\(\frac{\text{dN}}{\text{dt}}=\) \(q(N_{\max}-N)-\frac{\mu_{max,E}N}{K+N}P_{E}-\frac{\mu_{max,I}N}{K+N}P_{I}\), (1)
\(\frac{dP_{E}}{\text{dt}}=\) \(\frac{\mu_{max,E}N}{K+N}P_{E}-\frac{p_{Z}\cdot a_{Z}\cdot P_{E}^{2}}{1+h_{P_{E}}\cdot p_{Z}\cdot a_{Z}\cdot P_{E}^{2}+h_{F}\cdot\left(1-p_{Z}\right)\cdot a_{Z}\cdot F^{2}}Z-qP_{E}\), (2)
\(\frac{dP_{I}}{\text{dt}}=\) \(\frac{\mu_{max,I}N}{K+N}P_{I}-\beta P_{I}F-qP_{I}\ \), (3)
\(\frac{\text{dF}}{\text{dt}}=\) \(f_{F}\beta P_{I}F-\frac{\left(1-p_{Z}\right)\cdot a_{Z}\cdot F^{2}}{1+h_{P_{E}}\cdot p_{Z}\cdot a_{Z}\cdot P_{E}^{2}+h_{F}\cdot\left(1-p_{Z}\right)\cdot a_{Z}\cdot F^{2}}Z-qF\), (4)
\(\frac{\text{dZ}}{\text{dt}}=\) \(\frac{\left(e_{p}\cdot p_{Z}\cdot a_{Z}{\cdot P}_{E}^{2}+e_{F}\cdot\left(1-p_{Z}\right)\cdot a_{Z}\cdot F^{2}\right)}{1+h_{P_{E}}\cdot p_{Z}\cdot a_{Z}\cdot P_{E}^{2}+h_{F}\cdot\left(1-p_{Z}\right)\cdot a_{Z}\cdot F^{2}}Z-\left(q+m_{Z}\right)Z\). (5)
\(\frac{dp_{Z}}{\text{dt}}=\) \(V\frac{\partial W_{Z}}{\partial p_{Z}}+B(p_{Z}).\) (6)