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

Journal of Theoretical Biology
Ping Yan

Abstract

Two approximations are commonly used to describe the spread of an infectious disease at its early phase: (i) the branching processes based on the generation concept and (ii) the exponential growth over calendar time. The former is characterized by a mean parameter: the reproduction number R(0). The latter is characterized by a growth rate rho, also known as the Malthusian number. It is common to use empirically observed rho to assess R(0) using formulae derived either when both the latent and infectious periods follow exponential distributions or assuming both are fixed non-random quantities. This paper first points out that most of these formulae are special cases when the latent and infectious periods are gamma distributed, given by a closed-form solution in Anderson and Watson [1980. On the spread of a disease with gamma distributed latent and infectious periods. Biometrika 67 (1), 191-198]. A more general result will be then established which takes the result in Anderson and Watson [1980. On the spread of a disease with gamma distributed latent and infectious periods. Biometrika 67 (1), 191-198] as its special case. Three aspects separately shape the relationship between rho and R(0). They are: (i) the intensity of infectio...Continue Reading

Citations

Aug 30, 2014·Mathematical Biosciences·Sorana Froda, Hugues Leduc
Aug 19, 2010·Influenza and Other Respiratory Viruses·Dena L SchanzerTheresa W S Tam
Dec 22, 2009·Influenza and Other Respiratory Viruses·Shenghai ZhangJun Wang
Mar 13, 2014·Journal of Theoretical Biology·Carlos LlensaJoan Saldaña
Jun 24, 2020·Journal of the Royal Society, Interface·Sang Woo ParkJonathan Dushoff
Aug 15, 2021·Journal of Theoretical Biology·Shi ZhaoMaggie H Wang
Nov 23, 2021·Journal of Biological Dynamics·Milan Batista

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