First Consistent Determination of the Basic Reproduction Number for the First Covid-19 Wave in 71 Countries from the SIR-Epidemics Model with a Constant Ratio of Recovery to Infection Rate

Abstract

The box-shaped serial interval distribution and the analytical solution of the Susceptible Infectious-Recovered (SIR)-epidemics model with a constant time-independent ratio of the recovery (µ 0 ) to infection rate (a 0 ) are used to calculate the effective reproduction factor and the basic reproduction number R 0 . The latter depends on the positively valued net infection number x = 13.5(a 0 -µ 0 ) as R 0 (x) = x(1 -e -x ) -1 which for all values of x is greater unity. This dependence differs from the simple relation R 0 = a 0 /µ 0 . With the earlier determination of the values of k and a 0 of the Covid-19 pandemic waves in 71 countries the net infection rates and the basic reproduction numbers for these countries are calculated.