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covid-19.nlogo
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; Global constants
globals [
; Denotes the range of a person's heading
heading-range
; Denotes the range of a person's forward movement
forward-movement-range
; Denotes the range of a person's vision
vision
; Denotes the the maximum angle of a person's vision
angle
; Denotes the horizontal limit of the inside area
horizontal-inside-bound
; Denotes the vertical limit of the inside area
vertical-inside-bound
; Denotes a slight margin of error in order to avoid people spawning exactly on the edge of their area
margin-of-error
; Denotes the previous state of non-movement
is-non-movement-before
; Denotes the list of the only agents allowed to move
allowed-list
; Denotes the death rate for the COVID-19
; (https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200306-sitrep-46-covid-19.pdf?sfvrsn=96b04adf_2)
death-rate
; Denotes the mean incubation period for the virus (in hours)
; (https://www.jwatch.org/na51083/2020/03/13/covid-19-incubation-period-update)
mean-incubation-period
; Denotes the mean duration of the virus (in hours) from when symptoms start appearing (after the incubation period) to potential recovery
; (https://ourworldindata.org/coronavirus#how-long-does-covid-19-last)
mean-duration
]
; Patch variables
patches-own [
; Denotes whether this patch is part of the inside area or not
is-inside
]
; Turtle variables
turtles-own [
; Denotes whether this person is infected with the COVID-19 virus or not
is-infected
; Denotes whether this person is immune or not
; A person who survives the virus will be immune to it
; (https://www.independent.co.uk/life-style/health-and-families/coronavirus-immunity-reinfection-get-covid-19-twice-sick-spread-relapse-a9400691.html)
is-immune
; Denotes how long it will take until this person starts showing symptoms
incubation-period-left
; Denotes how long it will take until this person gets better from the time of infection (if the person doesn't die)
time-infected-left
]
; Set the breeds up
breed [insiders insider]
breed [outsiders outsider]
; Set the model up
to setup
; Start form a clean slate
clear-all
reset-ticks
; Set the global variables
set-globals
; Set the environment up
set-patches
; Set the agents up
set-people
end
; Set all global constants
to set-globals
set heading-range 45
set forward-movement-range 2
set vision 2
set angle 180
set horizontal-inside-bound 15
set vertical-inside-bound 15
set margin-of-error 1
set allowed-list turtles
ifelse non-movement [
set is-non-movement-before 0
][
set is-non-movement-before 1
]
set death-rate 0.03
set mean-incubation-period 132
set mean-duration 336
end
; Set all patches
to set-patches
; Label an inside square as the inside area, then color it appropriately
; Color the resulting outside areas appropriately as well
ask patches [
; If the patch is within the bounds specified as part of the inside area, label and color it as such
ifelse pxcor >= (- horizontal-inside-bound) and pxcor <= horizontal-inside-bound and pycor >= (- vertical-inside-bound) and pycor <= vertical-inside-bound [
set is-inside 1
set pcolor 7
] [
set is-inside 0
set pcolor 9
]
]
end
; Set all people
to set-people
; Use a person graphic
set-default-shape turtles "person"
; This person hasn't been infected yet (for now)
ask turtles [
set is-infected 0
set is-immune 0
set incubation-period-left 0
set time-infected-left 0
]
set-insiders
set-outsiders
end
; Set the insiders up
to set-insiders
; First of all, set the number of insiders initially inside (their area)
create-insiders insiders-inside-count [
setxy ((random-float (2 * (horizontal-inside-bound - margin-of-error) + 1)) - (horizontal-inside-bound - margin-of-error)) ((random-float (2 * (vertical-inside-bound - margin-of-error) + 1)) - (vertical-inside-bound - margin-of-error))
; Determine if this person will initially have the virus (depending on the user input)
ifelse random-float 100 < insiders-inside-infected [
get-infected
] [
set color 35
]
]
; Then set the number of insiders initially outside (not their area)
create-insiders insiders-outside-count [
let candidate-x random-xcor
let candidate-y random-ycor
while [candidate-x + margin-of-error >= (- horizontal-inside-bound) and candidate-x - margin-of-error <= horizontal-inside-bound and candidate-y + margin-of-error >= (- vertical-inside-bound) and candidate-y - margin-of-error <= vertical-inside-bound][
set candidate-x random-xcor
set candidate-y random-ycor
]
setxy candidate-x candidate-y
; Determine if this person will initially have the virus (depending on the user input)
ifelse random-float 100 < insiders-outside-infected [
get-infected
] [
set color 35
]
]
end
; Set the outsiders up
to set-outsiders
; First of all, set the number of outsiders initially outside (their area)
create-outsiders outsiders-outside-count [
let candidate-x random-xcor
let candidate-y random-ycor
while [candidate-x + margin-of-error >= (- horizontal-inside-bound) and candidate-x - margin-of-error <= horizontal-inside-bound and candidate-y + margin-of-error >= (- vertical-inside-bound) and candidate-y - margin-of-error <= vertical-inside-bound][
set candidate-x random-xcor
set candidate-y random-ycor
]
setxy candidate-x candidate-y
; Determine if this person will initially have the virus (depending on the user input)
ifelse random-float 100 < outsiders-outside-infected [
get-infected
] [
set color 36
]
]
; Then set the number of outsiders initially inside (not their area)
create-outsiders outsiders-inside-count [
setxy ((random-float (2 * (horizontal-inside-bound - margin-of-error) + 1)) - (horizontal-inside-bound - margin-of-error)) ((random-float (2 * (vertical-inside-bound - margin-of-error) + 1)) - (vertical-inside-bound - margin-of-error))
; Determine if this person will initially have the virus (depending on the user input)
ifelse random-float 100 < outsiders-inside-infected [
get-infected
] [
set color 36
]
]
end
; Infect this person
to get-infected
set is-infected 1
; Set the incubation period and duration (in hours) based on the given averages
set incubation-period-left floor (random-normal mean-incubation-period 1)
; Take the incubation period into consideration when setting up the countdown for the duration of the disease
set time-infected-left floor ((random-normal mean-duration 1) + incubation-period-left)
set color 63
end
; Run the model
to go
; If there are no more infections, halt
if count turtles with [is-infected = 1] = 0 [
stop
]
; If non-movement measures are proposed, prepare the list of only agents to be allowed
ifelse non-movement [
if is-non-movement-before = 0 [
set is-non-movement-before 1
let turtle-count count turtles
set allowed-list n-of ((100 - non-movement-percentage) / 100 * turtle-count) turtles
]
][
if is-non-movement-before = 1 [
set is-non-movement-before 0
]
]
ask turtles [
; Make the people move around
; If non-movement measures are in place, check if they are allowed
if (not non-movement) or (non-movement and member? self allowed-list) [
move-people
]
; Manage each person's infection status
manage-infection
]
tick
end
; Manage each person's infection status
to manage-infection
; Manage infected people
if is-infected = 1 [
; If the patch this person is on has other people on it and at least one of those people are infected, there is a chance that this person will infect the others too
ask other turtles-here with [
is-infected = 0 and is-immune = 0
][
if random-float 100 < infectiousness [
get-infected
]
]
; Should this person die?
; The average death rate is 3% - we assume that this is the case over the average duration of the virus (336 hours or 2 weeks)
; Hence, there should be a 3% / 336 (~0.009%) chance of dying each hour
if random-float 1 < (death-rate / mean-duration) [
die
]
; Count down the virus incubation and duration period
if incubation-period-left > 0 [
set incubation-period-left incubation-period-left - 1
]
ifelse time-infected-left > 0 [
set time-infected-left time-infected-left - 1
][
; If the time infected has lapsed, the person is now healthy again (and immune to the virus)
set is-infected 0
set is-immune 1
ifelse breed = insiders [
set color 35
][
set color 36
]
]
]
end
; Move each person
to move-people
; Try moving some heading and distance away
let candidate-heading (random-float (2 * heading-range + 1) - heading-range)
let candidate-movement ((random-float forward-movement-range) / 5)
right candidate-heading
let candidate-patch patch-ahead candidate-movement
; If there are avoidance measures enforced...
if avoidance [
if random-float 100 < avoidance-percentage [
; Decide whether to enforce it on this specific person (depends on the percentage of the avoidance)
if any? (other turtles in-cone vision angle) [
set candidate-movement 0
]
]
]
; If there is a lockdown enforced...
if is-lockdown [
; Decide whether to enforce it on this specific person (depends on the strictness of the lockdown)
if random-float 100 < lockdown-strictness [
; If the person is going from outside to inside, or from inside to outside, don't allow it to; make the person go another direction
while [(([is-inside] of patch-here = 0 and [is-inside] of candidate-patch = 1) or ([is-inside] of patch-here = 1 and [is-inside] of candidate-patch = 0))] [
set candidate-heading (random-float (2 * heading-range + 1) - heading-range)
right candidate-heading
set candidate-patch patch-ahead candidate-movement
]
]
]
forward candidate-movement
end
@#$#@#$#@
GRAPHICS-WINDOW
434
10
930
507
-1
-1
8.0
1
10
1
1
1
0
1
1
1
-30
30
-30
30
1
1
1
hours
30.0
BUTTON
50
10
223
43
NIL
setup
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1
BUTTON
235
10
430
43
NIL
go
T
1
T
OBSERVER
NIL
NIL
NIL
NIL
0
SLIDER
50
75
222
108
insiders-inside-count
insiders-inside-count
0
500
100.0
1
1
NIL
HORIZONTAL
SLIDER
50
197
223
230
outsiders-outside-count
outsiders-outside-count
0
500
100.0
1
1
NIL
HORIZONTAL
SLIDER
50
117
222
150
insiders-outside-count
insiders-outside-count
0
500
100.0
1
1
NIL
HORIZONTAL
SLIDER
50
157
222
190
outsiders-inside-count
outsiders-inside-count
0
500
100.0
1
1
NIL
HORIZONTAL
SWITCH
50
315
225
348
is-lockdown
is-lockdown
1
1
-1000
SLIDER
234
315
429
348
lockdown-strictness
lockdown-strictness
1
100
90.0
1
1
%
HORIZONTAL
SLIDER
235
77
430
110
insiders-inside-infected
insiders-inside-infected
0
100
1.0
1
1
%
HORIZONTAL
SLIDER
235
117
430
150
insiders-outside-infected
insiders-outside-infected
0
100
0.0
1
1
%
HORIZONTAL
SLIDER
235
157
430
190
outsiders-inside-infected
outsiders-inside-infected
0
100
0.0
1
1
%
HORIZONTAL
SLIDER
235
197
430
230
outsiders-outside-infected
outsiders-outside-infected
0
100
0.0
1
1
%
HORIZONTAL
SLIDER
50
255
430
288
infectiousness
infectiousness
1
100
10.0
1
1
%
HORIZONTAL
PLOT
935
10
1335
255
Total COVID-19 infections
time
number of people
0.0
10.0
0.0
10.0
true
true
"" ""
PENS
"total infected" 1.0 0 -2674135 true "" "plot count turtles with [is-infected = 1]"
"population" 1.0 0 -7500403 true "" "plot count turtles"
"insiders infected" 1.0 0 -13840069 true "" "plot count insiders with [is-infected = 1]"
"outsiders infected" 1.0 0 -13345367 true "" "plot count outsiders with [is-infected = 1]"
MONITOR
935
260
1025
305
Infected people
count turtles with [is-infected = 1]
17
1
11
MONITOR
1030
260
1115
305
Healthy people
count turtles with [is-infected = 0]
17
1
11
MONITOR
1120
260
1335
305
Population
count turtles
17
1
11
PLOT
935
310
1130
460
Insider infections
time
number of people
0.0
10.0
0.0
10.0
true
false
"" ""
PENS
"infected" 1.0 0 -13840069 true "" "plot count insiders with [is-infected = 1]"
"population" 1.0 0 -7500403 true "" "plot count insiders"
PLOT
1135
310
1335
460
Outsider infections
time
number of people
0.0
10.0
0.0
10.0
true
false
"" ""
PENS
"default" 1.0 0 -13345367 true "" "plot count outsiders with [is-infected = 1]"
"population" 1.0 0 -7500403 true "" "plot count outsiders"
MONITOR
935
465
1035
510
Infected insiders
count insiders with [is-infected = 1]
17
1
11
MONITOR
1040
465
1130
510
Healthy insiders
count insiders with [is-infected = 0]
17
1
11
MONITOR
1135
465
1235
510
Infected outsiders
count outsiders with [is-infected = 1]
17
1
11
MONITOR
1240
465
1335
510
Healthy outsiders
count outsiders with [is-infected = 0]
17
1
11
SWITCH
50
470
225
503
avoidance
avoidance
1
1
-1000
SWITCH
50
430
225
463
non-movement
non-movement
1
1
-1000
SLIDER
235
430
430
463
non-movement-percentage
non-movement-percentage
1
100
90.0
1
1
%
HORIZONTAL
TEXTBOX
50
60
200
78
Initial population controls
11
0.0
1
TEXTBOX
50
240
200
258
Virus infectiousness control
11
0.0
1
TEXTBOX
50
380
420
425
Social distancing measures\nNOTE: Changes to the non-movement percentage slider may only be made when the movement percentage slider is off.
11
0.0
1
TEXTBOX
50
300
200
318
Lockdown controls
11
0.0
1
SLIDER
235
470
430
503
avoidance-percentage
avoidance-percentage
1
100
90.0
1
1
%
HORIZONTAL
@#$#@#$#@
## WHAT IS IT?
On November or December 2019, a virus called the Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was first transmitted to humans, from what is thought to be an animal origin, causing a highly contagious disease. Many months later, it has become the cause of a full-blown pandemic with devastating worldwide ramifications. This disease was given the name **Coronavirus disease 2019 (COVID-19)**.
Numerous prevention measures have been devised by different authorities all around the world in an effort to "flatten the curve", referring to the attempt to decrease the peak of the disease's epidemic curve, or at to least prolong the incidence of infections over a larger period of time to avoid overwhelming health services. Some of these measures include:
- A forced quarantine, or a **lockdown**, referring to the practice of isolating a region to prevent infections from spilling over outside of it or spreading into it.
- **Social distancing** measures, referring to the practice of avoiding social contact in an effort to prevent oneself from being *infected* and/or to prevent oneself from being the *infector*.
Numerous studies and simulations have been conducted by researchers on the attempted dampening of the spread of the virus through the measures above. *This agent-based model attempts do the same, but introduces the concept of regions and how the virus spreads between them, as well as how the preventive measures affect the transmission of the virus not just between the people, but between different regions as well.*
## HOW IT WORKS
### Regions and people
There are two regions defined in this model, an inner region (**inside**) and an outer one (**outside**). There are people who live in these regions. People who live inside are called **insiders** while the ones who live outside our called **outsiders**. However, these people do not necessarily reside in their home regions at any given time. Outsiders may visit inside, and insiders may visit outside. Just like real-world regions, people who live in a place do not necessarily have to be *there* in that place. This model takes that observation into account.
### The virus and its effects
When a person gets COVID-19, that person likely won't immediately experience any symptoms. It may take some time for it to show (or maybe none at all, in the case of asymptomatic people, but that's out of this model's scope). This period is called the **incubation period** of the virus - the period between when a person first gets infected with the virus and when a person actually shows symptoms due to the virus. The mean incubation period of the virus is 5.5 days (132 hours) [1]. This has been considered in the model (go look at the code - it's there).
After a person starts displaying symptoms, the mean time until a person recovers from it is around two weeks (336 hours) [2]. This period is referred to as the **duration** of the virus - the period between when a person first shows symptoms of the virus and when a person recovers from it. That is, if the person *does* recover. The thing is, the virus carries a mortality rate of around 3% [3]. In reality, the morality rate differs with the age range of an infected patient. However, this model does not incorporate the concept of age. All persons are *ageless*, and no people die of old age in the model. What people *may* die of is the coronavirus, of course. However, when they don't, they recover. And when they do recover, that person is assumed to be permanently immune from the virus [4].
### Preventive measures
Three types of preventive measures are featured in this model. First is the **lockdown**, as explained earlier. When the lockdown is in place, people may not travel between the regions. The other measures fall under social distancing, and this model identifies two of them, **non-movement** and **avoidance**. Non-movement is the practice of simply staying put to maintain social distance with others, while avoidance is the practice of actively maintaining spaces between other people.
### Model overview
The model starts with a set number of people with the virus. The people move about randomly anywhere (except when preventive measures are in place, of course). The time in the model is measured in terms of **hours**, and it is every hour when the people try to move. When people occupy the same space in the model, there is a chance that the other people in that space gets infected. Otherwise, the virus stays with the person until that person either dies from it or recovers from it. The model stops when there are no more COVID-19 infections in all of the people.
## HOW TO USE IT
### Setup and go
The setup button is used to set the model's initial state up, while the go button is used to start running the model (or to pause it). Before clicking the setup button, make sure that you have set the initial population controls to what you desire. You may also choose the appropriate percentages of the population who initially have infections. Note that because the model stops immediately when there are no more infected people, you may have to press setup a few more times until a few infected people are initially created.
### Virus infectiousness control
As stated earlier, when an infected person occupies a space in the model with other people in it, there is a chance that at least one of those people will become infected. That chance is dictated by the virus infectiousness control slider wherein one may select an infection rate of 1% (very unlikely to infect someone) to 100% (all people who come in contact with an infected person become infected as well). Take note that in reality, the infection rate of the virus is denoted by far more complicated variables and parameters such as the virus' basic reproduction number, which says how many other infections a person is responsible for on average. But that is out of this model's scope for now.
### Lockdown controls
This dictates whether people may travel in between the regions or not. You may also choose how strict the lockdown is going to be, from 1% (very lax) to 100% (absolute lockdown).
### Social distancing measures
There are two classes of controls under the social distancing measures. First are the non-movement controls. The controls contain a switch to turn non-movement on or off. The percentage of people practicing non-movement are controlled by the non-movement percentage slider next to the switch, from 1% (very few people practicing it) to 100% (everyone does not move). Note that the non-movement percentage slider only takes effect on the model every time the non-movement switch has been turned on from the off position. Internally, what this does is create a list of "whitelisted" people that are allowed to move, of course reflecting the appropriate percentage as selected by the slider.
The second control, the avoidance switch, merely activates or deactivates the practice of separation between all people. When the avoidance switch is on, each person has a "visibility cone" 180 degrees wide and 2 units ahead. Whenever a person sees someone else in here, the person does not continue to make his/her planned move to avoid that person. The number of people who practice avoidance is controlled by the avoidance percentage slider.
## THINGS TO NOTICE
Set the initial population up. Remember the total number of people you have set up. Run the model and let the COVID-19 infections swell and then decline. Several plots and monitors are shown to the right. Note that the plots show a gray line which starts high and then may slightly decline. Also note a monitor called *population*. This describes the total population of all people in the model. You may notice that this number is slightly less than your initial population setup. This is because some people have actually died due to the infection. Though you may sometimes not observe deaths when your initial populations are small enough (meaning everyone survived the outbreak).
## THINGS TO TRY
How would you "flatten the curve"? The goal of the preventive measures is to flatten the epidemic curve. That is, the goal is to prevent a large acceleration in the number of cases.
Play around with the sliders and experiment with different combinations of preventive measures as well as with the differing population densities between of the regions. See how well each combination of measures and parameters flattens the epidemic curve. Here are some things you could explore:
- Which appears to be the most effective combination of measures to flatten the curve?
- Is there a single measure which appears to be the most effective way to flatten the curve?
- What happens when a measure is implemented when the virus has already infected a lot of people? Would it still be effective?
- What happens when a measure is lifted when a number of people have already recovered? Would it be safe to do so? Or would this trigger another surge of infection rates?
- What happens when the strictness of a measure is modified while it is in place? How would this affect the infection rate of the virus?
## EXTENDING THE MODEL
More parameters could be added to this model. Perhaps the basic reproduction number could be modeled in an agent-based context. Or maybe incorporate some crowd clumping characteristics which humans are known to do and see how that impacts the spread of the infections.
## RELATED MODELS
This model is inspired by the Virus model under the Biology section. I've omitted some of its features (e.g., the concept of aging and creating offspring) and pegged some values to a fixed constant (e.g., mortality rate) in order to focus on the aspects of the specific virus causing the COVID-19 pandemic.
## CREDITS AND REFERENCES
[1] https://www.jwatch.org/na51083/2020/03/13/covid-19-incubation-period-update
[2] https://ourworldindata.org/coronavirus#how-long-does-covid-19-last
[3] https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200306-sitrep-46-covid-19.pdf?sfvrsn=96b04adf_2
[4] https://www.independent.co.uk/life-style/health-and-families/coronavirus-immunity-reinfection-get-covid-19-twice-sick-spread-relapse-a9400691.html
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