Table 2 The expected positive real roots (EPRR) associated with g(z) for various cases of \(\mathscr {R}_1\), and \(\mathscr {R}_2\)
Case | \(k_1\) | \(k_2\) | \(k_3\) | \(k_4\) | \(k_5\) | \(\mathscr {R}_0\) | Sign changes | No. of EPRR (EE) |
|---|---|---|---|---|---|---|---|---|
1 | + | + | + | + | + | \(\mathscr {R}_0 < 1\) | 0 | 0 |
2 | + | + | + | − | – | \(\mathscr {R}_0 > 1\) | 1 | 1 |
3 | + | − | − | + | + | \(\mathscr {R}_0 < 1\) | 2 | 0, 2 |
4 | + | − | − | − | – | \(\mathscr {R}_0 > 1\) | 1 | 1 |
5 | + | + | − | + | + | \(\mathscr {R}_0 < 1\) | 2 | 0, 2 |
6 | + | + | − | − | – | \(\mathscr {R}_0 > 1\) | 1 | 1 |
7 | + | − | + | + | + | \(\mathscr {R}_0 < 1\) | 2 | 0, 2 |
8 | + | − | + | − | – | \(\mathscr {R}_0 > 1\) | 3 | 1, 3 |
