At time t = 0 and in the absence of interventions, the next generation matrix has the following elements where is the fraction of untreated extremely severe cases who die from the disease (see below for details). The dominant eigenvalue of this matrix is called the basic reproduction number R 0 . If κ (which determines the value of the contact rates ) is given, the eigenvectors of this matrix can numerically be calculated. The user-specified value of R 0 is now used to determine numerically the scaling factor κ. Let be the eigenvector which has the largest eigenvalue R 0 . 