Phytoplankton-chytrid-zooplankton dynamics via a reaction-diffusion-advection mycoloop model (Q6564472)

The authors propose a mathematical model of mycoloop in aquatic food web composed of pytoplankton, chytrids, and zooplankton\N\begin{align*}\NS_t&=d_pS_{xx}-vS_x+r_pS-m_pS-\eta S(S+I)-\theta SC-\alpha SZ \\\NI_t&=d_pI_{xx}-vI_x+\theta SC-m_pI-\omega I-\beta IZ \\\NC_t&=d_cC_{xx}+q\omega I-m_cC-\theta SC-\gamma CZ \\\NZ_t&=d_zZ_{xx}+(e_p(\alpha S+\beta I)+e_c\gamma C)Z-m_zZ\N\end{align*}\Non \([0,x_h]\) with the null flux boundary condition\N\[\N\left. ( d_pS_x-vS, d_pI_x-vI, C_x, Z_x)\right\vert_{x=0, x_h}=0,\N\]\Nwhere \(S\), \(I\), \(C\), and \(Z\) denote the biomass densities of susceptible, infected phytoplankton, density of free-living chytrid, and biomass density of zooplankton, respectively. Existence, uniqueness, and stability of the four forms of the stationary solution,\N\[\NE_0=(0,0,0,0), \ E_1=(S_1(x), 0, 0, 0), \ E_2=(S_2(x), 0, 0, Z_2(x))\N\]\Nand\N\[\NE_3=(S_3(x), I_3(x), C_3(x), 0), \ E_4=(S_4(x), I_4(x), C_4(x), Z_4(x)),\N\]\Nare clarified in accordance with \(R_p=r_p/m_p\), \(R_0\), denoting the basic reproduction number for chytrid transmission without zooplankton, and \(R_z\), associated with the linearlized eigenvalue. Numerical simulations are also given.