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On the basic reproduction number of general branching processes
Acta Mathematica Scientia, 2009Abstract Under a very general condition (TNC condition) we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching ...
Ma Zhiming, Sun Suyong, Lan Guo-lie
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Basic reproduction number of epidemic models on sparse networks
Physical Review E, 2022The basic reproduction number R_{0} is a standard indicator of infection control in epidemiology. Although R_{0} has been studied extensively for deterministic epidemic models, it has not been formulated accurately for models adopting network structures.
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Basic Reproduction Number $$R_0$$
2017The basic reproduction number \(R_0\) plays a central role in structured population dynamics. Although some roots of \(R_0\) can be traced back to the nineteenth century, the specific concept was introduced to the demography literature in 1925. It took a further half century for this number to mature as a key concept in mathematical epidemiology, and ...
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The estimation of the basic reproduction number for infectious diseases
Statistical Methods in Medical Research, 1993The basic reproduction number Ro is the number of secondary cases which one case would produce in a completely susceptible population. It depends on the duration of the infectious period, the probability of infecting a susceptible individual during one contact, and the number of new susceptible individuals contacted per unit of time.
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The basic reproduction number (R 0 ) of measles: a systematic review
The Lancet Infectious Diseases, 2017The basic reproduction number, R nought (R0), is defined as the average number of secondary cases of an infectious disease arising from a typical case in a totally susceptible population, and can be estimated in populations if pre-existing immunity can be accounted for in the calculation.
Ye Li +6 more
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On a new perspective of the basic reproduction number in heterogeneous environments
Journal of Mathematical Biology, 2011Although its usefulness and possibility of the well-known definition of the basic reproduction number R0 for structured populations by Diekmann, Heesterbeek and Metz (J Math Biol 28:365-382, 1990) (the DHM definition) have been widely recognized mainly in the context of epidemic models, originally it deals with population dynamics in a constant ...
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The basic reproduction number $$R_0$$ in time-heterogeneous environments
Journal of Mathematical Biology, 2019In the previous paper (Inaba in J Math Biol 65:309-348, 2012), we proposed a new (most biologically natural) definition of the basic reproduction number R 0 for structured population in general time-heterogeneous environments based on the generation evolution operator. Using the mathematical definition for cone spectral radius, we show that our R
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