A simplified estimate of the effective reproduction number $$R_t$$ using its relation with the doubling time and application to Italian COVID-19 data
Gianluca Bonifazi, L. Lista, D. Menasce, M. Mezzetto, Д. Педрини, R. Spighi, A. Zoccoli
Abstract
Abstract A simplified method to compute $$R_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> , the effective reproduction number, is presented. The method relates the value of $$R_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> to the estimation of the doubling time performed with a local exponential fit. The condition $$R_t=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> corresponds to a growth rate equal to zero or equivalently an infinite doubling time. Different assumptions on the probability distribution of the generation time are considered. A simple analytical solution is presented in case the generation time follows a gamma distribution.