Calculation of R0 and Rt

To calculate R₀ and R_t, we used the next generation method.17 This method uses two matrices of partial derivatives of compartments with infected individuals.18 In our model, this included exposed, asymptomatic infected, symptomatic infected, quarantined and hospitalised individuals. The first matrix, F, is the rate of appearance of new infections for each compartment. Each element, f_ij, of F is the partial derivative of any term in which new infections appear in compartment i with respect to compartment j where i, j ∈ [E, I_sym, I_{asym, undetected}, Q, Q_asym, H].

The second matrix, V, is the rate of transfer of individuals out of a compartment minus the rate of transfer of individuals into a compartment. Therefore, each element, v_ij, of V is the partial derivative of the additive inverse of any term other than the appearance of new infections in compartment i with respect to compartment j. The matrix V and its inverse are as follows:

The next generation method calculates R₀ as the dominant eigenvalue of the next generation matrix. The next generation matrix is defined as FV⁻¹:

In our model, FV⁻¹ has only one non-zero eigenvalue, λ=βSε(αb2−αbγ+αpdetected−α−b2+bγ+b−γ)N(b−ε)(b−1)(b−γ). Therefore, R₀=max (0, λ), and since λ≥0, R₀=λ. Since R₀ is directly proportional to β, we can calculate the values of R₀ of other phases simply by using phase 1 starting conditions combined with the reduced transmission rate.

To find the effective reproduction ratio, R_t, at time t, we used the next generation method with the same matrices but updated the values of S and β as appropriate. Because the number of susceptible individuals, S, is a function of time, we recalculate R_t each day. The functional form of R_t for our model is as follows:

We computed the 95% CrI of R_t as the range in which 95% of calibrated values of R_t fell.