Population dynamics

import numpy as np

def model(
    time: float,
    variables: list[float], 
):
    e_coli, c_gluta = variables
    mu_e = 0.4
    mu_c = 0.3
    a_e = 6
    a_c = 4
    theta = 0.001
    dEdt = e_coli * a_e * mu_e
    dCdt = (c_gluta * a_c * mu_c) - (theta * c_gluta * c_gluta)
    de_colidt = +dEdt
    dc_glutadt = +dCdt
    return [de_colidt, dc_glutadt]

def all_derived(
    time: float,
    variables: list[float], 
):
    e_coli, c_gluta = variables
    mu_e = 0.4
    mu_c = 0.3
    a_e = 6
    a_c = 4
    theta = 0.001
    dEdt = e_coli * a_e * mu_e
    dCdt = (c_gluta * a_c * mu_c) - (theta * c_gluta * c_gluta)
    return [dEdt, dCdt]

derived = all_derived
y0 = {"e_coli": 5, "c_gluta": 5}
    

\begin{align*}
      \frac{d E. coli}{dt} &= E. coli \cdot a_e \cdot \mu_e\\ 
\frac{d C. gluta}{dt} &= C. gluta \cdot a_c \cdot \mu_c - \theta \cdot C. gluta \cdot C. gluta
    \end{align*}