fglobals [ num-infected infected-size ] turtles-own [ infected? ;; true if agent has been infected ] ;;;;;;;;;;;;;;;;;;;;;;; ;;; Main Procedures ;;; ;;;;;;;;;;;;;;;;;;;;;;; to complex-spread if all? turtles [infected?] [stop] ask turtles with [ infected? = true ] [ ifelse (random-float 1 <= prob-recover) [ reset-node ] [ ;; infect neighbors ask link-neighbors [ if (( random-float 1 <= prob-infection ) and (count link-neighbors with [infected? = true] > 1)) ;; infect with probability p [ if not infected? ;; agents can be infected only once [ set infected? true show-turtle set color yellow set size infected-size ;; color the link with the node doing the infection ask link-with myself [set color yellow show-link] ;; increment the total number of infected agents ] ] ] ] ] do-plotting set num-infected count turtles with [infected? = true] tick end to spread ;; or if every agent has already been infected if all? turtles [infected?] [stop] ask turtles with [ infected? = true ] [ ifelse (random-float 1 <= prob-recover) [ reset-node ] [ ;; infect neighbors ask link-neighbors [ if ( random-float 1 <= prob-infection ) ;; infect with probability p [ if not infected? ;; agents can be infected only once [ set infected? true show-turtle set color yellow set size infected-size ;; color the link with the node doing the infection ask link-with myself [set color yellow show-link] ;; increment the total number of infected agents ] ] ] ] ] do-plotting set num-infected count turtles with [infected? = true] tick end ;;layout all nodes and links to do-layout repeat 5 [layout-spring turtles links 0.2 4 0.9] display end ;;;;;;;;;;;;;;;;;;;;;;;; ;;; Setup Procedures ;;; ;;;;;;;;;;;;;;;;;;;;;;;; to generate-topology ;; (for this model to work with NetLogo's new plotting features, ;; __clear-all-and-reset-ticks should be replaced with clear-all at ;; the beginning of your setup procedure and reset-ticks at the end ;; of the procedure.) __clear-all-and-reset-ticks set infected-size 4 set-default-shape turtles "outlined circle" ;; setup small world topology create-turtles num-nodes create-lattice rewire-network setup end to reinfect-two set infected-size 4 ask turtles [reset-node] ask links [set color gray + 1.5] ;; infect a single agent ask one-of turtles [ set infected? true set color yellow set size infected-size ask one-of link-neighbors [ set infected? true set color yellow set size infected-size ] ] set num-infected 1 ;; Layout turtles: layout-circle (sort turtles) max-pxcor - 8 ;; space out turtles to see clustering ask turtles [ facexy 0 0 if who mod 2 = 0 [fd 4] ] display end to setup set infected-size 4 ask turtles [reset-node] ask links [set color gray + 1.5] ;; infect a single agent ask one-of turtles [ set infected? true set color yellow set size infected-size ] set num-infected 1 ;; Layout turtles: layout-circle (sort turtles) max-pxcor - 8 ;; space out turtles to see clustering ask turtles [ facexy 0 0 if who mod 2 = 0 [fd 4] ] display end to reset-node set color gray + 1.5 set size 3 set infected? false end ;; WARNING: the simplified rewiring algorithm does not certain checks (ie disconnected graph) ;; for large networksthis shouldn't be too much of an issue. to rewire-network ask links [ ;; whether to rewire it or not? if (random-float 1) < rewiring-probability [ ask end1 [ create-link-with one-of other turtles with [not link-neighbor? myself ] [set color gray + 1.5] ] die ] ] end ;; creates a new lattice to create-lattice ;; iterate over the nodes let n 0 while [n < count turtles] [ ;; make links with the next two neighbors ;; this makes a lattice with average degree of 4 make-link-between turtle n turtle ((n + 1) mod count turtles) make-link-between turtle n turtle ((n + 2) mod count turtles) set n n + 1 ] end ;; connects the two nodes to make-link-between [node1 node2] ask node1 [ create-link-with node2 [ set color gray + 1.5] ] end ;;;;;;;;;;;;;;;; ;;; Plotting ;;; ;;;;;;;;;;;;;;;; to do-plotting ;; plot the number of infected individuals at each step set-current-plot "% infected" set-current-plot-pen "inf" let percent-inf 100 * (num-infected ) / (count turtles) plotxy ticks percent-inf end @#$#@#$#@ GRAPHICS-WINDOW 295 10 723 459 80 80 2.6 1 10 1 1 1 0 0 0 1 -80 80 -80 80 1 1 1 ticks 30.0 SLIDER 7 122 209 155 num-nodes num-nodes 100 500 100 1 1 NIL HORIZONTAL SLIDER 6 158 209 191 rewiring-probability rewiring-probability 0 1 0.05 0.01 1 NIL HORIZONTAL PLOT 6 265 283 459 % infected time n 0.0 1.0 0.0 100.0 true false "" "" PENS "inf" 1.0 0 -2674135 true "" "" BUTTON 6 47 155 80 reinfect-one setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 6 194 206 227 prob-infection prob-infection 0 1 0.24 0.01 1 NIL HORIZONTAL BUTTON 7 85 123 118 spread once spread NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 129 85 246 118 spread spread T 1 T OBSERVER NIL NIL NIL NIL 1 MONITOR 210 192 292 237 NIL num-infected 17 1 11 BUTTON 159 47 235 80 layout do-layout T 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 6 10 245 43 setup a new network generate-topology NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 6 229 206 262 prob-recover prob-recover 0 1 0 0.01 1 NIL HORIZONTAL BUTTON 726 59 860 92 NIL complex-spread\n T 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 726 25 834 58 NIL reinfect-two NIL 1 T OBSERVER NIL NIL NIL NIL 1 @#$#@#$#@ ## WHAT IS IT? This is an SIS model on a Watts-Strogatz small world topology. Nodes are either susceptible (S) or infected (I). ## HOW IT WORKS "This model is an adaptation of a model proposed by Duncan Watts and Steve Strogatz (1998). It begins with a network where each person (or "node") is connected to his or her two neighbors on either side... The REWIRING-PROBABILITY slider determines the probability that an edge will get rewired" (so that one of its endpoints goes to a random node instead of a neighbor). Clicking the setup button will produce different network configurations, all with the same rewiring probability. You can also experiment with complex contagion: a node will become infected if at least two of its neighbors are. ## HOW TO USE IT "The NUM-NODES slider controls the size of the network. Choose a size and press SETUP. Changing the REWIRING-PROBABILITY slider changes the fraction of nodes rewired." Press SETUP to generate the new network. SETUP will also infect one node. The PROB-INFECTION slider determines the probability that an infected individual will infect a susceptible contact at every time step, i.e. the infectiousness of the spreading agent. The PROB-RECOVER slider determines the probability that an infected individual will recover and itself rejoin the susceptible population rather than infecting its neighbors. To re-infect a single individual while keeping the same topology - press REINFECT-ONE. Now to allow the disease to spread, you can advance one time step at a time (each infected node will infect each of its neighbors with probability prob-infection) with the "spread once" button. To let the disease run its full course, you can click the "spread complete" button. You can also slow down the process using the slower-faster slider at the top of the model interface. To try complex contagion, you need to infect two neighboring individuals with REINFECT-TWO. Then apply COMPLEX-SPREAD. ## THINGS TO TRY Try plotting the values for different rewiring probabilities and observe how long the infection survives in the network, and how far it spreads. What happens as the probability of recovery increases? What happens as the probability of infection increases? Can you find a critical threshold in the infection and recovery probabilities such that for a given rewiring probability, below these threshold values the disease always dies out, and above the threshold value, it tends to persist in the network? In this case you are looking for the conditions under which you will observe epidemics - outbreaks that affect a significant fraction of the network, vs. conditions under which the outbreak remains small and contained. Also consider the differing effect of rewiring on simple and complex contagion. ## RELATED MODELS See other models in the Networks section of the Models Library, such as Giant Component and Preferential Attachment. Also check out Lada's other NetLogo models: http://www.ladamic.com/netlearn ## CREDITS AND REFERENCES This model was adapted from: Wilensky, U. (2005). NetLogo Small Worlds model. http://ccl.northwestern.edu/netlogo/models/SmallWorlds. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. It was written by Lada Adamic and Eytan Bakshy in 2007 and 2008, revised 2012 @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 225 225 255 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