Lotka Volterra model

import numpy as np

def model(
    time: float,
    variables: list[float], 
):
    Prey, Predator = variables
    Alpha = 0.1
    Beta = 0.02
    Gamma = 0.4
    Delta = 0.02
    prey_growth = Alpha * Prey
    predation = Predator * Prey
    predator_death = Gamma * Predator
    dPreydt = +prey_growth+(- Beta)*predation
    dPredatordt = +(Delta)*predation-predator_death
    return [dPreydt, dPredatordt]

def all_derived(
    time: float,
    variables: list[float], 
):
    Prey, Predator = variables
    Alpha = 0.1
    Beta = 0.02
    Gamma = 0.4
    Delta = 0.02
    prey_growth = Alpha * Prey
    predation = Predator * Prey
    predator_death = Gamma * Predator
    return [prey_growth, predation, predator_death]

derived = all_derived
y0 = {"Prey": 10, "Predator": 10}
    

\begin{align*}
      \frac{d Prey}{dt} &= \alpha \cdot Prey - \beta \cdot Predator \cdot Prey\\ 
\frac{d Predator}{dt} &= \delta \cdot Predator \cdot Prey - \gamma \cdot Predator
    \end{align*}