Covid-19 variation on the theme

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ACKNOWLEDGMENT

This model has been developed from the "COVID19Spread", developed by Anamaria Berea - see http://blog.modelingcommons.org/?id=801 . It's an alternate visualization of the Virus model from the Biology section of the NetLogo Models Library. It uses visualization techniques as recommended in the paper:

Kornhauser, D., Wilensky, U., & Rand, W. (2009). Design guidelines for agent based model visualization. Journal of Artificial Societies and Social Simulation (JASSS), 12(2), 1. http://ccl.northwestern.edu/papers/2009/Kornhauser,Wilensky&Rand_DesignGuidelinesABMViz.pdf.

WHAT IS IT?

This model simulates the transmission and perpetuation of a virus in a human population. This version includes alternative visualizations of the model.

Ecological biologists have suggested a number of factors which may influence the survival of a directly transmitted virus within a population. (Yorke, et al. "Seasonality and the requirements for perpetuation and eradication of viruses in populations." Journal of Epidemiology, volume 109, pages 103-123)

HOW IT WORKS

The model is initialized with a number of 10 to 1000 number-people, of which a subset of 1 to 100 are init-infected. People move randomly about the world in one of three states: healthy but susceptible to infection (green), sick and infectious (red), and healthy and immune (gray). People may die of infection or old age. When the population dips below the environment's "carrying capacity" (set at 300 in this model) healthy people may produce healthy (but susceptible) offspring.

The parameter "mobility" (see its relative slide) set the amplitude of the movements.

Some of these factors are summarized below with an explanation of how each one is treated in this model.

The density of the population

Population density affects how often infected, immune and susceptible individuals come into contact with each other. You can change the size of the initial population through the NUMBER-PEOPLE slider.

Population turnover

As individuals die, some who die will be infected, some will be susceptible and some will be immune. All the new individuals who are born, replacing those who die, will be susceptible. People may die from the virus, the chances of which are determined by the slider CHANCE-RECOVER, or they may die of old age.

In this model, people die of old age at the age of 50 years. Reproduction rate is constant in this model. Each turn, if the carrying capacity hasn't been reached, every healthy individual has a 1% chance to reproduce.

Degree of immunity

If a person has been infected and recovered, how immune are they to the virus? We often assume that immunity lasts a lifetime and is assured, but in some cases immunity wears off in time and immunity might not be absolutely secure. In this model, immunity is secure, but it only lasts for a year.

Infectiousness (or transmissibility)

How easily does the virus spread? Some viruses with which we are familiar spread very easily. Some viruses spread from the smallest contact every time. Others (the HIV virus, which is responsible for AIDS, for example) require significant contact, perhaps many times, before the virus is transmitted. In this model, infectiousness is determined by the INFECTIOUSNESS slider.

Duration of infectiousness

How long is a person infected before they either recover or die? This length of time is essentially the virus's window of opportunity for transmission to new hosts. In this model, duration of infectiousness is determined by the DURATION slider.

Hard-coded parameters

Four important parameters of this model are set as constants in the code (See setup-constants procedure). They can be exposed as sliders if desired. The turtles’ lifespan is set to 50 years, the carrying capacity of the world is set to 300, the duration of immunity is set to 52 weeks, and the birth-rate is set to a 1 in 100 chance of reproducing per tick when the number of people is less than the carrying capacity.

HOW TO USE IT

Each "tick" represents a week in the time scale of this model.

The INFECTIOUSNESS slider determines how great the chance is that virus transmission will occur when an infected person and susceptible person occupy the same patch. For instance, when the slider is set to 50, the virus will spread roughly once every two chance encounters.

The DURATION slider determines the number of weeks before an infected person either dies or recovers.

The CHANCE-RECOVER slider controls the likelihood that an infection will end in recovery/immunity. When this slider is set at zero, for instance, the infection is always deadly.

The SETUP button resets the graphics and plots and randomly distributes NUMBER-PEOPLE in the view. All but 10 of the people are set to be green susceptible people and 10 red infected people (of randomly distributed ages). The GO button starts the simulation and the plotting function.

The TURTLE-SHAPE chooser controls whether the people are visualized as person shapes or as circles.

When the SHOW-AGE? switch is on, each agent's age in years is displayed as its label.

When the WATCH-A-PERSON? switch is on, a single person at random, the subject, is selected for watching. The subject leaves a trail when it moves, green when the subject is healthy and red when it is sick. An inspector window is opened for that person. When the subject becomes infected, a link is created between the subject and the person who infected him. If one of those people dies, the link disappears. If the subject dies, a new subject is selected.

Three output monitors show the percent of the population that is infected, the percent that is immune, and the number of years that have passed. The plot shows (in their respective colors) the number of susceptible, infected, and immune people. It also shows the number of individuals in the total population in blue.

THINGS TO NOTICE

The factors controlled by the three sliders interact to influence how likely the virus is to thrive in this population. Notice that in all cases, these factors must create a balance in which an adequate number of potential hosts remain available to the virus and in which the virus can adequately access those hosts.

Often there will initially be an explosion of infection since no one in the population is immune. This approximates the initial "outbreak" of a viral infection in a population, one that often has devastating consequences for the humans concerned. Soon, however, the virus becomes less common as the population dynamics change. What ultimately happens to the virus is determined by the factors controlled by the sliders.

Notice that viruses that are too successful at first (infecting almost everyone) may not survive in the long term. Since everyone infected generally dies or becomes immune as a result, the potential number of hosts is often limited. The exception to the above is when the DURATION slider is set so high that population turnover (reproduction) can keep up and provide new hosts.

THINGS TO TRY

Think about how different slider values might approximate the dynamics of real-life viruses. The famous Ebola virus in central Africa has a very short duration, a very high infectiousness value, and an extremely low recovery rate. For all the fear this virus has raised, how successful is it? Set the sliders appropriately and watch what happens.

The HIV virus, which causes AIDS, has an extremely long duration, an extremely low recovery rate, but an extremely low infectiousness value. How does a virus with these slider values fare in this model?

EXTENDING THE MODEL

Add additional sliders controlling the carrying capacity of the world (how many people can be in the world at one time), the average lifespan of the people and their birth-rate.

Build a similar model simulating viral infection of a non-human host with very different reproductive rates, lifespans, and population densities.

Add a slider controlling how long immunity lasts. You could also make immunity imperfect, so that immune turtles still have a small chance of getting infected. This chance could get higher over time.

VISUALIZATION

The alternative visualization of the model comes from guidelines presented in Kornhauser, D., Wilensky, U., & Rand, W. (2009). http://ccl.northwestern.edu/papers/2009/Kornhauser,Wilensky&Rand_DesignGuidelinesABMViz.pdf.

The SHOW-AGE? visualization enables the user to track individual agents' lifespans.
The WATCH-A-PERSON visualization enables the user to focus on one subject and to see the "micro-level" interactions, to view which agent infects the subject. You can observe the green trail of a healthy individual, which becomes red when the person gets infected. Additionally, you can see the individual who transmitted the virus linked to the subject by a line.

RELATED MODELS

HIV
Virus
Virus on a Network

CREDITS AND REFERENCES

This model shows alternate visualizations of the Virus model. It uses visualization techniques as recommended in the paper:

Kornhauser, D., Wilensky, U., & Rand, W. (2009). Design guidelines for agent based model visualization. Journal of Artificial Societies and Social Simulation, JASSS, 12(2), 1.

HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

Wilensky, U. (1998). NetLogo Virus - Alternative Visualization model. http://ccl.northwestern.edu/netlogo/models/Virus-AlternativeVisualization. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Please cite the NetLogo software as:

Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

COPYRIGHT AND LICENSE

CC BY-NC-SA 3.0

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227.

Comments and Questions

Please start the discussion about this model! (You'll first need to log in.)

Click to Run Model

turtles-own
  [ sick?                ;; if true, the turtle is infectious
    remaining-immunity   ;; how many weeks of immunity the turtle has left
    sick-time            ;; how long, in days, the turtle has been infectious
    age ]                ;; how many weeks old the turtle is

globals
  [ %infected            ;; what % of the population is infectious
    %immune              ;; what % of the population is immune
    max-%infected        ;; maximun % infected population reached (at the peak)
    peak                 ;; day of the peak
    alive                ;; total population alive that tick
    now-infected         ;; number of people infected at the current day
    immune               ;; number of people immune at the present day
    total-infected       ;; total infected from the beginning
    lifespan             ;; the lifespan of a turtle
    chance-reproduce     ;; the probability of a turtle generating an offspring each tick
    chance-recover       ;; the probability of recovery at each tick
    carrying-capacity    ;; the number of turtles that can be in the world at one time
    immunity-duration ]  ;; how many weeks immunity lasts

;; The setup is divided into four procedures

to setup
  clear-all
  reset-ticks
  setup-constants
  setup-turtles
  update-global-variables
  update-display

  reset-ticks
end 

;; We create a variable number of turtles of which 1 are infectious,
;; and distribute them randomly

to setup-turtles
  create-turtles number-people
    [ setxy random-xcor random-ycor
      set age random lifespan
      set sick-time 0
      set remaining-immunity 0
      if age < 10 * 52 * 7 [set color blue]
      if age > 60 * 52 * 7 [set color yellow]
      set size .7 ;; easier to see
      get-healthy ]
  ask n-of init-infected turtles
    [ get-sick ]
  set total-infected (count turtles with [sick?])
end 

to get-sick ;; turtle procedure
  set sick? true
  set remaining-immunity 0
  set total-infected (total-infected + 1)
end 

to get-healthy ;; turtle procedure
  set sick? false
  set remaining-immunity 0
  set sick-time 0
end 

to become-immune ;; turtle procedure
  set sick? false
  set sick-time 0
  set remaining-immunity immunity-duration
  ask my-links [ die ] ;; remove link to turtle who infected us, if there was one
end 

;; This sets up basic constants of the model.

to setup-constants
  set lifespan 80 * 52 * 7     ;; 80 times 52 weeks times 7 days = 50 years = 2600 weeks old = 18200 days
  set carrying-capacity 1000
  set chance-reproduce 0.005 ;; birth rate per 1000 people per day
  set immunity-duration 52 * 7
  if Weather = "Hot-Humid" [set chance-recover .98]
  if Weather = "Hot-Dry" [set chance-recover .96]
  if Weather = "Cold-Dry" [set chance-recover .95]
  if Weather = "Cold-Humid" [set chance-recover .94]
end 

to go
  if all? turtles [not sick?]
  [stop]
  ask turtles [
    get-older
    move
    if sick? [ recover-or-die ]
    ifelse sick? [ infect ] [ reproduce ]
  ]
  update-global-variables
  update-display
  tick
end 

to update-global-variables
  if count turtles > 0
    [ set %infected (count turtles with [ sick? ] / count turtles) * 100
      set %immune (count turtles with [ immune? ] / count turtles) * 100
      set alive (count turtles)
      set now-infected (count turtles with [sick?])
      set immune (count turtles with [immune?])
      if %infected > max-%infected [set peak ticks + 1]
      if %infected > max-%infected [set max-%infected %infected]
      ;;set peak ticks + 1]
      ]
end 

to update-display
  ask turtles
    [ if shape != turtle-shape [ set shape turtle-shape ]
      set label ifelse-value show-age? [ floor (age / 364) ] [ "" ]
      set color ifelse-value sick? [ red ] [ ifelse-value immune? [ grey ] [ green ] ] ]
  stop-inspecting-dead-agents
  if watch-a-person? and subject = nobody
    [ watch one-of turtles with [ not hidden? ]
      clear-drawing
      ask subject [ pen-down ]
      inspect subject ]
  if not watch-a-person? and subject != nobody
    [ stop-inspecting subject
      ask subject
        [ pen-up
          ask my-links [ die ] ]
      clear-drawing
      reset-perspective ]
  ask patches [
  if Weather = "Hot-Humid" [set pcolor 68]
  if Weather = "Hot-Dry" [set pcolor 48]
  if Weather = "Cold-Dry" [set pcolor 38]
  if Weather = "Cold-Humid" [set pcolor 108]
  ]
end 

;;Turtle counting variables are advanced.

to get-older ;; turtle procedure
  ;; Turtles die of old age once their age exceeds the
  ;; lifespan (set at 80 years in this model).
  set age age + 1
  if age > lifespan [ die ]
  if age > 60 * 52 * 7 [ set chance-recover .93]
  if age < 60 * 52 * 7 [ set chance-recover .97]
  if immune? [ set remaining-immunity remaining-immunity - 1 ]
  if sick? [ set sick-time sick-time + 1 ]
end 

;; Turtles move about at random.

to move ;; turtle procedure
  rt random 100
  lt random 100
  fd mobility
end 

;; If a turtle is sick, it infects other turtles on the same patch.
;; Immune turtles don't get sick.

to infect ;; turtle procedure
  ask other turtles-here with [ not sick? and not immune? ]
    [ if random-float 100 < infectiousness
      [ get-sick
        if self = subject             ;; if its the watched turtle getting sick
          [ create-link-with myself   ;; create a link with the one that infected it
            [ set color red
              set thickness .3 ] ] ] ]
end 

;; Once the turtle has been sick long enough, it
;; either recovers (and becomes immune) or it dies.

to recover-or-die ;; turtle procedure
  if sick-time > duration * 7                       ;; If the turtle has survived past the virus' duration, then
    [ ifelse random-float 100 < chance-recover * 100   ;; either recover or die
      [ become-immune ]
      [ die ] ]
end 

;; If there are less turtles than the carrying-capacity
;; then turtles can reproduce.

to reproduce
  if count turtles < carrying-capacity and random-float 100 < chance-reproduce
    [ hatch 1
      [ set age 1
        lt 45 fd 1
        pen-up ;; in case we're hatched from the watched turtle
        get-healthy ] ]
end 

to-report immune?
  report remaining-immunity > 0
end 

to startup
  setup-constants ;; so that carrying-capacity can be used as upper bound of number-people slider
end 


; Copyright 1998 Uri Wilensky.
; See Info tab for full copyright and license.

There are 2 versions of this model.

		Uploaded by	When	Description	Download
		Davide Vignoni	over 5 years ago	at least 1 init. infected!	Download this version
		Davide Vignoni	over 5 years ago	Initial upload	Download this version

Attached files

File	Type	Description	Last updated
COVID_19_DaVig view.png	png	view	over 5 years ago, by Davide Vignoni	Download
Screenshot_2020-04-14_14:34:54.png	png	screenshot	over 5 years ago, by Davide Vignoni	Download

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