# American Institute of Mathematical Sciences

2007, 4(3): 457-470. doi: 10.3934/mbe.2007.4.457

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

 1 Center for Nonlinear Studies (MS B284), Los Alamos National Laboratory, Los Alamos, NM 87545, United States 2 Institute of Social and Preventive Medicine, Faculty of Medicine, CMU, PoBox 1211, Geneva 4, Switzerland 3 Discrete Simulation Sciences (CCS-5), Los Alamos National Laboratory, Los Alamos, NM 87545, United States

Received  November 2006 Revised  February 2007 Published  May 2007

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.
Citation: Gerardo Chowell, Catherine E. Ammon, Nicolas W. Hengartner, James M. Hyman. Estimating the reproduction number from the initial phase of the Spanish flu pandemic waves in Geneva, Switzerland. Mathematical Biosciences & Engineering, 2007, 4 (3) : 457-470. doi: 10.3934/mbe.2007.4.457
 [1] Eunha Shim. Prioritization of delayed vaccination for pandemic influenza. Mathematical Biosciences & Engineering, 2011, 8 (1) : 95-112. doi: 10.3934/mbe.2011.8.95 [2] Julien Arino, Chris Bauch, Fred Brauer, S. Michelle Driedger, Amy L. Greer, S.M. Moghadas, Nick J. Pizzi, Beate Sander, Ashleigh Tuite, P. van den Driessche, James Watmough, Jianhong Wu, Ping Yan. Pandemic influenza: Modelling and public health perspectives. Mathematical Biosciences & Engineering, 2011, 8 (1) : 1-20. doi: 10.3934/mbe.2011.8.1 [3] Andrew J. Majda, Michal Branicki. Lessons in uncertainty quantification for turbulent dynamical systems. Discrete & Continuous Dynamical Systems, 2012, 32 (9) : 3133-3221. doi: 10.3934/dcds.2012.32.3133 [4] Jing Li, Panos Stinis. Mori-Zwanzig reduced models for uncertainty quantification. Journal of Computational Dynamics, 2019, 6 (1) : 39-68. doi: 10.3934/jcd.2019002 [5] H. T. Banks, Robert Baraldi, Karissa Cross, Kevin Flores, Christina McChesney, Laura Poag, Emma Thorpe. Uncertainty quantification in modeling HIV viral mechanics. Mathematical Biosciences & Engineering, 2015, 12 (5) : 937-964. doi: 10.3934/mbe.2015.12.937 [6] Alex Capaldi, Samuel Behrend, Benjamin Berman, Jason Smith, Justin Wright, Alun L. Lloyd. Parameter estimation and uncertainty quantification for an epidemic model. Mathematical Biosciences & Engineering, 2012, 9 (3) : 553-576. doi: 10.3934/mbe.2012.9.553 [7] Ryan Bennink, Ajay Jasra, Kody J. H. Law, Pavel Lougovski. Estimation and uncertainty quantification for the output from quantum simulators. Foundations of Data Science, 2019, 1 (2) : 157-176. doi: 10.3934/fods.2019007 [8] Hiroshi Nishiura. Joint quantification of transmission dynamics and diagnostic accuracy applied to influenza. Mathematical Biosciences & Engineering, 2011, 8 (1) : 49-64. doi: 10.3934/mbe.2011.8.49 [9] Qingling Zeng, Kamran Khan, Jianhong Wu, Huaiping Zhu. The utility of preemptive mass influenza vaccination in controlling a SARS outbreak during flu season. Mathematical Biosciences & Engineering, 2007, 4 (4) : 739-754. doi: 10.3934/mbe.2007.4.739 [10] Rodolfo Acuňa-Soto, Luis Castaňeda-Davila, Gerardo Chowell. A perspective on the 2009 A/H1N1 influenza pandemic in Mexico. Mathematical Biosciences & Engineering, 2011, 8 (1) : 223-238. doi: 10.3934/mbe.2011.8.223 [11] Diána H. Knipl, Gergely Röst. Modelling the strategies for age specific vaccination scheduling during influenza pandemic outbreaks. Mathematical Biosciences & Engineering, 2011, 8 (1) : 123-139. doi: 10.3934/mbe.2011.8.123 [12] Tom Burr, Gerardo Chowell. The reproduction number $R_t$ in structured and nonstructured populations. Mathematical Biosciences & Engineering, 2009, 6 (2) : 239-259. doi: 10.3934/mbe.2009.6.239 [13] Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 37-56. doi: 10.3934/dcdsb.2013.18.37 [14] Raimund Bürger, Gerardo Chowell, Pep Mulet, Luis M. Villada. Modelling the spatial-temporal progression of the 2009 A/H1N1 influenza pandemic in Chile. Mathematical Biosciences & Engineering, 2016, 13 (1) : 43-65. doi: 10.3934/mbe.2016.13.43 [15] Olivia Prosper, Omar Saucedo, Doria Thompson, Griselle Torres-Garcia, Xiaohong Wang, Carlos Castillo-Chavez. Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza. Mathematical Biosciences & Engineering, 2011, 8 (1) : 141-170. doi: 10.3934/mbe.2011.8.141 [16] Sherry Towers, Katia Vogt Geisse, Chia-Chun Tsai, Qing Han, Zhilan Feng. The impact of school closures on pandemic influenza: Assessing potential repercussions using a seasonal SIR model. Mathematical Biosciences & Engineering, 2012, 9 (2) : 413-430. doi: 10.3934/mbe.2012.9.413 [17] José Miguel Pasini, Tuhin Sahai. Polynomial chaos based uncertainty quantification in Hamiltonian, multi-time scale, and chaotic systems. Journal of Computational Dynamics, 2014, 1 (2) : 357-375. doi: 10.3934/jcd.2014.1.357 [18] Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595 [19] Ling Xue, Caterina Scoglio. Network-level reproduction number and extinction threshold for vector-borne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565-584. doi: 10.3934/mbe.2015.12.565 [20] Nitu Kumari, Sumit Kumar, Sandeep Sharma, Fateh Singh, Rana Parshad. Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021170

2018 Impact Factor: 1.313