Real-time epidemic forecasting for pandemic influenza

Abstract

The ongoing worldwide spread of the H5N1 influenza virus in birds has increased concerns of a new human influenza pandemic and a number of surveillance initiatives are planned, or are in place, to monitor the impact of a pandemic in near real-time. Using epidemiological data collected during the early stages of an outbreak, we show how the timing of the maximum prevalence of the pandemic wave, along with its amplitude and duration, might be predicted by fitting a mass-action epidemic model to the surveillance data by standard regression analysis. This method is validated by applying the model to routine data collected in the United Kingdom during the different waves of the previous three pandemics. The success of the method in forecasting historical prevalence suggests that such outbreaks conform reasonably well to the theoretical model, a factor which may be exploited in a future pandemic to update ongoing planning and response.

Fig. 1

Figure showing R_E/ρ from the model as more data is incorporated. The x-axis shows the distance from the week of maximum prevalence. Solid black line: 1968–1969 first wave; dashed black line: 1968–1969 second wave; dotted black line: main wave 1957; solid grey line: 1918–1919 first wave; dashed grey line: 1918–1919 second wave; dotted grey line: 1918–1919 third wave.

Fig. 2

Figures showing the first wave of the 1968–1969 influenza pandemic with modelled week on week projections arising from fitting procedure. Solid diamonds: known incidence; open diamonds: future prevalence rates (currently unknown); solid curve: the optimal bounded MLE fit; dashed lines: 95% credible intervals on epidemic curve trajectories; dotted line: best formal MLE fit (in panels where no dotted curve appears it is coincident with the solid curve). Week 0 corresponds to the week ending 3 January 1969.

Fig. 3

Figures showing the second wave of the 1968–1969 influenza pandemic with modelled projections (lines and symbols as in Fig. 2). Week 0 corresponds to the week ending 21 November 1969.

Fig. 4

Figure showing the first wave of the 1918–1919 influenza pandemic with modelled projections (lines and symbols as in Fig. 2). Week 0 corresponds to the week ending 25 June 1918.

Fig. 5

Figure showing the second wave of the 1918–1919 influenza pandemic with modelled projections (lines and symbols as in Fig. 2). Week 0 corresponds to the week ending 14 September 1918.

Fig. 6

Figure showing the third wave of the 1918–1919 influenza pandemic with modelled projections (lines and symbols as in Fig. 2). Week 0 corresponds to the week ending 25 January 1919.

Fig. 7

Figure showing major wave of 1957–1958 influenza pandemic with modelled projections (lines and symbols as in Fig. 2). Week 0 corresponds to the week ending 31 August 1957.