title: Updating parameter value with slider (python)
body: <p>I have a system of differential equations. The solutions depend on a parameter <em>beta</em>. I want to create a slider so I can change this parameter and display the changes of the solution curves directly in my plot. I almost got it I think, but I miss one piece.</p>
  
  <p>My code</p>
  
  <pre><code>N = 1
  
  #Initial conditions
  I0 = 0.01
  S0= N - I0
  
  #System of diff. equations
  def system(x, t, beta, gamma ):
      I, S = x
  
      dIdt = (beta/gamma*S-1)*I*gamma
      dSdt = -(beta/gamma*S-1)*I*gamma
  
      return dIdt, dSdt
  
  #Parameters initial value
  beta = 0.03
  gamma = 0.017
  
  #Initial cond. vector
  y0 = I0, S0
  
  #time grid
  t = np.linspace(0, 1300, 1300)
  
  # Solution 
  sol = odeint(system, y0, t, args=(beta, gamma))
  
  
  ################ Animations part ##################
  
  fig, ax = plt.subplots()
  plt.subplots_adjust(bottom = 0.25)
  
  #solution curves for I and S
  infected, = plt.plot(t, sol[:,0])
  recovered, = plt.plot(t, sol[:,1])
  
  axbeta = plt.axes([0.125, 0.1, 0.5, 0.05])
  
  sliderbeta = Slider(axbeta, 'beta', 0, 1, valinit=beta)
  
  def update_beta(val):
      beta_value = sliderbeta.val
      ??????????????????????????????????????
      fig.canvas.draw_idle()
  
  sliderbeta.on_changed(update_beta)
  
  plt.show()
  
  </code></pre>
  
  <p>I don't know how to acces my initial beta value and how to replace it by <em>beta_value</em>. I guess there is some line missing where I put the question marks. </p>