(1) \(\frac{dx(t)}{\text{dτ}}=\sigma(t)-\delta\left(t\right)x(t)+\rho x(t)\frac{y(t)}{y(t)+n}-\mu x(t)y(t)-K_{x}M(t)x(t)\)
(2) \(\frac{dy(t)}{\text{dτ}}=\alpha y(t)\left(1-\beta y(t)\right)-x(t)y(t)-K_{y}M(t)y(t)\)
(3) \(\frac{dM(t)}{\text{dτ}}=-\xi M(t)+v_{M}(t)\)
(4) \(\frac{d\sigma(t)}{\text{dτ}}=\mu_{\sigma}v_{v}\left(t\right)\left(1-\frac{\sigma(t)}{k_{\sigma}}\right)\)
(5) \(\frac{d\delta(t)}{\text{dτ}}=\mu_{\delta}v_{v}\left(t\right)\left(1-\frac{\delta(t)}{k_{\delta}}\right)\)