On the reproduction number in epidemics

References

• N.P. Jewell, Statistics for Epidemiology, Chapman & Hall/CRC, Boca Raton, 2004.
   Google Scholar
• M. Woodward, Epidemiology Study Design and Data Analysis, CRC Press, Boca Raton, 2014.
   Google Scholar
• J.A.P. Heesterbeek, A brief history of R0 and a recipe for its calculation. Acta Biotheor. 50 (2002), pp. 189–204.
   PubMed Web of Science ®Google Scholar
• J.M. Heffernan, R.J. Smith, and L.M. Wahl, Perspectives on the basic reproductive ratio. J. R Soc. Interface 2 (2005), pp. 281–293.
   PubMed Web of Science ®Google Scholar
• R. Breban, R. Vardavas, and S. Blower, Theory versus data: how to calculate R0? Plos One 2 (2007), pp. 1–4.
   Google Scholar
• L.M.A. Bettencourt, and R.M. Ribeiro, Real time Bayesian estimation of the epidemic potential of Emerging infectious diseases. Plos One 3 (2008), pp. 1–9.
   Google Scholar
• B. Ridenhour, J.M. Kowalik, and D.K. Shay, Unraveling R0: considerations for public health applications. Am. J. Public Health 108 (2018), pp. S445–S454.
   PubMed Web of Science ®Google Scholar
• P.L. Delamater, E.J. Street, T.F. Leslie, Y.T. Yang, and K.H. Jacobsen, Complexity of the basic reproduction number (R0). Emerg. Infect. Dis. 25 (2019), pp. 1–4.
   PubMed Web of Science ®Google Scholar
• N.C. Grassly, and C. Fraser, Mathematical models of infectious disease transmission. Nat. Rev. Microbiol. 6 (2008), pp. 477–487.
   PubMed Web of Science ®Google Scholar
• K. Dietz, Transmission and contol of arbovirus diseases, in Proceedings of SIMS Conference on Epidemiology Alta - Ut., July 8–12, 1974, D. Ludwig, K.L. Cooke, eds., Society for industrial and applied mathematics, Philadelphia, 1975. pp. 104–121.
   Google Scholar
• H.W. Hethcote, The mathematics of infectious diseases. SIAM Rev. 42 (2000), pp. 599–653.
   Web of Science ®Google Scholar
• O. Diekmann, J.A.P. Heesterbeek, and J.A.J. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious–diseases in heterogeneous populations. J. Math. Biol. 28 (1990), pp. 365–382.
   PubMed Web of Science ®Google Scholar
• K. Dietz, The estimation of the basic reproduction number for infectious diseases. Stat. Methods Med. Res. 2 (1993), pp. 23–41.
   PubMedGoogle Scholar
• J.A.P. Heesterbeek, and K. Dietz, The concept of R0 in epidemic theory. Stat. Neerl. 50 (1996), pp. 89–110.
   Google Scholar
• P. van den Driessche, and J. Watmough, Reproduction numbers and sub–threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002), pp. 29–48.
   PubMed Web of Science ®Google Scholar
• C.P. Farrington, M.N. Kanaan, and N.J. Gay, Estimation of the basic reproduction number for infectious diseases from age–stratified serological survey data. J R Stat Soc C–Appl 50 (2001), pp. 251–283.
   Web of Science ®Google Scholar
• M.G. Roberts, and J.A.P. Heesterbeek, Model–consistent estimation of the basic reproduction number from the incidence of an emerging infection. J. Math. Biol. 55 (2007), pp. 803–816.
   PubMed Web of Science ®Google Scholar
• H. Nishiura, Correcting the actual reproduction number: A simple method to estimate R0 from early epidemic growth data. Int J Env Res Pub He 7 (2010), pp. 291–302.
   PubMedGoogle Scholar
• J.L. Ma, Estimating epidemic exponential growth rate and basic reproduction number. Infect Dis Model 5 (2020), pp. 129–141.
   PubMedGoogle Scholar
• L. Pellis, F. Ball, and P. Trapman, Reproduction numbers for epidemic models with households and other social structures. I. definition and calculation of R0. Math. Biosci. 235 (2012), pp. 85–97.
   PubMedGoogle Scholar
• P. van den Driessche, Reproduction numbers of infectious disease models. Infect Dis Model 2 (2017), pp. 288–303.
   PubMedGoogle Scholar
• G. Chowell, and F. Brauer, The basic reproduction number of infectious diseases: Computation and estimation Using compartmental epidemic models, in Mathematical and Statistical Estimation Approaches in Epidemiology, G. Chowell, J.M. Hyman, L.M.A. Bettencourt, C. Castillo–Chavez, ed., Springer, Dordrecht, 2009. pp. 363.
   Google Scholar
• P. Yan, Separate roles of the latent and infectious periods in shaping the relation between the basic reproduction number and the intrinsic growth rate of infectious disease outbreaks. J. Theor. Biol. 251 (2008), pp. 238–252.
   PubMedGoogle Scholar
• R. Ke, E. Romero-Severson, S. Sanche, and N. Hengartner, Estimating the reproductive number R0 of SARS–CoV–2 in the United States and eight european countries and implications for vaccination. J. Theor. Biol. 517 (2021), pp. 1–10.
   Google Scholar
• J. Wallinga, and P. Teunis, Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures, (2004).
   Google Scholar
• C. Fraser, Estimating individual and household reproduction numbers in an emerging epidemic. Plos One 2 (2007), pp. 1–12.
   Web of Science ®Google Scholar
• L.F. White, and M. Pagano, A likelihood-based method for real-time estimation of the serial interval and reproductive number of an epidemic. Stat. Med. 27 (2008), pp. 2999–3016.
   PubMedGoogle Scholar
• G. Chowell, C. Viboud, L. Simonsen, and S.M. Moghadas, Characterizing the reproduction number of epidemics with early subexponential growth dynamics. J. R Soc. Interface 13 (2016), pp. 1–12.
   Google Scholar
• G. Chowell, and H. Nishiura, Quantifying the transmission potential of pandemic influenza. Phys. Life. Rev. 5 (2008), pp. 50–77.
   Google Scholar
• H. Nishiura, and G. Chowell, The effective reproduction number as a prelude to statistical estimation of time–dependent epidemic trends, in Mathematical and Statistical Estimation Approaches in Epidemiology, G. Chowell, J.M. Hyman, L.M.A. Bettencourt, C. Castillo–Chavez, ed., Springer, Dordrecht, 2009. pp. 103–122.
   Google Scholar
• J. Li, D. Blakeley, and R.J. Smith, The failure of R0. Comput Math Method M 2011 (2011), pp. 1–17.
   Google Scholar
• W.O. Kermack, and A.G. McKendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 115 (1927), pp. 700–721.
   Google Scholar
• A.G. McKendrick, Applications of mathematics to medical problems. Proceedings of the Edinburgh Mathematical Society 44 (1925), pp. 98–130.
   Google Scholar
• J. Wallinga, and M. Lipsitch, How generation intervals shape the relationship between growth rates and reproductive numbers. P Roy Soc B–Biol Sci 274 (2007), pp. 599–604.
   PubMed Web of Science ®Google Scholar
• T. Obadia, R. Haneef, and P.Y. Boelle, The R0 package: a toolbox to estimate reproduction numbers for epidemic outbreaks. BMC Med Inform Decis 12 (2012), pp. 1–9.
   PubMedGoogle Scholar
• A. Cori, N.M. Ferguson, C. Fraser, and S. Cauchemez, A new framework and software to estimate time–varying reproduction numbers during epidemics. Am. J. Epidemiol. 178 (2013), pp. 1505–1512.
   PubMed Web of Science ®Google Scholar
• R.N. Thompson, J.E. Stockwin, R.D. van Gaalen, J.A. Polonsky, Z.N. Kamvar, P.A. Demarsh, E. Dahlqwist, S. Li, E. Miguel, T. Jombart, J. Lessler, S. Cauchemez, and A. Cori, Improved inference of time–varying reproduction numbers during infectious disease outbreaks. Epidemics–Neth 29 (2019), pp. 1–11.
   Google Scholar
• F.Z. Brauer, and C. Castillo–Chávez, Discrete epidemic models. Math. Biosci. Eng. 7 (2010), pp. 1–15.
   PubMed Web of Science ®Google Scholar
• O. Diekmann, and J.A.P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases Model Building, Analysis and Interpretation, Wiley, Chichester, 2000.
   Google Scholar
• A. Svensson, A note on generation times in epidemic models. Math. Biosci. 208 (2007), pp. 300–311.
   PubMed Web of Science ®Google Scholar
• S.W. Park, D. Champredon, J.S. Weitz, and J. Dushoff, A practical generation–interval–based approach to inferring the strength of epidemics from their speed. Epidemics–Neth 27 (2019), pp. 12–18.
   PubMedGoogle Scholar
• H. Nishiura, N.M. Linton, and A.R. Akhmetzhanov, Serial interval of novel coronavirus (COVID–19) infections. Int. J. Infect. Dis. 93 (2020), pp. 284–286.
   PubMed Web of Science ®Google Scholar
• H. Nishiura, Time variations in the transmissibility of pandemic influenza in Prussia, Germany, from 1918–19. Theor. Biol. Med. Model. 4 (2007), pp. 1–9.
   PubMedGoogle Scholar