Why was the 2009 influenza pandemic in England so small?

Abstract

The "Swine flu" pandemic of 2009 caused world-wide infections and deaths. Early efforts to understand its rate of spread were used to predict the probable future number of cases, but by the end of 2009 it was clear that these predictions had substantially overestimated the pandemic's eventual impact. In England, the Health Protection Agency made announcements of the number of cases of disease, which turned out to be surprisingly low for an influenza pandemic. The agency also carried out a serological survey half-way through the English epidemic. In this study, we use a mathematical model to reconcile early estimates of the rate of spread of infection, weekly data on the number of cases in the 2009 epidemic in England and the serological status of the English population at the end of the first pandemic wave. Our results reveal that if there are around 19 infections (i.e., seroconverters) for every reported case then the three data-sets are entirely consistent with each other. We go on to discuss when in the epidemic such a high ratio of seroconverters to cases of disease might have been detected, either through patterns in the case reports or through even earlier serological surveys.

Figure 1. HPA case data and cumulative number of cases.

The bars show the number of estimated new cases per week. The cumulative number of cases per week is presented as black line on a separate axis. The plot is separated into three phases, I–III, divided by dashed lines in week 30 and 36 between which state schools in England were closed . Phase I is the initial growth phase before 22 July 2009, phase II is the school holiday phase until 3 September 2009, and at this date phase III with another growth and decline begins.

Figure 2. Comparison of serological data by age group.

The number of individuals in each age group is shown with large, grey bars. Red bars show the number of individuals immune before the pandemic. Blue bars represent numbers who seroconverted between April and September 2009. Green bars show the number immune by early September 2009. All numbers are calculated using serological data and demographic data from England (see Table S1).

Figure 3. Comparison of HPA case estimates with theoretical predictions of new cases.

The HPA case estimates per week are represented in a bar plot. The model in equation (1) was fitted to these data with state variable representing reported cases. The initial conditions were set at the observed value of of the population immune before week 22. Four different values of parameter were assumed corresponding to four different fits: - brown line, - green line, - blue line and - red line. The figure illustrates that gives the best agreement between model and data with the smallest least square error, and allows our model to reproduce the case estimates. The fitting procedure yields estimates for the model's three parameters, shown in Table 2. Only when do these parameter estimates agree with previously published values, compare Table 2 with Tables 1, 3 and 4.

Figure 4. When did growth data reveal that the English epidemic would be small?

A. shows that it was unlikely that the first wave would indicate that susceptible hosts were becoming exhausted. If there had been no school break we expect that the epidemic would have gone on growing for several weeks after week 30 when they actually shut. The red line shows predicted dynamics of the English epidemic if the schools had not closed (i.e. if and other parameters are the best fits for the model of equation (1)). B. This is confirmed in regression analyses of the natural logarithm of the cumulative number of cases. Data are filled circles, linear fit is the solid line and quadratic fit is the dashed line. Linear fit: ln(cumulative cases) . Quadratic fit: ln(cumulative cases) . The quadratic term is significant () but small and positive, signifying that, if anything, the epidemic was accelerating just before the schools broke up for summer. C. compares growth rates of the first wave (green dots) and second wave (blue dots). An analysis of covariance reveals that the two slopes are significantly different (). Linear fit for second wave: ln(cumulative cases) .