#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 12 17:37:29 2022
%qProblem2_4_6.py
%Figure 2.14
%imulation and quasi steady state approximation

@author: bingalls
"""
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint



#assign parameter values
k=1

#set time_grid for simulation
t_min=0; t_max=10; dt=0.01
times=np.arange(t_min, t_max+dt, dt) #generate time-grid list

###Original model#####
#set initial conditions for original model: S(1)=a, S(2)=b
S0=[0];
#declare right-hand-side for original model
def dSdt_original(S,t):
    dS=[0] #generate a list to store derivatives
    dS[0]=k*(-S[0]+1)
    return dS


S=odeint(dSdt_original, S0, times) #run simulation




#plot simulation
plt.figure() #generate figure
plt.plot(times, S[:,0], label="c", linewidth=2)
plt.xlabel("Time")
plt.ylabel("concentration")
plt.legend()