\(\dot {M} = D k_{M} P_{D} P_{R} - \gamma _{M} M\) | (5) |
\(\dot {E} = k_{E} M - \gamma _{E} E\) | (6) |
\(\dot {L} = k_{L} \beta _{L} \beta _{G} Q - 2 \phi _{M} \mathcal {M} B - \gamma _{L} L\) | (7) |
A=L | (8) |
Q=E | (9) |
B=E/4 | (10) |
\(P_{D} = \frac {p_{p} (1\, +\, p_{c} (K_{\textit {pc}}\, -\, 1))}{1\, +\, p_{p} p_{c} (k_{\textit {pc}}\, -\, 1)}\) | (11) |
\(p_{c} = \frac {K^{n_{h}}_{G}}{K^{n_{h}}_{G}\, +\, Ge^{n_{h}}}\) | (12) |
\(P_{R} = \frac {1}{1\, +\, \rho (A)\, +\, \frac {\xi _{123} \rho (A)}{(1\, +\, \xi _{2} \rho (A))(1\, +\, \xi _{3} \rho (A))}}\) | (13) |
\(\rho (A) = \rho _{\textit {max}} \left (\frac {K_{A}}{K_{A}\, +\, A}\right)^{\!\!4}\) | (14) |
\(\beta _{L} = \frac {Le}{k_{L}\, +\, Le}\) | (15) |
\(\beta _{G} = 1 - \phi _{G} \frac {Ge}{k_{G}\, +\, Ge}\) | (16) |
\(\mathcal {M}= \frac {L}{k_{M}\, +\, L}\) | (17) |