Primary: 00A71, 37N25; Secondary: 92C60, 92D30.

Export file:

Format

• RIS(for EndNote,Reference Manager,ProCite)
• BibTex
• Text

Content

• Citation Only
• Citation and Abstract

Time variations in the generation time of an infectious disease: Implications for sampling to appropriately quantify transmission potential

1. PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama 332-0012

## Abstract    Related pages

Although the generation time of an infectious disease plays a key role in estimating its transmission potential, the impact of the sampling time of generation times on the estimation procedure has yet to be clarified. The present study defines the period and cohort generation times, both of which are time-inhomogeneous, as a function of the infection time of secondary and primary cases, respectively. By means of analytical and numerical approaches, it is shown that the period generation time increases with calendar time, whereas the cohort generation time decreases as the incidence increases. The initial growth phase of an epidemic of Asian influenza A (H2N2) in the Netherlands in 1957 was reanalyzed, and estimates of the basic reproduction number, $R_0$, from the Lotka-Euler equation were examined. It was found that the sampling time of generation time during the course of the epidemic introduced a time-effect to the estimate of $R_0$. Other historical data of a primary pneumonic plague in Manchuria in 1911 were also examined to help illustrate the empirical evidence of the period generation time. If the serial intervals, which eventually determine the generation times, are sampled during the course of an epidemic, direct application of the sampled generation-time distribution to the Lotka-Euler equation leads to a biased estimate of $R_0$. An appropriate quantification of the transmission potential requires the estimation of the cohort generation time during the initial growth phase of an epidemic or adjustment of the time-effect (e.g., adjustment of the growth rate of the epidemic during the sampling time) on the period generation time. A similar issue also applies to the estimation of the effective reproduction number as a function of calendar time. Mathematical properties of the generation time distribution in a heterogeneously mixing population need to be clarified further.
Figure/Table
Supplementary
Article Metrics

Citation: Hiroshi Nishiura. Time variations in the generation time of an infectious disease: Implications for sampling to appropriately quantify transmission potential. Mathematical Biosciences and Engineering, 2010, 7(4): 851-869. doi: 10.3934/mbe.2010.7.851

• 1. Marek Laskowski, Amy L. Greer, Seyed M. Moghadas, Alessandro Vespignani, Antiviral Strategies for Emerging Influenza Viruses in Remote Communities, PLoS ONE, 2014, 9, 2, e89651, 10.1371/journal.pone.0089651
• 2. Hiroshi Nishiura, Gerardo Chowell, Carlos Castillo-Chavez, Alessandro Vespignani, Did Modeling Overestimate the Transmission Potential of Pandemic (H1N1-2009)? Sample Size Estimation for Post-Epidemic Seroepidemiological Studies, PLoS ONE, 2011, 6, 3, e17908, 10.1371/journal.pone.0017908
• 3. Keisuke Ejima, Kazuyuki Aihara, Hiroshi Nishiura, Probabilistic differential diagnosis of Middle East respiratory syndrome (MERS) using the time from immigration to illness onset among imported cases, Journal of Theoretical Biology, 2014, 346, 47, 10.1016/j.jtbi.2013.12.024
• 4. Hiroshi Nishiura, Akira Endo, Masaya Saitoh, Ryo Kinoshita, Ryo Ueno, Shinji Nakaoka, Yuichiro Miyamatsu, Yueping Dong, Gerardo Chowell, Kenji Mizumoto, Identifying determinants of heterogeneous transmission dynamics of the Middle East respiratory syndrome (MERS) outbreak in the Republic of Korea, 2015: a retrospective epidemiological analysis, BMJ Open, 2016, 6, 2, e009936, 10.1136/bmjopen-2015-009936
• 5. Michael George Roberts, Hiroshi Nishiura, Maciej F. Boni, Early Estimation of the Reproduction Number in the Presence of Imported Cases: Pandemic Influenza H1N1-2009 in New Zealand, PLoS ONE, 2011, 6, 5, e17835, 10.1371/journal.pone.0017835
• 6. Claudia T. Codeço, Daniel A.M. Villela, Flavio C. Coelho, Estimating the effective reproduction number of dengue considering temperature-dependent generation intervals, Epidemics, 2018, 10.1016/j.epidem.2018.05.011
• 7. Henrik Salje, Derek A.T. Cummings, Justin Lessler, Estimating infectious disease transmission distances using the overall distribution of cases, Epidemics, 2016, 17, 10, 10.1016/j.epidem.2016.10.001
• 8. Sebastian Funk, Adam J. Kucharski, Anton Camacho, Rosalind M. Eggo, Laith Yakob, Lawrence M. Murray, W. John Edmunds, Michael A Johansson, Comparative Analysis of Dengue and Zika Outbreaks Reveals Differences by Setting and Virus, PLOS Neglected Tropical Diseases, 2016, 10, 12, e0005173, 10.1371/journal.pntd.0005173
• 9. N. Hens, L. Calatayud, S. Kurkela, T. Tamme, J. Wallinga, Robust Reconstruction and Analysis of Outbreak Data: Influenza A(H1N1)v Transmission in a School-based Population, American Journal of Epidemiology, 2012, 176, 3, 196, 10.1093/aje/kws006
• 10. Matthew Biggerstaff, Simon Cauchemez, Carrie Reed, Manoj Gambhir, Lyn Finelli, Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature, BMC Infectious Diseases, 2014, 14, 1, 10.1186/1471-2334-14-480
• 11. Bradford P. Taylor, Jonathan Dushoff, Joshua S. Weitz, Stochasticity and the limits to confidence when estimating R0 of Ebola and other emerging infectious diseases, Journal of Theoretical Biology, 2016, 408, 145, 10.1016/j.jtbi.2016.08.016
• 12. Hiroshi Nishiura, Ping Yan, Candace K. Sleeman, Charles J. Mode, Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks, Journal of Theoretical Biology, 2012, 294, 48, 10.1016/j.jtbi.2011.10.039
• 13. Íde Cremin, Oliver Watson, Alastair Heffernan, Natsuko Imai, Norin Ahmed, Sandra Bivegete, Teresia Kimani, Demetris Kyriacou, Preveina Mahadevan, Rima Mustafa, Panagiota Pagoni, Marisa Sophiea, Charlie Whittaker, Leo Beacroft, Steven Riley, Matthew C. Fisher, An infectious way to teach students about outbreaks, Epidemics, 2018, 23, 42, 10.1016/j.epidem.2017.12.002
• 14. Hiroshi Nishiura, Gerardo Chowell, Theoretical perspectives on the infectiousness of Ebola virus disease, Theoretical Biology and Medical Modelling, 2015, 12, 1, 10.1186/1742-4682-12-1
• 15. David Champredon, Jonathan Dushoff, Intrinsic and realized generation intervals in infectious-disease transmission, Proceedings of the Royal Society B: Biological Sciences, 2015, 282, 1821, 20152026, 10.1098/rspb.2015.2026
• 16. Nicholas H. Ogden, Milka Radojevic´, Xiaotian Wu, Venkata R. Duvvuri, Patrick A. Leighton, Jianhong Wu,  Estimated Effects of Projected Climate Change on the Basic Reproductive Number of the Lyme Disease Vector Ixodes scapularis , Environmental Health Perspectives, 2014, 122, 6, 631, 10.1289/ehp.1307799
• 17. Sang Woo Park, David Champredon, Joshua S. Weitz, Jonathan Dushoff, A practical generation-interval-based approach to inferring the strength of epidemics from their speed, Epidemics, 2019, 10.1016/j.epidem.2018.12.002
• 18. Ryosuke Omori, Hiroshi Nishiura, Theoretical basis to measure the impact of short-lasting control of an infectious disease on the epidemic peak, Theoretical Biology and Medical Modelling, 2011, 8, 1, 10.1186/1742-4682-8-2
• 19. Hyojung Lee, Hiroshi Nishiura, Sexual transmission and the probability of an end of the Ebola virus disease epidemic, Journal of Theoretical Biology, 2019, 10.1016/j.jtbi.2019.03.022
• 20. Giorgio Guzzetta, Household transmission and disease transmissibility of a large HAV outbreak in Lazio, Italy, 2016–2017, Epidemics, 2019, 100351, 10.1016/j.epidem.2019.100351
• 21. Baoyin Yuan, Hyojung Lee, Hiroshi Nishiura, Robert C Reiner, Assessing dengue control in Tokyo, 2014, PLOS Neglected Tropical Diseases, 2019, 13, 6, e0007468, 10.1371/journal.pntd.0007468
• 22. Ping Yan, Gerardo Chowell, , Quantitative Methods for Investigating Infectious Disease Outbreaks, 2019, Chapter 7, 217, 10.1007/978-3-030-21923-9_7
• 23. George Livadiotis, Oscar Millet, Statistical analysis of the impact of environmental temperature on the exponential growth rate of cases infected by COVID-19, PLOS ONE, 2020, 15, 5, e0233875, 10.1371/journal.pone.0233875
• 24. Sang Woo Park, David Champredon, Jonathan Dushoff, Inferring generation-interval distributions from contact-tracing data, Journal of The Royal Society Interface, 2020, 17, 167, 20190719, 10.1098/rsif.2019.0719
• 25. ChristopherE. Overton, HelenaB. Stage, Shazaad Ahmad, Jacob Curran-Sebastian, Paul Dark, Rajenki Das, Elizabeth Fearon, Timothy Felton, Martyn Fyles, Nick Gent, Ian Hall, Thomas House, Hugo Lewkowicz, Xiaoxi Pang, Lorenzo Pellis, Robert Sawko, Andrew Ustianowski, Bindu Vekaria, Luke Webb, Using statistics and mathematical modelling to understand infectious disease outbreaks: COVID-19 as an example, Infectious Disease Modelling, 2020, 10.1016/j.idm.2020.06.008
• 26. Yuhao Deng, Chong You, Yukun Liu, Jing Qin, Xiao‐Hua Zhou, Estimation of incubation period and generation time based on observed length‐biased epidemic cohort with censoring for COVID‐19 outbreak in China, Biometrics, 2020, 10.1111/biom.13325