turtles-own [ sick? ;; if true, the turtle is infectious immune? ;; if true, the turtle can't be infected sick-count ;; how long the turtle has been infectious age ] ;; how many weeks old the turtle is globals [ weeks ;; each tick is called a week %infected ;; what % of the population is infectious %immune ;; what % of the population is immune lifespan ;; the average lifespan of a turtle average-offspring ;; the average number of offspring a turtle could have carrying-capacity ] ;; the number of turtles that can be in the world at one time ;; The setup is divided into three subroutines to setup ca set weeks 0 setup-constants setup-turtles update-plot update-global-variables end ;; We create a variable number of turtles of which 10 are infectious, ;; and distribute them randomly to setup-turtles set-default-shape turtles "person" crt people [ setxy random-xcor random-ycor set age random lifespan set sick-count 0 set immune? false set size 1.5 ;; easier to see get-healthy ] ask n-of (count turtles * initial-sick-people / 100) turtles [ get-sick ] if watch-turtle? [ watch one-of turtles ask subject [ pd ask other turtles [ ht ] ] ] end to get-sick ;; turtle procedure set sick? true set immune? false set color red end to get-healthy ;; turtle procedure set sick? false set immune? false set sick-count 0 set color green end to become-immune ;; turtle procedure set sick? false set sick-count 0 set immune? true set color violet + 2 end to setup-constants set lifespan 100 set carrying-capacity 750 set average-offspring 4 end to go if hide-children? [ ask turtles with [ self != subject ] [ ht ] ] if watch-turtle? [ if subject = nobody [ ifelse hide-children? [ stop ] [ if any? turtles with [ not hidden? ] [ watch one-of turtles with [ not hidden? ] ] ] ] ] ifelse hide-green? [ ask turtles with [ color = green ] [ ht ] ] [ ask turtles with [ color = green ] [ st ] ] ifelse hide-violet? [ ask turtles with [ color = violet + 2 ] [ ht ] ] [ ask turtles with [ color = violet + 2 ] [ st ] ] ifelse hide-red? [ ask turtles with [ color = red ] [ ht ] ] [ ask turtles with [ color = red ] [ st ] ] set weeks (weeks + 1) get-older move infect recover reproduce update-global-variables update-plot 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 ] end ;;Turtle counting variables are advanced. to get-older ask turtles [ set age (age + 1) if sick? [ set sick-count (sick-count + 1) ] ;; Turtles die of old age once their age equals the ;; lifespan (set at 1500 in this model). if age > lifespan [ die ] ] end ;;Turtles move about at random. to move ask turtles [ rt random-float 100 - random-float 100 fd 1 ] end ;; If a turtle is sick, it infects other turtles on the same patch. ;; Immune turtles don't get sick. to infect ask turtles with [sick?] [ ask other turtles-here with [ not immune? and not sick? ] [ if (random-float 100) < infectiousness [ get-sick if connect? [ create-link-from myself ] ] ] ] end ;; Once the turtle has been sick long enough, it ;; either recovers (and becomes immune) or it dies. to recover ask turtles with [sick?] [ if (random sick-count) > (lifespan * (duration / 100)) ;; If the turtle has survived past the virus' duration, then [ ifelse ((random-float 100) < chance-recover) ;; either recover or die [ become-immune ] [ die ] ] ] end ;; If there are less turtles than the carrying-capacity ;; then turtles can reproduce. ;; The probability of reproduction depends on average number ;; of offspring per life. In this model it is 4 per life (e.g. ;; 4 per 100 weeks. The chance, therefore, for a turtle to ;; reproduce at any given turn is 0.04 (if the population ;; is below carrying-capacity). to reproduce ask turtles with [not sick?] [ if (count turtles) < carrying-capacity and (random lifespan) < average-offspring [ hatch 1 [ set age 1 lt 45 fd 1 get-healthy ] ] ] end to update-plot set-current-plot "Populations" set-current-plot-pen "sick" plot count turtles with [sick?] set-current-plot-pen "immune" plot count turtles with [immune?] set-current-plot-pen "healthy" plot count turtles with [not sick? and not immune?] set-current-plot-pen "total" plot count turtles end @#$#@#$#@ GRAPHICS-WINDOW 262 10 777 546 50 50 5.0 1 10 1 1 1 0 1 1 1 -50 50 -50 50 CC-WINDOW 5 701 786 796 Command Center 0 SLIDER 33 210 227 243 duration duration 0.0 99.0 56 1.0 1 weeks SLIDER 33 176 227 209 chance-recover chance-recover 0.0 99.0 49 1.0 1 % SLIDER 33 142 227 175 infectiousness infectiousness 0.0 99.0 65 1.0 1 % BUTTON 53 25 123 60 NIL setup NIL 1 T OBSERVER T NIL NIL BUTTON 129 25 200 61 NIL go T 1 T OBSERVER T NIL NIL PLOT 8 333 260 497 Populations weeks people 0.0 52.0 0.0 200.0 true true PENS "sick" 1.0 0 -2674135 true "immune" 1.0 0 -5204280 true "healthy" 1.0 0 -10899396 true "total" 1.0 0 -13345367 true SLIDER 33 244 227 277 people people 0 300 150 1 1 NIL MONITOR 31 281 106 330 NIL %infected 1 1 MONITOR 108 281 178 330 NIL %immune 1 1 MONITOR 180 281 230 330 years weeks / 52 1 1 SWITCH 150 584 289 617 watch-turtle? watch-turtle? 1 1 -1000 SWITCH 149 619 289 652 hide-children? hide-children? 1 1 -1000 SLIDER 36 90 208 123 initial-sick-people initial-sick-people 0 100 43 1 1 NIL SWITCH 149 654 289 687 connect? connect? 0 1 -1000 SWITCH 293 585 425 618 hide-green? hide-green? 1 1 -1000 SWITCH 293 619 425 652 hide-red? hide-red? 0 1 -1000 SWITCH 292 653 425 686 hide-violet? hide-violet? 1 1 -1000 @#$#@#$#@ WHAT IS IT? ----------- This model simulates the transmission and perpetuation of a virus in a human population. 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) The model is initialized with 150 people, of which 10 are 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 700 in this model) healthy people may reproduce healthy and susceptible offspring. 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 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 approximately 27 years. Reproduction rate is constant in this model. Each turn, every healthy individual has a chance to reproduce. That chance is set so that each person will on average reproduce four times if they live 27 years. 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. Nonetheless, in this model, immunity does last forever and is secure. 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 a 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 a slider. 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 percent of the average life-span (which is 1500 weeks, or approximately 27 years, in this model) that an infected person goes through before the infection ends in either death or recovery. Note that although zero is a slider possibility, it produces an infection of very short duration (approximately 2 weeks) not an infection with no duration at all. The CHANCE-RECOVERY 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 140 green susceptible people and 10 red infected people (of randomly distributed ages). The GO button starts the simulation and the plotting function. 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 and the population density is at its maximum. 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 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) and the average lifespan of the people. 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 so that immunity is not perfect or eternal. CREDITS AND REFERENCES ---------------------- To refer to this model in academic publications, please use: Wilensky, U. (1998). NetLogo Virus model. http://ccl.northwestern.edu/netlogo/models/Virus. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. In other publications, please use: Copyright 1998 Uri Wilensky. All rights reserved. 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