turtles-own [ sick? ;; if true, the turtle is infectious old? ;; if true, tur turtle is older than 60 years my-chance-recover ;; if old? is chnance-recover-elders else chance-recover remaining-immunity ;; how many days of immunity the turtle has left sick-time ;; how long, in days, the turtle has been infectious age ;; how many days old the turtle is allowed-movement? ] ;; if the turtle is part of the % population allowed to move globals [ %infected ;; what % of the population is infectious %immune ;; what % of the population is immune lifespan ;; the lifespan of a turtle immunity-duration ;; how many days immunity lasts ended-simulation? ] ;; if the simulation is ended because no one is sick ;; The setup is divided into four procedures to setup clear-all setup-constants setup-turtles update-global-variables update-display reset-ticks end ;; We create a variable number of turtles of which 10 are infectious, ;; and distribute them randomly to setup-turtles create-turtles initial-number-people [ setxy random-xcor random-ycor set age random lifespan ifelse age > 365 * 60 [ set old? true ] [ set old? false ] set sick-time 0 set remaining-immunity 0 set size 1.5 ;; easier to see get-healthy ifelse random 100 < %movement-allowed [set allowed-movement? true] [set allowed-movement? false] ] ask n-of 1 turtles [ get-sick ] end to get-sick ;; turtle procedure set sick? true set remaining-immunity 0 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 end ;; This sets up basic constants of the model. to setup-constants set lifespan 90 * 365 ;; 90 times 365 days = 50 years = 32850 days old set immunity-duration 260 ;; this value is approximated for the sake of testing, not based in scientific knowledge. set ended-simulation? false end to go if not ended-simulation? [ ask turtles [ get-older move if sick? [ recover-or-die ] if sick? [infect ] ] 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 ended-simulation? %infected = 0 ] ;;the simulation ends when no turtles are infected end to update-display ask turtles [ if turtle-shape = "circle" [set shape "circle" ] if turtle-shape = "person" [set shape "person" ] if turtle-shape = "person-age" [ ifelse age > 60 * 365 [ set shape "person farmer" ][ set shape "person"]] set color ifelse-value sick? [ red ] [ ifelse-value immune? [ grey ] [ green ] ] ] end ;;Turtle counting variables are advanced. to get-older ;; turtle procedure ifelse age > lifespan [ die ] [if age > 60 * 360 [ set old? true ] ] 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 ;; ifelse random 100 < %movement-allowed [set allowed-movement? true] [set allowed-movement? false] uncomment this line if want to change the proportion of population that can move while executing the model if allowed-movement? [ fd 1 ] ;;fd 1 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 ] ] end ;; Once the turtle has been sick long enough, it ;; either recovers (and becomes immune) or it dies. to recover-or-die ;; turtle procedure ifelse old? [ set my-chance-recover chance-recover-elders ] [ set my-chance-recover chance-recover ] if sick-time > duration ;; If the turtle has survived past the virus' duration, then [ ifelse random-float 100 < my-chance-recover ;; either recover or die [ become-immune ] [ die ] ] end to-report immune? report remaining-immunity > 0 end to startup setup-constants end ; Code adapted by Maite Lopez-Sanchez from the Virus Model (by Uri Wilensky). @#$#@#$#@ GRAPHICS-WINDOW 280 10 778 509 -1 -1 14.0 1 10 1 1 1 0 1 1 1 -17 17 -17 17 1 1 1 ticks 30.0 SLIDER 40 210 234 243 duration duration 0.0 99.0 20.0 1.0 1 days HORIZONTAL SLIDER 40 285 234 318 chance-recover chance-recover 0.0 100.0 75.0 1.0 1 % HORIZONTAL SLIDER 40 167 234 200 infectiousness infectiousness 0.0 100.0 100.0 1.0 1 % HORIZONTAL BUTTON 62 48 132 83 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 138 48 209 84 NIL go T 1 T OBSERVER NIL NIL NIL NIL 0 PLOT 815 170 1067 334 Populations days people 0.0 52.0 0.0 200.0 true true "" "" PENS "sick" 1.0 0 -2674135 true "" "plot count turtles with [ sick? ]" "immune" 1.0 0 -7500403 true "" "plot count turtles with [ immune? ]" "healthy" 1.0 0 -10899396 true "" "plot count turtles with [ not sick? and not immune? ]" "no-sick" 1.0 0 -13345367 true "" "plot count turtles with [ immune? or not sick? ]" SLIDER 40 100 234 133 initial-number-people initial-number-people 2 200 200.0 1 1 NIL HORIZONTAL MONITOR 815 100 890 145 NIL %infected 1 1 11 MONITOR 892 100 966 145 NIL %immune 1 1 11 MONITOR 1000 100 1074 145 months ticks / 30 1 1 11 CHOOSER 40 460 185 505 turtle-shape turtle-shape "person" "circle" "person-age" 2 MONITOR 815 25 927 70 current population count turtles 17 1 11 MONITOR 935 25 1077 70 current elders count turtles with [ old? = true ] 0 1 11 SLIDER 40 325 227 358 chance-recover-elders chance-recover-elders 0 100 25.0 1 1 % HORIZONTAL SLIDER 40 395 222 428 %movement-allowed %movement-allowed 0 100 100.0 1 1 % HORIZONTAL TEXTBOX 30 10 250 56 Covid-19 virus simulator 20 105.0 1 PLOT 820 350 1020 500 sick curve days people 0.0 10.0 0.0 10.0 true false "" "" PENS "sick" 1.0 0 -2674135 true "" "plot count turtles with [ sick? ] " @#$#@#$#@ ## WHAT IS IT? Inspired in the covid-19 (aka coronavirus) pandemia, this simplified model simulates the transmission of a virus in a human population. This model is an adaptation by Maite Lopez-Sanchez (Universitat de Barcelona) of the Virus model from the NetLogo library. Wilensky, U. (1998). http://ccl.northwestern.edu/netlogo/models/Virus. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. ## HOW IT WORKS The model is initialized with 200 people, of which only 1 is 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. Upon setup, population is assigned a random age. Elders (those older than 60 years old) have a different risk to die from the disease. 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 INITIAL-NUMBER-PEOPLE slider. ### Population decrease People may die from the virus, the chances of which are determined by the slider CHANCE-RECOVER. Elder people can have a different (usually lower) chance. This slider is CHANCE-RECOVER-ELDERS. ### 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 260 days. ### 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.Since covid-19 spreads quite easily 100% is the default value. ### 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 90 years and the duration of immunity is set to 260 days. ## HOW TO USE IT Each "tick" represents a day 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 days 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 CHANCE-RECOVER-ELDERS slider controls the likelihood that an infection of an elder (age > 60 years) 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 1 of the people are set to be green susceptible people and 1 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. Furthermore, person-age distinguishes elders (shown with a walking stick) from the rest. Three output monitors show the percent of the population that is infected, the percent that is immune, and the number of days that have passed. The plot shows (in their respective colors) the number of susceptible, infected, and immune people. It also shows the number of non-sick (healthy and immune) population in blue. ## THINGS TO NOTICE The factors controlled by the five 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. ## THINGS TO TRY Think about how different slider values might approximate the dynamics of different scenarios. 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? For the covid-19, it tipically produces a single bell-shaped distribution. ## VISUALIZATION The circle 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 circle visualization in this model is supposed to make it easier to see when agents interact because overlap is easier to see between circles than between the "people" shapes. In the circle visualization, the circles merge to create new compound shapes. Thus, it is easier to perceive new compound shapes in the circle visualization. Does the circle visualization make it easier for you to see what is happening? ## RELATED MODELS * Virus * HIV * Virus on a Network ## CREDITS AND REFERENCES This model is an adaptation by Maite Lopez-Sanchez (Universitat de Barcelona) of the Virus model from the NetLogo library. Wilensky, U. (1998). http://ccl.northwestern.edu/netlogo/models/Virus. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. ## HOW TO CITE Please cite the NetLogo software as: * Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. 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