globals [
  tscale
  period
  mu
  circadian_amplitude
  upper_asymptote
  upper_threshold
  lower_threshold
  mean_upper_threshold
  mean_lower_threshold
  MSFshift
  phase
  H_max
  H_min
  H_shift
  H_scale
  H_level
  circadian
  T_start
  sleepiness
  Alertness
]

turtles-own [
  H_0  ;
  T_0 ;
  Y_0 ;
  X_0 ;
  H ;
  T ;
  X ;
  Y ;
  chi_s ;
  chi_w ;
  wake ;
  ]

to setup
   clear-all
   set-default-shape turtles "circle"
   set tscale 5
   set period 24
   set MSFshift 2.34
   set mu ( 1 / ( 0.2683 - 0.1716 * exp( - 0.0788 * age ) ) )
   set upper_asymptote (mu * 4.85)
   set circadian_amplitude (- 7.5 + 2900 * exp( - 1.7 * mu))
   set mean_upper_threshold 12.65
   set mean_lower_threshold 11.65
   set phase ((-87.8 + 41.4 * mu - 4.7 * mu * mu + reduce-social-jetlag + MSFshift) * 360 / 24 )
    if Listening-to-your-body-clock = "Yes" [
    set T_start  round( -103.2 + 48.9 * mu - 5.4 * mu * mu  + MSFshift )
    ]
    if Listening-to-your-body-clock = "No" [
    set T_start Sun_wake
    ]
   set H_max 30
   set H_min 0
   set H_scale ( (0.85 * max-pycor - min-pycor ) / (H_max - H_min) )
   set H_shift ( min-pycor - H_scale * H_min )
   crt 1 [
     set size 10
     set color black
     set H_0 ( mean_lower_threshold + circadian_amplitude * cos (360 * T_start / period  - phase) )
     set Y_0 H_scale * H_0 + H_shift
     set T_0 T_start
     set X_0 T_0 * tscale
     set H H_0
     set T T_0
     set X X_0
     set Y Y_0
     set chi_s sleep_timeconstant
     set chi_w wake_timeconstant
     set wake 1
     setxy X Y
     set pen-size 3
   ]
   crt 1 [
     set size 10
     set color black
     set T_0 T_start
     set Y_0 ((H_scale * (mean_upper_threshold + circadian_amplitude * cos( 360 * T_start / period - phase)) )+ H_shift )
     set X_0 T_0 * tscale
     setxy X_0 Y_0
     set wake 1
     set pen-size 2
]
   draw-protocol
   draw-daynight
   reset-ticks
end

to draw-protocol
; This shades the region when sleep occurs if you are not listening to your body clock.
  ask patches [ set pcolor white ]
    if Sat_sleep <= 24 [
      ask patches with [ (pycor < ( max-pycor ) ) and ( pxcor > 0 )] [ set pcolor gray + 4 ]
    ]
    if Sat_sleep > 24 [
      ask patches with [ (pycor < ( max-pycor ) ) and (pxcor >  int ( ( Sat_sleep mod 24 ) * tscale ) ) ] [ set pcolor gray + 4 ]
      ]
;  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor < int ( Sun_wake * tscale ))]     [ set pcolor gray + 4 ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( Sun_wake * tscale ))]     [ set pcolor white ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( Sun_sleep * tscale ))]     [ set pcolor gray + 4 ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Mon_wake + 24) * tscale ))] [ set pcolor white ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Mon_sleep + 24) * tscale ))] [ set pcolor gray + 4 ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Tues_wake + 48) * tscale ))] [ set pcolor white ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Tues_sleep + 48) * tscale ))] [ set pcolor gray + 4 ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Wed_wake + 72) * tscale ))] [ set pcolor white ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Wed_sleep + 72) * tscale ))] [ set pcolor gray + 4 ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Thurs_wake + 96) * tscale ))] [ set pcolor white ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Thurs_sleep + 96) * tscale ))] [ set pcolor gray + 4 ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Fri_wake + 120) * tscale ))] [ set pcolor white ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Fri_sleep + 120) * tscale ))] [ set pcolor gray + 4 ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Sat_wake + 144) * tscale ))] [ set pcolor white ]
  ask patches with [ (pycor < ( max-pycor ) ) and (pxcor > int ( (Sat_sleep + 144) * tscale ))] [ set pcolor gray + 4 ]
end

to draw-daynight
; This draws on the stars at midnight and the suns at mid-day.
     crt 7 [
     set size 30
     set color yellow
     set shape "sun"
     ]
     ask turtle 2 [ setxy ( 12 * tscale ) (0.85 * max-pycor) ]
     ask turtle 3 [ setxy ( 36 * tscale ) (0.85 * max-pycor) ]
     ask turtle 4 [ setxy ( 60 * tscale ) (0.85 * max-pycor) ]
     ask turtle 5 [ setxy ( 84 * tscale ) (0.85 * max-pycor) ]
     ask turtle 6 [ setxy ( 108 * tscale ) (0.85 * max-pycor) ]
     ask turtle 7 [ setxy ( 132 * tscale ) (0.85 * max-pycor) ]
     ask turtle 8 [ setxy ( 156 * tscale ) (0.85 * max-pycor) ]
     crt 7 [
     set size 30
     set color sky
     set shape "star"
     ]
     ask turtle 9 [ setxy ( 0 * tscale ) (0.85 * max-pycor) ]
     ask turtle 10 [ setxy ( 24 * tscale ) (0.85 * max-pycor) ]
     ask turtle 11 [ setxy ( 48 * tscale ) (0.85 * max-pycor) ]
     ask turtle 12 [ setxy ( 72 * tscale ) (0.85 * max-pycor) ]
     ask turtle 13 [ setxy ( 96 * tscale ) (0.85 * max-pycor) ]
     ask turtle 14 [ setxy ( 120 * tscale ) (0.85 * max-pycor) ]
     ask turtle 15 [ setxy ( 144 * tscale ) (0.85 * max-pycor) ]
end

to go
; Turtle 0 is the homeostat.
  ask turtle 0 [
    pd
    set T  (T_start * tscale + ticks ) / tscale
    set X T * tscale
    if Listening-to-your-body-clock = "No" [
       if Sat_sleep > 24 [
         if (T = Sat_sleep mod 24) [ set T_0 ( Sat_sleep mod 24 )
                          set wake  0
                          set H_0 H
                          set color black
         ]
      ]
      if (T = Sun_wake) [ set T_0 Sun_wake
                          set wake  1
                          set H_0 H
                          set color black
      ]
      if (T = Sun_sleep ) [ set T_0 Sun_sleep
                          set H_0 H
                          set wake 0
                          set color black
      ]
      if (T = Mon_wake + 24) [ set T_0 Mon_wake + 24
                             set H_0 H
                             set wake 1
                             set color black
      ]
      if (T = Mon_sleep + 24 ) [ set T_0 Mon_sleep + 24
                               set H_0 H
                               set wake 0
                               set color black
      ]
      if (T = Tues_wake + 48) [ set T_0 Tues_wake + 48
                             set H_0 H
                             set wake 1
                             set color black
      ]
      if (T = Tues_sleep + 48 ) [ set T_0 Tues_sleep + 48
                               set H_0 H
                               set wake 0
                               set color black
      ]
      if (T = Wed_wake + 72) [ set T_0 Wed_wake + 72
                             set H_0 H
                             set wake 1
                             set color black
      ]
      if (T = Wed_sleep + 72 ) [ set T_0 Wed_sleep + 72
                               set H_0 H
                               set wake 0
                               set color black
      ]
      if (T = Thurs_wake + 96) [ set T_0 Thurs_wake + 96
                             set H_0 H
                             set wake 1
                             set color black
      ]
      if (T = Thurs_sleep + 96 ) [ set T_0 Thurs_sleep + 96
                               set H_0 H
                               set wake 0
                               set color black
      ]
      if (T = Fri_wake + 120) [ set T_0 Fri_wake + 120
                             set H_0 H
                             set wake 1
                             set color black
      ]
      if (T = Fri_sleep + 120 ) [ set T_0 Fri_sleep + 120
                               set H_0 H
                               set wake 0
                               set color black
      ]
      if (T = Sat_wake + 144) [ set T_0 Sat_wake + 144
                             set H_0 H
                             set wake 1
                             set color black
      ]
      if (T = Sat_sleep + 144 ) [ set T_0 Sat_sleep + 144
                               set H_0 H
                               set wake 0
                               set color black
      ]
    ]
    if Listening-to-your-body-clock = "Yes" [
      if (wake = 1) and  (H > ( mean_upper_threshold + circadian_amplitude * cos( 360 * T / period - phase ))) [
        set wake 0
        set H_0 H
        set T_0 T
      ]
      if (wake = 0) and (H < ( mean_lower_threshold + circadian_amplitude * cos( 360 * T / period - phase ))) [
        set wake 1
        set H_0 H
        set T_0 T
      ]
   ]
;
      if wake = 1 [
        set H  ( (H_0 - upper_asymptote ) * exp( - (T - T_0) / chi_w ) + upper_asymptote )
          if H > (mean_upper_threshold + circadian_amplitude * cos( 360 * T / period - phase) ) [ set color red ]
          if H < (mean_upper_threshold + circadian_amplitude * cos( 360 * T / period - phase) ) [ set color black ]
        set sleepiness ( H - ( mean_upper_threshold + circadian_amplitude * cos( 360 * T / period - phase )) )
       ]
       if wake = 0 [
         set H ( H_0 * exp( - (T - T_0) / chi_s ))
           if H < (mean_lower_threshold + circadian_amplitude * cos( 360 * T / period - phase) ) [ set color yellow ]
           if H > (mean_lower_threshold + circadian_amplitude * cos( 360 * T / period - phase) ) [ set color black ]
         set sleepiness 0
       ]
        set Y H_scale * H + H_shift
     setxy X Y
     set H_level H
  ]
; turtle 1 is the circadian
      ask turtle 1 [
    pd
    set T  (T_start * tscale + ticks ) / tscale
  if Listening-to-your-body-clock = "No" [
      if (Sat_sleep > 24) [
        if (T = Sat_sleep mod 24) [ set wake 0 ]
      ]
      if (T = Sun_wake)  [ set wake  1 ]
      if (T = Sun_sleep ) [ set wake 0]
      if (T = Mon_wake + 24) [ set wake 1  ]
      if (T = Mon_sleep + 24 ) [ set wake 0 ]
      if (T = Tues_wake + 48) [ set wake 1 ]
      if (T = Tues_sleep + 48 ) [ set wake 0 ]
      if (T = Wed_wake + 72) [ set wake 1 ]
      if (T = Wed_sleep + 72 ) [set wake 0 ]
      if (T = Thurs_wake + 96) [ set wake 1 ]
      if (T = Thurs_sleep + 96 ) [set wake 0 ]
      if (T = Fri_wake + 120) [ set wake 1 ]
      if (T = Fri_sleep + 120 ) [set wake 0 ]
      if (T = Sat_wake + 144) [ set wake 1 ]
      if (T = Sat_sleep + 144 ) [set wake 0 ]
    ]
    if Listening-to-your-body-clock = "Yes" [
      if (wake = 1) and  (H_level > ( mean_upper_threshold + circadian_amplitude * cos( 360 * T / period - phase ))) [
        set wake 0
      ]
      if (wake = 0) and (H_level < ( mean_lower_threshold + circadian_amplitude * cos( 360 * T / period - phase ))) [
        set wake 1
      ]
    ]
    if wake = 1 [
    set Y_0 H_scale * (mean_upper_threshold + circadian_amplitude * cos( 360 * T / period - phase) ) + H_shift
      if H_level > (mean_upper_threshold + circadian_amplitude * cos( 360 * T / period - phase) ) [ set color red ]
      if H_level < (mean_upper_threshold + circadian_amplitude * cos( 360 * T / period - phase) ) [ set color gray ]
    ]
    if wake = 0 [
    set Y_0 H_scale * (mean_lower_threshold + circadian_amplitude * cos( 360 * T / period - phase) ) + H_shift
      if H_level < (mean_lower_threshold + circadian_amplitude * cos( 360 * T / period - phase) ) [ set color yellow ]
      if H_level > (mean_lower_threshold + circadian_amplitude * cos( 360 * T / period - phase) ) [ set color gray ]
    ]
  set X_0 T * tscale
  setxy X_0 Y_0
  ]
  tick
    if ticks = (841 - T_start * tscale) [
    reset-ticks
    ask turtle 0 [
      pu
      set T_0  0
      set H_0  H
      set T_start 0
      set Y H_scale * H + H_shift
      setxy 0 Y
     ]
    ask turtle 1 [
      pu
      setxy 0 Y_0
     ]
  ]
end

to Re-start
  set sleepiness 0
  set mu ( 1 / ( 0.2683 - 0.1716 * exp( - 0.0788 * age ) ) )
  set upper_asymptote (mu * 4.85)
  set circadian_amplitude (- 7.5 + 2900 * exp( - 1.7 * mu))
  set phase ((-87.8 + 41.4 * mu - 4.7 * mu * mu + reduce-social-jetlag + MSFshift) * 360 / 24 )
   if Listening-to-your-body-clock = "Yes" [
    set T_start  round( -103.2 + 48.9 * mu - 5.4 * mu * mu  + MSFshift )
    ]
    if Listening-to-your-body-clock = "No" [
    set T_start Sun_wake
    ]
     ask turtle 0 [
     pu
     set H_0 ( mean_lower_threshold + circadian_amplitude * cos (360 * T_start / period  - phase) )
     set Y_0 H_scale * H_0 + H_shift
     set T_0 T_start
     set X_0 T_0 * tscale
     set H H_0
     set T T_0
     set X X_0
     set Y Y_0
     set wake 1
     setxy X Y
     ]
     ask turtle 1 [
     pu
     set H_0 ( mean_upper_threshold + circadian_amplitude * cos (360 * T_start / period  - phase) )
     set Y_0 H_scale * H_0 + H_shift
     set T_0 T_start
     set X_0 T_0 * tscale
     set H H_0
     set T T_0
     set X X_0
     set Y Y_0
     set wake 1
     setxy X Y
     ]
     reset-ticks
end

to Clear-screen
  clear-drawing
  clear-all-plots
end
@#$#@#$#@
GRAPHICS-WINDOW
213
89
1244
439
-1
-1
1.21641
1
10
1
1
1
0
0
0
1
0
840
0
280
1
1
1
ticks
30.0

BUTTON
30
25
210
58
set up 
setup
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1

BUTTON
65
70
157
103
go / stop
go
T
1
T
OBSERVER
NIL
NIL
NIL
NIL
0

INPUTBOX
270
10
329
70
Sun_wake
8.0
1
0
Number

INPUTBOX
337
11
398
71
Sun_sleep
24.0
1
0
Number

INPUTBOX
405
11
467
71
Mon_wake
7.0
1
0
Number

INPUTBOX
478
10
541
70
Mon_sleep
23.0
1
0
Number

INPUTBOX
547
10
612
70
Tues_wake
7.0
1
0
Number

INPUTBOX
620
10
685
70
Tues_sleep
23.0
1
0
Number

INPUTBOX
690
10
755
70
Wed_wake
7.0
1
0
Number

INPUTBOX
760
10
825
70
Wed_sleep
23.0
1
0
Number

INPUTBOX
25
355
135
415
reduce-social-jetlag
0.0
1
0
Number

PLOT
210
460
1245
580
Alertness
NIL
NIL
0.0
168.0
-10.0
10.0
false
false
"" ""
PENS
"Alertness" 1.0 2 -1513240 false "" "if (sleepiness = 0) [ plot-pen-up ] \nif (sleepiness != 0) [plot-pen-down ]\nset Alertness (- sleepiness)\nif (Alertness < 0) [ set-plot-pen-color red ]\nif (Alertness > 0) [ set-plot-pen-color black ]\nplotxy (T_start + ticks / tscale) Alertness"
"zero" 1.0 0 -7500403 true "" "plotxy (ticks * 100) 0"

SLIDER
10
305
190
338
age
age
9
80
30.0
1
1
NIL
HORIZONTAL

CHOOSER
10
245
192
290
Listening-to-your-body-clock
Listening-to-your-body-clock
"Yes" "No"
1

BUTTON
55
170
165
203
Re-initialise
Re-start
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
0

SLIDER
15
450
187
483
sleep_timeconstant
sleep_timeconstant
4
80
45.0
1
1
NIL
HORIZONTAL

SLIDER
15
495
187
528
wake_timeconstant
wake_timeconstant
4
80
45.0
1
1
NIL
HORIZONTAL

INPUTBOX
835
10
905
70
Thurs_wake
7.0
1
0
Number

INPUTBOX
910
10
980
70
Thurs_sleep
23.0
1
0
Number

INPUTBOX
985
10
1045
70
Fri_wake
7.0
1
0
Number

INPUTBOX
1050
10
1110
70
Fri_sleep
26.0
1
0
Number

INPUTBOX
1115
10
1180
70
Sat_wake
12.0
1
0
Number

INPUTBOX
1190
10
1250
70
Sat_sleep
24.0
1
0
Number

BUTTON
50
120
172
153
Clear screen
Clear-screen
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1

@#$#@#$#@
## WHAT IS IT?

Biologists believe that there are two fundamental biorhythms or processes that underly sleep/wake regulation.  These are:

   1. The body clock (the "circadian process") that keeps our bodies operating on a daily cycle, with different functions of our body being most active at different points. Biologists have been able to see this daily rhythm right down at the gene level.  

   2. A sleep pressure (the "homeostatic process").  This sleep pressure builds up during the day and dies down during the night.  The sleep pressure has been associated with the build-up of chemicals that are associated with activity, such as adenosine.  

The most influential model of sleep-wake regulation to-date has been the two-process model that takes the circadian process and the homeostatic process and uses them to describe the timing of sleep and wake [1].  The idea is that the longer we are awake the higher the sleep pressure.  If we are listening to our bio-rhythms and going to sleep when we feel sleepy then we fall asleep when the sleep pressure reaches an upper threshold value.   How sleepy we feel depends on how far from the upper threshold we are.  During sleep, sleep pressure decreases until we reach a lower threshold, at which point we wake up.  The upper and lower thresholds are modulated by a 24 hour cycle, mimicking the effect of the circadian process.  

Of course, one important fact about sleep is that we are able to over-ride our bodies cues and remain awake even when we are tired, or get up before we have had adequate rest. Historically, this was important for survival, enabling us to adapt our sleep patterns according to our environment.  These days, many of us abuse this ability and live in a state of chronic sleep deprivation.

Sleep patterns also change systematically with age.  Babies have multiple short sleeps during the day, gradually reducing their number of daily sleep episodes until, by school age, many have dropped their day time sleeps altogether.  The body clock of teenagers is typically programmed for them to wake up late and go to bed late, making getting up for school challenging.  As we age, sleep becomes shorter, we wake up earlier and sleep becomes more fragmented.  These systematic changes mean that we tend to shift from being more "owl-like" as a teenager to more "lark-like" as we get older.


## HOW IT WORKS

The model shows the homeostatic process and the circadian modulated thresholds that cause switching and how they evolve with time over a sequence of 4 days.  For clarity, only the upper threshold is shown during wake and the lower threshold during sleep.   These can be viewed as representing the two different biorhythms: the homeostatic rhythm and the circadian rhythm.

You can select whether or not the sleep-wake cycle is following the body clock.  If the body clock is followed, then switching between wake and sleep occurs when the two different rhythms meet.  If the body clock is not followed, then switching between wake and sleep occurs at the times set by the boxes at the top of the display, labelled as Sun_wake, Sun_sleep etc.  The selected times are shaded in light grey in the main display window.

There are systematic changes in sleep with age.  It is not known exactly what changes occur in the body to cause these changes: but there is some evidence that as we get older the circadian and homeostatic processes weaken.  Within this NETLOGO model, changing the age slider does three things (i) reduces the amplitude of the circadian oscillation (ii) reduces the mean value of the upper threshold which is equivalent to reducing the strength of the homeostatic process (iii) the phase of the circadian rhythm compared with the light/dark cycle changes.  The motivation for the particular way in which these changes occur in the simulation comes from comparing experimental data on timing of sleep across the lifespan [2] with a mathematical model of sleep-wake regulation constructed by Phillips and Robinson [3], see [4] for more details.  Although the Phillips and Robinson model is more sophisticated than the two process presented in this NETLOGO model, nevertheless it has many of the same features and the two can be related in a systematic way, see [5].


## TERMS OF USE

This model is licensed under a Creative Commons License: see

[Creative Commons License](http://creativecommons.org/licenses/by-nd/3.0/)

## HOW TO USE IT

1. Set the age slider at the age you are interested in.
2. Set whether the model is running according to the body clock or not.  If not, then set up the wake and sleep times at the top of the main window.
3. Click on setup. 
4. Click on go/stop. You should see two lines move across the page, one oscillates up and down in an approximately regular way, this is the circadian modulated threshold.  The other is more of a saw-tooth shape.  This is the sleep pressure (the homeostat) and increases during wake and reduces during sleep.
 

## THINGS TO NOTICE

 If you run the model in the "not listening to your body clock" mode, then you may see that the biorhythms change color from black to red and from black to yellow.  The red parts correspond to times when your body clock is telling you that you really want to be asleep, but you have had to get up.  The yellow parts correspond to times when your body clock is telling you that you should be awake, and yet you are trying to sleep.  

  The times when you are feeling sleepy are also shown in the plot of alertness.  Alertness is measured by how widely separated the circadian and sleep pressure rhythms are.  Regions of "negative" alertness are shaded in red and correspond to points when your natural body rhythm is telling you that you should be asleep.

## THINGS TO TRY

Once you have run the model with one setting of the sliders, you can run the model again with a different setting by changing the sliders and then clicking on "Re-initialise".  This will plot the new rhythms without clearing the screen.  If you want to clear the screen, then press "Set-up".

Try setting the sleep and wake times so that you stay up all night on Sunday night.  What does the model say about how you should feel on Monday during the day?

If you fly to a different part of the world, then the times that your body wants to sleep are not the same as the times that societal pressures say that you should sleep.  You can see the impact of this by changing the jetlag button from zero.  Putting in a positive value of five is like moving East to a time zone that is five hours ahead of us; putting in a value of minus five is like moving West to a time zone that is five hours behind us. Note that the adaptation that our bodies make to a new time zone is not included in this version of the model: in real life, the effects of jetlag diminish after a few days because our body clock shifts to be in tune with the day-night (light-dark) cycle of our new location.  

There are two buttons, one labelled wake_timeconstant and one labelled sleep_timeconstant.  These describe how quickly sleep pressure builds up during wake and dissipates during sleep.  What happens if you make these smaller, say to 6, and set the "Listening to your biology" to Yes?   You should see that there are now multiple sleep episodes each day.  Any idea what this could describe?

## WHAT IF IT DOESN'T DESCRIBE MY SLEEP PATTERNS?

This particular model is set up to fit one particular measure of sleep, mid-sleep on free days, for an average population.  Mid-sleep on free days is the time of the middle of your sleep on a day that you could choose when you went to bed and when you got up.  So, for example, if you went to bed at midnight and got up at 10am, then your mid-sleep would be 5am.  There are, in fact, systematic differences between men and women and also large individual differences. For example, for any one age group, the mid-sleep on free days reported in [2] varied by two hours; even more for adults over 70.  One of the challenges for sleep researchers is taking account of this individual variability.

Another feature of this particular simulation is that it is assumed that you wake up naturally on Sunday morning at the time given by Sun_wake. Of course, this might not have been the case.  It would be possible to extend the model to run for more days and typically, if you follow the same daily pattern of when you go to bed and when you get up, then your sleepiness/alertness will settle in to a regular pattern over a period of a week or so.

## CREDITS AND REFERENCES

This netlogo model was coded by Anne Skeldon and is based on the two process model discussed in [1], with changes with age as described in [4].  For further information, please contact a.skeldon@surrey.ac.uk.

[1] S. Daan, D.G. Beersma and A.A. Borbely (1984) "Timing of human sleep: recovery process gated by a circadian pacemaker", Am. J. Physiol, 246, R161-83.
[2] T. Roenneberg et al (2012) "A marker for the end of adolescence", Current Biology, 14 pR1-38-R1039 [web address ](http://www.cell.com/current-biology/fulltext/S0960-9822(04)00928-5)
[3] A.J.K. Phillips, P.Y. Chen and P.A. Robinson (2010) "Proving the mechanisms of chronotype using quantitative modelling", J. Biol. Rhythms, 25: 217-227.
[4] D-J. Dijk, A.C. Skeldon, G.Derks, (2014) preprint.
[5] A.C. Skeldon, D-J. Dijk, G. Derks, (2014) "Mathematical models for sleep-wake dynamics: a comparison", [preprint](http://arxiv.org/abs/1311.1734).
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default
true
0
Polygon -7500403 true true 150 5 40 250 150 205 260 250

airplane
true
0
Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15

arrow
true
0
Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150

box
false
0
Polygon -7500403 true true 150 285 285 225 285 75 150 135
Polygon -7500403 true true 150 135 15 75 150 15 285 75
Polygon -7500403 true true 15 75 15 225 150 285 150 135
Line -16777216 false 150 285 150 135
Line -16777216 false 150 135 15 75
Line -16777216 false 150 135 285 75

bug
true
0
Circle -7500403 true true 96 182 108
Circle -7500403 true true 110 127 80
Circle -7500403 true true 110 75 80
Line -7500403 true 150 100 80 30
Line -7500403 true 150 100 220 30

butterfly
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0
Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 150 240
Polygon -7500403 true true 150 165 89 198 75 225 75 255 105 270 135 255 150 240
Polygon -7500403 true true 139 148 100 105 55 90 25 90 10 105 10 135 25 180 40 195 85 194 139 163
Polygon -7500403 true true 162 150 200 105 245 90 275 90 290 105 290 135 275 180 260 195 215 195 162 165
Polygon -16777216 true false 150 255 135 225 120 150 135 120 150 105 165 120 180 150 165 225
Circle -16777216 true false 135 90 30
Line -16777216 false 150 105 195 60
Line -16777216 false 150 105 105 60

car
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0
Polygon -7500403 true true 300 180 279 164 261 144 240 135 226 132 213 106 203 84 185 63 159 50 135 50 75 60 0 150 0 165 0 225 300 225 300 180
Circle -16777216 true false 180 180 90
Circle -16777216 true false 30 180 90
Polygon -16777216 true false 162 80 132 78 134 135 209 135 194 105 189 96 180 89
Circle -7500403 true true 47 195 58
Circle -7500403 true true 195 195 58

circle
false
0
Circle -7500403 true true 0 0 300

circle 2
false
0
Circle -7500403 true true 0 0 300
Circle -16777216 true false 30 30 240

cow
false
0
Polygon -7500403 true true 200 193 197 249 179 249 177 196 166 187 140 189 93 191 78 179 72 211 49 209 48 181 37 149 25 120 25 89 45 72 103 84 179 75 198 76 252 64 272 81 293 103 285 121 255 121 242 118 224 167
Polygon -7500403 true true 73 210 86 251 62 249 48 208
Polygon -7500403 true true 25 114 16 195 9 204 23 213 25 200 39 123

cylinder
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0
Circle -7500403 true true 0 0 300

dot
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0
Circle -7500403 true true 90 90 120

face happy
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0
Circle -7500403 true true 8 8 285
Circle -16777216 true false 60 75 60
Circle -16777216 true false 180 75 60
Polygon -16777216 true false 150 255 90 239 62 213 47 191 67 179 90 203 109 218 150 225 192 218 210 203 227 181 251 194 236 217 212 240

face neutral
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0
Circle -7500403 true true 8 7 285
Circle -16777216 true false 60 75 60
Circle -16777216 true false 180 75 60
Rectangle -16777216 true false 60 195 240 225

face sad
false
0
Circle -7500403 true true 8 8 285
Circle -16777216 true false 60 75 60
Circle -16777216 true false 180 75 60
Polygon -16777216 true false 150 168 90 184 62 210 47 232 67 244 90 220 109 205 150 198 192 205 210 220 227 242 251 229 236 206 212 183

fish
false
0
Polygon -1 true false 44 131 21 87 15 86 0 120 15 150 0 180 13 214 20 212 45 166
Polygon -1 true false 135 195 119 235 95 218 76 210 46 204 60 165
Polygon -1 true false 75 45 83 77 71 103 86 114 166 78 135 60
Polygon -7500403 true true 30 136 151 77 226 81 280 119 292 146 292 160 287 170 270 195 195 210 151 212 30 166
Circle -16777216 true false 215 106 30

flag
false
0
Rectangle -7500403 true true 60 15 75 300
Polygon -7500403 true true 90 150 270 90 90 30
Line -7500403 true 75 135 90 135
Line -7500403 true 75 45 90 45

flower
false
0
Polygon -10899396 true false 135 120 165 165 180 210 180 240 150 300 165 300 195 240 195 195 165 135
Circle -7500403 true true 85 132 38
Circle -7500403 true true 130 147 38
Circle -7500403 true true 192 85 38
Circle -7500403 true true 85 40 38
Circle -7500403 true true 177 40 38
Circle -7500403 true true 177 132 38
Circle -7500403 true true 70 85 38
Circle -7500403 true true 130 25 38
Circle -7500403 true true 96 51 108
Circle -16777216 true false 113 68 74
Polygon -10899396 true false 189 233 219 188 249 173 279 188 234 218
Polygon -10899396 true false 180 255 150 210 105 210 75 240 135 240

house
false
0
Rectangle -7500403 true true 45 120 255 285
Rectangle -16777216 true false 120 210 180 285
Polygon -7500403 true true 15 120 150 15 285 120
Line -16777216 false 30 120 270 120

leaf
false
0
Polygon -7500403 true true 150 210 135 195 120 210 60 210 30 195 60 180 60 165 15 135 30 120 15 105 40 104 45 90 60 90 90 105 105 120 120 120 105 60 120 60 135 30 150 15 165 30 180 60 195 60 180 120 195 120 210 105 240 90 255 90 263 104 285 105 270 120 285 135 240 165 240 180 270 195 240 210 180 210 165 195
Polygon -7500403 true true 135 195 135 240 120 255 105 255 105 285 135 285 165 240 165 195

line
true
0
Line -7500403 true 150 0 150 300

line half
true
0
Line -7500403 true 150 0 150 150

pentagon
false
0
Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120

person
false
0
Circle -7500403 true true 110 5 80
Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90
Rectangle -7500403 true true 127 79 172 94
Polygon -7500403 true true 195 90 240 150 225 180 165 105
Polygon -7500403 true true 105 90 60 150 75 180 135 105

plant
false
0
Rectangle -7500403 true true 135 90 165 300
Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285
Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285
Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210
Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135
Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135
Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60
Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90

sheep
false
15
Circle -1 true true 203 65 88
Circle -1 true true 70 65 162
Circle -1 true true 150 105 120
Polygon -7500403 true false 218 120 240 165 255 165 278 120
Circle -7500403 true false 214 72 67
Rectangle -1 true true 164 223 179 298
Polygon -1 true true 45 285 30 285 30 240 15 195 45 210
Circle -1 true true 3 83 150
Rectangle -1 true true 65 221 80 296
Polygon -1 true true 195 285 210 285 210 240 240 210 195 210
Polygon -7500403 true false 276 85 285 105 302 99 294 83
Polygon -7500403 true false 219 85 210 105 193 99 201 83

square
false
0
Rectangle -7500403 true true 30 30 270 270

square 2
false
0
Rectangle -7500403 true true 30 30 270 270
Rectangle -16777216 true false 60 60 240 240

star
false
0
Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108

sun
false
0
Circle -7500403 true true 75 75 150
Polygon -7500403 true true 300 150 240 120 240 180
Polygon -7500403 true true 150 0 120 60 180 60
Polygon -7500403 true true 150 300 120 240 180 240
Polygon -7500403 true true 0 150 60 120 60 180
Polygon -7500403 true true 60 195 105 240 45 255
Polygon -7500403 true true 60 105 105 60 45 45
Polygon -7500403 true true 195 60 240 105 255 45
Polygon -7500403 true true 240 195 195 240 255 255

target
false
0
Circle -7500403 true true 0 0 300
Circle -16777216 true false 30 30 240
Circle -7500403 true true 60 60 180
Circle -16777216 true false 90 90 120
Circle -7500403 true true 120 120 60

tree
false
0
Circle -7500403 true true 118 3 94
Rectangle -6459832 true false 120 195 180 300
Circle -7500403 true true 65 21 108
Circle -7500403 true true 116 41 127
Circle -7500403 true true 45 90 120
Circle -7500403 true true 104 74 152

triangle
false
0
Polygon -7500403 true true 150 30 15 255 285 255

triangle 2
false
0
Polygon -7500403 true true 150 30 15 255 285 255
Polygon -16777216 true false 151 99 225 223 75 224

truck
false
0
Rectangle -7500403 true true 4 45 195 187
Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194
Rectangle -1 true false 195 60 195 105
Polygon -16777216 true false 238 112 252 141 219 141 218 112
Circle -16777216 true false 234 174 42
Rectangle -7500403 true true 181 185 214 194
Circle -16777216 true false 144 174 42
Circle -16777216 true false 24 174 42
Circle -7500403 false true 24 174 42
Circle -7500403 false true 144 174 42
Circle -7500403 false true 234 174 42

turtle
true
0
Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210
Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105
Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105
Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87
Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210
Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99

wheel
false
0
Circle -7500403 true true 3 3 294
Circle -16777216 true false 30 30 240
Line -7500403 true 150 285 150 15
Line -7500403 true 15 150 285 150
Circle -7500403 true true 120 120 60
Line -7500403 true 216 40 79 269
Line -7500403 true 40 84 269 221
Line -7500403 true 40 216 269 79
Line -7500403 true 84 40 221 269

wolf
false
0
Polygon -16777216 true false 253 133 245 131 245 133
Polygon -7500403 true true 2 194 13 197 30 191 38 193 38 205 20 226 20 257 27 265 38 266 40 260 31 253 31 230 60 206 68 198 75 209 66 228 65 243 82 261 84 268 100 267 103 261 77 239 79 231 100 207 98 196 119 201 143 202 160 195 166 210 172 213 173 238 167 251 160 248 154 265 169 264 178 247 186 240 198 260 200 271 217 271 219 262 207 258 195 230 192 198 210 184 227 164 242 144 259 145 284 151 277 141 293 140 299 134 297 127 273 119 270 105
Polygon -7500403 true true -1 195 14 180 36 166 40 153 53 140 82 131 134 133 159 126 188 115 227 108 236 102 238 98 268 86 269 92 281 87 269 103 269 113

x
false
0
Polygon -7500403 true true 270 75 225 30 30 225 75 270
Polygon -7500403 true true 30 75 75 30 270 225 225 270
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NetLogo 6.0.1
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default
0.0
-0.2 0 0.0 1.0
0.0 1 1.0 0.0
0.2 0 0.0 1.0
link direction
true
0
Line -7500403 true 150 150 90 180
Line -7500403 true 150 150 210 180
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1
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