I have been trying for more than a week to find the equilibrium points of this system: $\begin{aligned} \frac{d A}{d t} & =\theta_1-\mu_{A D} A-\mu_{A B} A \\ \frac{d B}{d t} & =\theta_2+\mu_{A B} A+\mu_{D B} D-\mu_{B D} B-\mu_{B C} B-\mu_{B E} B-\gamma_2 B \\ \frac{d C}{d t} & =\theta_3+\mu_{B C} B+\mu_{D C} D-\mu_{C D} C-\mu_{C E} C-\gamma_3 C \\ \frac{d D}{d t} & =\mu_{A D} A+\mu_{B D} B+\mu_{C D} C-\mu_{D B} D-\mu_{D C} D-\mu_{D E} D \\ \frac{d E}{d t} & =\mu_{D E} D+\mu_{C E} C+\mu_{B E} B-\gamma_1 E\end{aligned}$
The problem is that I have to find that for example the equilibrium point B and D is written in the form : $B^*=\frac{\alpha}{k_1 \rho}$ and $D^*=\frac{\sigma}{k_1 \rho}$
with $\begin{aligned} \alpha= & \left(k_3 \mu_{D B}+\left(\mu_{D E}+\mu_{D C}\right) \gamma_3+\left(\mu_{D E}+\mu_{D C}\right) \mu_{C E}+\mu_{D E} \mu_{C D}\right) \theta_2 \mu_{A B} \\ & +\left(k_3 \theta_1+\mu_{C D} \theta_3\right) \mu_{D B}+\theta_1\left(\left(\mu_{D E}+\mu_{D C}\right) \gamma_3+\left(\mu_{D E}+\mu_{D C}\right) \mu_{C E}+\mu_{D E} \mu_{C D}\right) \mu_{A B} \\ & +\mu_{A D}\left(\left(k_3 \mu_{D B}+\left(\mu_{D E}+\mu_{D C}\right) \gamma_3+\left(\mu_{D E}+\mu_{D C}\right) \mu_{C E}+\mu_{D E} \mu_{C D}\right) \theta_2+\left(k_3 \theta_1+\mu_{C D} \theta_3\right) \mu_{D B}\right)\end{aligned}$ \ $$\begin{aligned} \rho= & k_3 k_2 \mu_{D E}+\left(\left(\mu_{D B}+\mu_{D C}\right) \gamma_2+\left(\mu_{D B}+\mu_{D C}\right) \mu_{B E}+\mu_{B C} \mu_{D B}+\left(\mu_{B C}+\mu_{B D}\right) \mu_{D C}\right) \gamma_3 \\ & +\left(\left(\mu_{D B}+\mu_{D C}\right) \gamma_2+\left(\mu_{D B}+\mu_{D C}\right) \mu_{B E}+\mu_{B C} \mu_{D B}+\left(\mu_{B C}+\mu_{B D}\right) \mu_{D C}\right) \mu_{C E}+\mu_{C D} \mu_{D B}\left(\gamma_2+\mu_{B E}\right)\end{aligned}$$ $$ \begin{aligned} \sigma= & \left(\left(k_2 \theta_1+\left(\theta_2+\theta_3\right) \mu_{B D}+\mu_{B C} \theta_2+\theta_3\left(\gamma_2+\mu_{B C}+\mu_{B E}\right)\right) \mu_{C D}+\left(k_2 \theta_1+\mu_{B D} \theta_2\right)\left(\gamma_3+\mu_{C E}\right)\right) \mu_{A D} \\ & +\mu_{A B}\left(\left(\left(\mu_{B C}+\mu_{B D}\right) \theta_1+\left(\theta_2+\theta_3\right) \mu_{B D}+\mu_{B C} \theta_2+\theta_3\left(\gamma_2+\mu_{B C}+\mu_{B E}\right)\right) \mu_{C D}+\mu_{B D}\left(\theta_1+\theta_2\right)\left(\gamma_3+\mu_{C E}\right)\right) \end{aligned} $$ and $$ k_1=\mu_{A D}+\mu_{A B} $$ I tried to start with D and replace A and B in the system but I couldn't.