, conditional on clinical data. The model is used to reconstruct the temporal pattern of the pandemic in Israel in five age-groups and evaluate the factors that shaped it. We estimate the reproductive number at the beginning of the pandemic to beR= 1.4. We find that the combined effect of varying absolute humidity conditions and school vacations (SVs) is responsible for the infection pattern, characterized by three epidemic waves. Overall attack rate is estimated at 32% (28-35%) with a large variation among the age-groups: the highest attack rates within school children and the lowest within the elderly. This pattern of infection is explained by a combination of the age-group contact structure and increasing immunity with age. We assess that SVs increased the overall attack rates by prolonging the pandemic into the winter. Vaccinating school children would have been the optimal strategy for minimizing infection rates in all age-groups.

Keywords: absolute humidity; age structure; disease transmission model; school vacations; serology; vaccine allocation.

Figure 1.

(a) Weekly ILI incidence rates per 10 000 (solid line), average daily absolute humidity (dashed line), average daily temperature (dotted line) and vacation periods (vertical dotted lines) during the pandemic in Israel. (b) Results of the search term ‘flu’ (in Hebrew) using Google Trends between June 2009 and March 2010. Alphabet letters mark key events during the pandemic in Israel coinciding with peaks in the public interest in the flu. (A) WHO declares ‘swine flu’ a global pandemic (12 June 2009), (B) first cases of mortality from ‘swine flu’ in Israel (27 July 2009, 3 August 2009), Israeli Ministry of Health orders the acquisition of vaccinations for the entire Israeli population (30 July 2009), (C) beginning of national vaccination campaign for individuals belonging to risk groups (2 November 2009), (D) opening of vaccination campaign to the entire population (18 December 2009). (Online version in colour.)

Figure 2.

A diagram describing the components of the modelling scheme. Ovals represent model components. Rectangles represent data used by the model. Trapezoids represent model parameters that are estimated by the model fitting. Rounded rectangles represent model outputs. The transmission model output feeds into the observation model whose two types of output are compared with the available virological and serological data. (Online version in colour.)

Figure 3.

Observed (dots and bars) and estimated (curved lines) weekly rates of influenza-positive eILI cases (a–e) and weekly seroprevalence rates (f–j) in the five age-groups: 0–4 (a,f), 5–19 (b,g), 20–44 (c,h), 45–64 (d,i) and 65+ (e,j). The observed data are the results of the virological and serological tests (given in electronic supplementary material, tables S1 and S2). Binomial 95% CI for the observed data were calculated using the Clopper–Pearson method. The estimated curves were obtained from the model fit using equations (2.2) and (2.3b). (Online version in colour.)

Figure 4.

Results of the model fit (using equations (2.2) and (2.3b), see also table 3). (a) Weekly influenza incidence rate in the five age-groups. (b) Attack rate in the five age groups with bootstrapped 95% CI. (c) Relative susceptibility of individuals in the five age groups with bootstrapped 95% CI. (Online version in colour.)

Figure 5.

(a) The combined and separate effect of absolute humidity (AH) and school vacations (SV) on influenza incidence in the population as a whole. Using the parameter estimates obtained by the model fit incorporating both factors (equations (2.2) and (2.3b)), we project the dynamics of the pandemic without the effect of one or both factors by running the model while setting the relevant parameter(s) (κ and/or δ) to zero. The inset shows the overall attack rates in each of the scenarios. (b) The combined and separate effect of AH and SV on the reproductive number R in the four scenarios described in (a). (Online version in colour.)

Figure 6.

(a) Effect of timing of school vacations on the pandemic dynamics. Using the parameter estimates obtained by the model fit (equations (2.2) and (2.3b)), we project the dynamics of the pandemic if the timing of school vacations were shifted, so that summer vacation would start on 1 June, 1 July (actual), 1 August and so forth. The inset shows the overall attack rates in each of the scenarios. According to the model, postponing the epidemic to winter increased the overall epidemic size. (b) Effect of optimal vaccine allocation on the pandemic dynamics with hypothetical vaccination campaigns during September 2009, after the first wave of the pandemic in Israel. Using the parameter estimates obtained by the model fit (equations (2.2) and (2.3b)), we project the dynamics of the pandemic assuming overall vaccine coverage of 0–20% of the population. The inset shows the overall attack rates in each of the scenarios. According to the model, with a coverage of 15% using optimal allocation consisting of vaccinating almost only school children, the outbreak would have been mitigated (see electronic supplementary material, figure S14 for more details). (Online version in colour.)