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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 ( ) to infection rate ( ) are used to calculate the effective reproduction factor and the basic reproduction number . The latter depends on the positively valued net infection number as which for all values of is greater unity. This dependence differs from the simple relation . With the earlier determination of the values of and of the Covid-19 pandemic waves in 71 countries the net infection rates and the basic reproduction numbers for these countries are calculated. μ0 a0 R0 x = 13.5(a0−μ0) R0(x) = x(1− e−x)−1 x R0= a0/μ0 k a0 factors R(t). Most frequently, for the serial interval distribution W(t) either, the gamma distribution with the mean value days, or the box-shaped distribution (3) with the two-sided Heaviside function Θ(x, A; B) = 1 for A ≤ x ≤ B and Θ(x) = 0 otherwise, are chosen. The box-shaped serial distribution (3) readily yields for the effective reproduction factor (1) that for any given number of daily new cases c(t). The calculated effective reproduction factors R(t) are then used to infer the basic reproduction number R0 which has been defined as the average number of secondary infections produced when one infected individual is introduced into a host population where everyone is susceptible. As such R0 = R(t0) is identical to the value of the effective reproduction factor R(t0) at the starting time of the outbreak. 2 If a specific mathematical model for the time evolution of the pandemic outbreak such as e.g. the SIR-model is used, this model should then obey the initial condition that one infected individual occurs at time t0. We are particularly interested in the relation of the SIRbasic reproduction number R0 with the ratio = of the initial recovery ( ) and infection ( ) rates entering the SIR-model rate equations. The inverse of this ratio is often referred to as the inverse microscopic SIRbasic reproduction number. However, the recent application of analytical approximations of the solution of the SIR-model to the monitored death and infection rates in many countries provided values of > 0.9 close to unity for the majority of countries investigated corresponding to microsciopic SIR-basic reproduction numbers R0 = 1/ < 1.11 only slightly greater than unity. These values are significantly smaller than the estimates of R0 ∈ [2.4, 5.6] in the mainstream literature on Covid-19 based on the monitored effective reproduction factors. It is the purpose of the present manuscript to resolve this discrepancy by calculating the relation between the SIR-basic reproduction number and the value of the ratio . It is shown that this relationship is different from the simple microscopic = 1 relationship. W (t) = b 2 s2e−bt, b = 4/9, (2) 〈t〉 = 3/b = 27/4 = 6.75 Wbox(t) = Θ(0, t, tb) tb , tb = 2 〈t〉 = 13.5, Rbox(t) = c(t)tb ∫ tb 0 ds c(t− s) = c(t)tb ∫ t t−tb dx c(x) (4)

global journal of science frontier research

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