Estimating the reproduction number from the initial phase of the Spanish flu pandemic waves in Geneva, Switzerland

At the outset of an influenza pandemic, early estimates of the number of secondary cases generated by a primary influenza case (reproduction number, R) and its associated uncertainty can help determine the intensity of interventions necessary for control. Using a compartmental model and hospital notification data of the first two waves of the Spanish flu pandemic in Geneva, Switzerland in 1918, we estimate the reproduction number from the early phase of the pandemic waves. For the spring and fall pandemic waves, we estimate reproduction numbers of 1:57 (95% CI: 1:45, 1:70) and 3:10 (2:81, 3:39), respectively, from the initial epidemic phase comprising the first 10 epidemic days of the corresponding wave. Estimates of the variance of our point estimates of R were computed via a parametric bootstrap. We compare these estimates with others obtained using different observation windows to provide insight into how early into an epidemic the reproduction number can be estimated.

References:

• G. Chowell, H. Nishiura. Quantifying the transmission potential of pandemic influenza. Physics of Life Reviews, doi:10.1016/j.plrev.2007.12.001 (pdf)
• G. Chowell, L.M.A. Bettencourt, N. Johnson, W.J. Alonso, C. Viboud.The 1918-1919 influenza pandemic in England and Wales: Spatial patterns in transmissibility and mortality impact. Proc. Roy. Soc. B, doi:10.1098/rspb.2007.1477 (pdf)
• H. Nishiura and G. Chowell. Household and community transmission of the Asian influenza A (H2N2) and influenza B viruses in 1957 and 1961. Southeast Asian J. Trop. Med. Pub. Health. 38(6), 1075-1083 (2007) (pdf)
• G. Chowell, C. E. Ammon, N. W. Hengartner, J. M. Hyman. Estimating the reproduction number from the initial phase of the Spanish flu pandemic waves in Geneva, Switzerland. Math Biosci Eng. 2007 Jul;4(3):457-70.(pdf)
• M. Nuno, G. Chowell, A. Gumel. Assessing the role of basic control measures, antivirals and vaccine in curtailing pandemic infuenza: Scenarios for the US, UK, and the Netherlands. J R Soc Interface 2007 Jun 22;4(14):505-21. (pdf)
• G. Chowell, C. E. Ammon, N. W. Hengartner, J. M. Hyman. Estimation of the Reproductive number of the Spanish Flu Epidemic in Geneva, Switzerland. Proceedings of the Second European Influenza Conference (St-Julians, Malta, September, 2005). Vaccine 24, 6747-6750 (2006) (pdf)
• G. Chowell, C. E. Ammon, N. W. Hengartner, J. M. Hyman. Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: Assessing the effects of hypothetical interventions. J. Theor. Biol. 241(2), 193-204 (2006) (pdf)
• T.L. Burr, G. Chowell. Observation and model error effects on parameter estimates in susceptible-infected-recovered epidemic model. Far East J. Theor. Stat. 19(2), 163-183 (2006) (pdf)
• G. Chowell, H. Nishiura, L.M.A. Bettencourt. Comparative estimation of the reproduction number for pandemic influenza from daily case notification data. J R Soc Interface 4, 155-166 (2007) (pdf)
• A.B. Gumel, M. Nuno, G. Chowell. Mathematical assessment of Canada's pandemic influenza preparedness plan. Can. J. Inf. Dis. & Med. Microb. (in press).

Figure 1: Model fits (log-lin scale) and the resulting distributions of the reproduction number and the proportion of the clinical re- porting obtained after fitting the epidemic model to the initial phase of the spring wave using 10 and 15 epidemic days of the Spanish flu pandemic in Geneva, Switzerland. (top) The data are the dots, the solid line is the model best fit, and the lighter blue bands are 1000 realizations of the model fit to the data obtained through parametric bootstrapping as explained in the text. (mid- dle) The distribution of the reproduction number and (bottom) the distribution of the clinical reporting proportion obtained from the simulation study with 1000 realizations.

Figure 2. Scaled residual plots of the epidemic model best fit to the cumulative number of influenza notifications of the fall wave using 10, 15, 20, 25, 30, and 35 days of epidemic data. A moder- ate systematic deviation is observed around epidemic day 9. The residuals are scaled by the standard deviation of the distribution of residuals. These residuals are within +/-2 standard deviations (95% confidence level). wave as a result of a moderate system