Estimation of the basic reproduction number from the SIRD model
Let us first start with the estimation of R0. Initially, when the spread of the epidemic starts, all the population is considered to be susceptible, i.e. S ≈ N. Based on this assumption, by Eqs (2), (3) and (4), the basic reproduction number can be estimated by the parameters of the SIRD model as: R0=αβ+γ(5) 
Let us denote with ΔI(t) = I(t) − I(t − 1), ΔR(t) = R(t) − R(t − 1), ΔD(t) = D(t) − D(t − 1), the reported new cases of infectious, recovered and dead at time t, with CΔI(t), CΔR(t), CΔD(t) the cumulative numbers of confirmed cases at time t. Thus: CΔX(t)=∑i=1tΔX(t),(6)  where, X = I, R, D.
Let us also denote by Δ X(t) = [ΔX(1), ΔX(2), ⋯, ΔX(t)]T the t × 1 column vector containing all the reported new cases up to time t and by C Δ X(t) = [CΔX(1), CΔX(2), ⋯, CΔX(t)]T, the t × 1 column vector containing the corresponding cumulative numbers up to time t. On the basis of Eqs (2), (3) and (4), one can provide a coarse estimation of the parameters R0, β and γ as follows.
Starting with the estimation of R0, we note that as the province of Hubei has a population of 59m, one can reasonably assume that for any practical means, at least at the beginning of the outbreak, S ≈ N. By making this assumption, one can then provide an approximation of the expected value of R0 using Eqs (5), (2), (3) and (4). In particular, substituting in Eq (2), the terms βI(t − 1) and γI(t − 1) with ΔR(t) = R(t) − R(t − 1) from Eq (3), and ΔD(t) = D(t) − D(t − 1) from Eq (4) and bringing them into the left-hand side of Eq (2), we get: I(t)−I(t−1)+R(t)−R(t−1)+D(t)−D(t−1)=αNS(t−1)I(t−1)(7) 
Adding Eqs (3) and (4), we get: R(t)−R(t−1)+D(t)−D(t−1)=βI(t−1)+γI(t−1)(8) 
Finally, assuming that for any practical means at the beginning of the spread that S(t − 1) ≈ N and dividing Eq (7) by Eq (8) we get: I(t)−I(t−1)+R(t)−R(t−1)+D(t)−D(t−1)R(t)−R(t−1)+D(t)−D(t−1)=αβ+γ=R0(9) 
Note that one can use directly Eq (9) to compute R0 with regression, without the need to compute first the other parameters, i.e. β, γ and α.
At this point, the regression can be done either by using the differences per se, or by using the corresponding cumulative functions (instead of the differences for the calculation of R0 using Eq (9)). Indeed, it is easy to prove that by summing up both sides of Eqs (7) and (8) over time and then dividing them, we get the following equivalent expression for the calculation of R0. CΔI(t)+CΔR(t)+CΔD(t)CΔR(t)+CΔD(t)=αβ+γ=R0(10) 
Here, we used Eq (10) to estimate R0 in order to reduce the noise included in the differences. Note that the above expression is a valid approximation only at the beginning of the spread of the disease.
Thus, based on the above, a coarse estimation of R0 and its corresponding confidence intervals can be provided by solving a linear regression problem using least-squares problem as: R0^=([CΔR(t)+CΔD(t)]T[CΔR(t)+CΔD(t)])−1[CΔR(t)+CΔD(t)]T[CΔI(t)+CΔR(t)+CΔD(t)],(11)