Time variations in the transmissibility of pandemic influenza in Prussia, Germany, from 1918-19 - PubMed (original) (raw)

Time variations in the transmissibility of pandemic influenza in Prussia, Germany, from 1918-19

Hiroshi Nishiura. Theor Biol Med Model. 2007.

Abstract

Background: Time variations in transmission potential have rarely been examined with regard to pandemic influenza. This paper reanalyzes the temporal distribution of pandemic influenza in Prussia, Germany, from 1918-19 using the daily numbers of deaths, which totaled 8911 from 29 September 1918 to 1 February 1919, and the distribution of the time delay from onset to death in order to estimate the effective reproduction number, Rt, defined as the actual average number of secondary cases per primary case at a given time.

Results: A discrete-time branching process was applied to back-calculated incidence data, assuming three different serial intervals (i.e. 1, 3 and 5 days). The estimated reproduction numbers exhibited a clear association between the estimates and choice of serial interval; i.e. the longer the assumed serial interval, the higher the reproduction number. Moreover, the estimated reproduction numbers did not decline monotonically with time, indicating that the patterns of secondary transmission varied with time. These tendencies are consistent with the differences in estimates of the reproduction number of pandemic influenza in recent studies; high estimates probably originate from a long serial interval and a model assumption about transmission rate that takes no account of time variation and is applied to the entire epidemic curve.

Conclusion: The present findings suggest that in order to offer robust assessments it is critically important to clarify in detail the natural history of a disease (e.g. including the serial interval) as well as heterogeneous patterns of transmission. In addition, given that human contact behavior probably influences transmissibility, individual countermeasures (e.g. household quarantine and mask-wearing) need to be explored to construct effective non-pharmaceutical interventions.

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Figures

Figure 1

Figure 1

Epidemic curve of pandemic influenza in Prussia, Germany, from 1918–19. Reported daily number of influenza deaths (solid line) and the back-calculated temporal distribution of onset cases (dashed line). Daily counts of onset cases were obtained using the time delay distribution from onset to death (see Table 1). Data source: ref [18] (see [Additional file 1]).

Figure 2

Figure 2

Distribution of the time delay from onset to death during the influenza epidemic in Prussia, Germany, from 1918–19. Time from disease onset (i.e. fever) to death is given for 6233 influenza deaths. A simple 5-day moving average was applied to the original data. Data source: ref [18] (see [Additional file 2]).

Figure 3

Figure 3

Epidemic curve and the corresponding effective reproduction numbers (R) with variable serial intervals. Time variation in the effective reproduction number (the number of secondary infections generated per case by generation) assuming three different serial intervals is shown. The serial interval was assumed to be 1 (second from the top), 3 (lower middle) and 5 days (bottom). Days are counted from September 9, 1918, onwards.

Figure 4

Figure 4

Comparison of the effective reproduction number assuming different serial intervals. Expected values of the effective reproduction number with a serial interval of 1 (grey), 3 (dashed black) and 5 days (solid black). The horizontal solid line represents the threshold value, R = 1, below which the epidemic will decline to extinction. Days are counted from September 9, 1918, onwards.

Figure 5

Figure 5

Simulated epidemic curve of pandemic influenza in Prussia, Germany, from 1918–19. Comparison of observed epidemic curves of onset (top) and death (bottom) with simulated curves. Expected values of influenza cases and deaths (solid line) mainly overlapped with the observed numbers (dot). Dashed lines indicate the corresponding upper and lower 95% confidence intervals (CI) based on 1000 simulation runs. The 95% CI of cases and deaths were determined by 2.5th and 97.5th percentiles of the simulated cases and deaths at each time point.

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