Seasonal influenza in the United States, France, and Australia: transmission and prospects for control

Abstract

Recurrent epidemics of influenza are observed seasonally around the world with considerable health and economic consequences. A key quantity for the control of infectious diseases is the reproduction number, which measures the transmissibility of a pathogen and determines the magnitude of public health interventions necessary to control epidemics. Here we applied a simple epidemic model to weekly indicators of influenza mortality to estimate the reproduction numbers of seasonal influenza epidemics spanning three decades in the United States, France, and Australia. We found similar distributions of reproduction number estimates in the three countries, with mean value 1.3 and important year-to-year variability (range 0.9-2.1). Estimates derived from two different mortality indicators (pneumonia and influenza excess deaths and influenza-specific deaths) were in close agreement for the United States (correlation=0.61, P60%) in healthy individuals who respond well to vaccine, in addition to periodic re-vaccination due to evolving viral antigens and waning population immunity.

Fig. 1

Time-series of weekly number of pneumonia and influenza (P&I) and influenza-specific deaths per 100 000 in three countries (France, United States and Australia, blue curve). The red dashed line indicates the baseline mirroring the expected level of P&I mortality in the absence of influenza epidemic activity.

Fig. 2

Compartmental model indicating the transition of individuals among the different epidemiological stages during an influenza outbreak. β=transmission rate; N=total population; 1/κ=latent period; 1/γ=recovery period; δ=mortality rate (see Table for parameter values).

Fig. 3

Boxplots of the reproduction number (R_p) of influenza seasons (1972–1997) in the United States, France, and Australia. The boxes have lines at 25, 50 and 75 percentiles. The whiskers show the extent of the rest of the data extending to a maximum of 1·5 times the interquartile range. Points outside the ends of the whiskers are indicated with a ‘+’ symbol.

Fig. 4

Model fits to the epidemic rise of a number of representative influenza seasons in (a) the United States, (b) France, and (c) Australia. The data are the circles and the solid lines are 200 realizations of the model fitted to the data obtained through the parametric bootstrap as explained in the text.

Fig. 5

Correlation of the reproduction number estimates derived from pneumonia and influenza excess mortality and influenza-specific mortality data in three countries (a) United States, (b) France and (c) Australia. While a significant and positive correlation was observed for the United States and France, a weaker correlation was found in Australia, probably due to the few overlapping seasons for which it was possible to estimate the reproduction number (n=6) and the larger demographic noise and spatial heterogeneity.

Fig. 6

Sensitivity analysis: boxplots of the reproduction number (R_p) as a function of the number of epidemic weeks used in the estimation, for the United States, France and Australia. Our estimates of R_p are robust to increasing the number of epidemic weeks used in the estimation to 5 or 6 epidemic weeks, given a sufficient time period of epidemic take-off (Wilcoxon test for differences in mean R_p between 4 and 6 wks: P>0·66, United States; P>0·34, France; P>0·25, Australia).

Fig. 7

Probability of interrupting transmission of seasonal influenza for various vaccination scenarios. Values are based on the empirical cumulative distribution of reproduction number estimates in the three countries (y axis) and different vaccine coverage in the healthy population aged 2–64 years (x axis), who is supposed to respond well to influenza vaccines (see online Supplement for methods). Different curves represent different assumptions about vaccine efficacy in the healthy population.