SIR_CA.nlogo

globals[
susceptibles_  ;the number of susceptible people
infecteds_ ;the number of infected people
recovereds_  ;the number of recovered people
width  ;;the width of the world
]

patches-own[
status ;1 for susceptible, 2 for infected, 3 for recovered
]

to setup
  ca
  reset-ticks
  ;;set the world size equal to the number of agents
  set susceptibles_ read-from-string susceptibles
  set width (sqrt susceptibles_) - 1
  resize-world 0 width 0 width
  ;;one of the cells is infected
  ask patches [set status 1]
  ask n-of 1 patches [set status 2]

  change-colors
end


to go
  ;;stop if no agent is infected
  if count patches with [status = 2] = 0 [stop]

  ;;infected agents may infect agents in the same cell by a
  ;;probability = infection rate / the probability to be neighbors * change in time
  ask patches with [status = 2][
    let suspectible-neighbors neighbors with [status = 1]
    if count suspectible-neighbors > 0 [
      ask suspectible-neighbors [
           if random-float 1 < (InfectionRate * ( width * width / 8 )) * dt [
           set status 2]
      ]]]

    ;;infected agents may recover by a probability = recovery rate * change in time
    ask patches with [status = 2][

    if random-float 1 < RecoveryRate * dt [
      set status 3]
  ]

;;update the number of each type of cells
  set susceptibles_ count patches with [status = 1]
  set infecteds_ count patches with [status = 2]
  set recovereds_ count patches with [status = 3]


  change-colors
  do-plot

  tick

end


to change-colors
;;susceptibles are green, infecteds are red, recovereds are blue
  ask patches with [status = 1][set pcolor green]
  ask patches with [status = 2][set pcolor red]
  ask patches with [status = 3][set pcolor blue]

end


to do-plot
;;plot the numbers of susceptibles, infecteds, recovereds over time
  if plot-pen-exists? "susceptibles" [
    set-current-plot-pen "susceptibles"
    plotxy ticks susceptibles_
  ]
  if plot-pen-exists? "infecteds" [
    set-current-plot-pen "infecteds"
    plotxy ticks infecteds_
  ]
  if plot-pen-exists? "recovereds" [
    set-current-plot-pen "recovereds"
    plotxy ticks recovereds_
  ]
end
@#$#@#$#@
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"625" "900" "2500" "10000"
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"" ""
PENS
"susceptibles" 1.0 0 -13840069 true "" ""
"infecteds" 1.0 0 -2674135 true "" ""
"recovereds" 1.0 0 -13345367 true "" ""

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

This is a Cellular Automata version of the SIR model.

## HOW IT WORKS

At the beginning, one cell will get infected. During each iteration (dt), the infected cell can infect other cells in its Moore neighborhood. Similarly as the ABM, I would like to map the probability of getting infected to the one in the SD model. In this CA model, the probability to get infected is equal to the infection rate divided by the probability to be in the Moore neighborhood, times the change in time. Each infected cell has a probability to recover in each time period, which equals the recovery rate times the change in time. The equations can be expressed as:

probability that a cell will get infected = infection rate / probability to be a neighbor * change in time

prebability that a cell will recovered = recover rate * change in time

## HOW TO USE IT

Press setup to create the cells, randomly select the first infected cell.

Press go to run the simulation.


## RELATED MODELS

I have re-built the original System Dynamics SIR model into three different models, using Agent-Based Modeling, Cellular Automata, and Discrete Event Simulation.
The models are posted on my blog: http://geospatialcss.blogspot.com/
@#$#@#$#@
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@#$#@#$#@
NetLogo 5.3.1
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@
<experiments>
  <experiment name="experiment" repetitions="10" runMetricsEveryStep="true">
    <setup>setup</setup>
    <go>go</go>
    <exitCondition>count patches with [status = 2] = 0</exitCondition>
    <metric>susceptibles_</metric>
    <metric>infecteds_</metric>
    <metric>recovereds_</metric>
    <enumeratedValueSet variable="RecoveryRate">
      <value value="0.5"/>
    </enumeratedValueSet>
    <enumeratedValueSet variable="dt">
      <value value="0.001"/>
    </enumeratedValueSet>
    <enumeratedValueSet variable="susceptibles">
      <value value="&quot;2500&quot;"/>
    </enumeratedValueSet>
    <enumeratedValueSet variable="InfectionRate">
      <value value="0.002"/>
    </enumeratedValueSet>
  </experiment>
</experiments>
@#$#@#$#@
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