2b:null 2c:["$","title",null,{"children":"A graphical experiment of exponential spread | Nick Strayer | Observable"}] 31:T15bb,set_parameters = { const data_sliders = {}; for (const parameter_id in data_gen_parameters){ const parameter_settings = { id: parameter_id, ...(data_gen_parameters[parameter_id]), on_update: update_data_button}; data_sliders[parameter_id] = inline_slider(parameter_settings); } const sim_sliders = {}; for (const parameter_id in simulation_parameters){ const parameter_settings = { id: parameter_id, ...(simulation_parameters[parameter_id]), on_update: update_sim_button}; sim_sliders[parameter_id] = inline_slider(parameter_settings); } const container = md` ## Why? When a disease is "spreading" it is doing so by hopping from person to person. It's not possible for you to give the disease to someone you never interact with. This means that the spread of diseases is not truly exponential as there isn't an infinite pool of people to infect and it can only infect through interactions with others. Unfortunately as a society we are very connected, so even if you don't interact with the first person to get sick, someone you know may, or someone you know may know someone, and so on. This means there are lots of variables that can govern the way a disease spreads. ## The Model In an attempt to gain an intuition for these processes, we can reduce the complexity of human interactions to a simple network, where nodes are people and edges are physical interactions between those people. We will assume that a disease has a constant probability of being passed in an interaction, or __probability of infection:__ ${sim_sliders.prob_of_infect}. One method of slowing the spread of a disease is social distancing. In our model, this is analogous to reducing the number of edges a node has, or reducing the total number of interactions someone has in a day. We will control this by setting a network-wide __average number of edges per node:__ ${data_sliders.avg_num_edges} In addition to the "normal" nodes our network also has what we will call "popular" nodes. These are nodes that are connected to more nodes than normal. An example of this is a cashier at a grocery store who interacts with hundreds of people a day. We can set the __average number of edges for "popular" nodes: __ ${data_sliders.avg_num_edges_pop}. In addition, we need to set the __% of the nodes that are "popular":__ ${data_sliders.prop_popular_nodes}. Another variable that can influence the spread of the disease are nodes exposing other nodes to potential infection that are not neccesarily close to them, or __probability of random exposure:__ ${sim_sliders.prob_of_long_edge}. This can be thought of like someone taking an unneccesary plane flight to Florida from Maine for spring break. _This 👆feature was proposed by [Robert Ziff of University of Michigan](https://che.engin.umich.edu/people/robert-ziff/) and [Anna Ziff of Duke University.](https://econ.duke.edu/people/anna-ziff) Learn more about power-law networks and disease spread in their preprint, [Fractal kinetics of COVID-19 pandemic.](https://www.medrxiv.org/content/10.1101/2020.02.16.20023820v2)_ Another variable in our simulation is the number of days after becoming infected that the person is contagious __contagious period length:__ ${sim_sliders.contagious_period}. A shorter duration will prevent a person from infecting everyone around them, especially as the probability of infection decreases. The last important variable in our simulation is the population. In our model, simply the __number of nodes:__ ${data_sliders.num_nodes}. A larger population will take longer for a disease to get through (but perhaps not as much longer as you would think). ### Running the simulation To kick of a simulation with the parameter's you have set, just select a node in the network to be the first infection. Alternatively you can ; If you want to try again you can or if you want to get a new set of data after changing parameters (or not), you can `; const new_data_button = container.querySelector("#new_data"); function update_data_button(){ new_data_button.style.background = colors.newly_infected; new_data_button.innerHTML = "Generate network with new parameters"; } function reset_data_button(){ new_data_button.innerHTML = "Generate a new network"; } new_data_button.addEventListener("click", () => { const new_params = {}; for(let param_id in data_sliders) { new_params[param_id] = { ...data_gen_parameters[param_id], val: data_sliders[param_id].value }; } mutable data_gen_parameters = new_params; reset_data_button(); }); const new_sim_button = container.querySelector("#new_sim"); function update_sim_button(){ new_sim_button.style.background = colors.newly_infected; new_sim_button.innerHTML = "Reset simulation with new parameters"; } function reset_sim_button(){ new_sim_button.innerHTML = "Restart simulation"; } new_sim_button.addEventListener("click", () => { const new_params = {}; for(let param_id in sim_sliders) { new_params[param_id] = { ...simulation_parameters[param_id], val: sim_sliders[param_id].value }; } mutable simulation_parameters = new_params; reset_sim_button(); }); reset_data_button(); reset_sim_button(); return container; }32:T4d5,sim_status = { switch(sim_results.status) { case "waiting": return md`## Start simulation by selecting initial node` break; case "running": return md`## Simulation Running` break; default: // Gather stats about simulation const percentage_infected = (100*sim_results.ids.length / data_gen_parameters.num_nodes.val).toPrecision(4); const peak_new_infections = d3.max(sim_results.history, t => t.n_new); const peak_active_infectors = d3.max(sim_results.history, t => t.potential_infectors); const print_stat = num => `${num}`; const print_line = txt => `

${txt}

`; return md`## Simulation Results:

${[`${print_stat(sim_results.history.length)}: Outbreak length in "days"`, `${print_stat(percentage_infected)}: % of nodes infected`, `${print_stat(peak_new_infections)}: Highest number of new infections for a day`, `${print_stat(peak_active_infectors)}: Highest active number of active infectors nodes` ].reduce((all, line) => all + print_line(line), "")}

` } }33:Tad1,canvas_net = { const time_step = sim_results.timestep; const newly_infected = sim_results.history[time_step-1].new_infections; const canvas = DOM.canvas(width*2,height*2); const context = canvas.getContext("2d"); const color_node_while_sim = node => { if (node.inactive) { context.fillStyle = colors.inactive; context.strokeStyle = "white"; } else if (newly_infected.includes(node.id)) { context.fillStyle = colors.newly_infected; context.strokeStyle = colors.newly_infected; } else if (node.infected) { context.fillStyle = colors.infected; context.strokeStyle = colors.infected; } else { context.fillStyle = colors.healthy; context.strokeStyle = "white"; } }; const infection_time_scale = d3.scaleLinear() .domain([0,time_step+1]) .range([colors.early_infection, colors.late_infection]) const color_node_after_sim = node => { context.fillStyle = node.time_infected > 0 ? infection_time_scale(node.time_infected): colors.healthy; context.strokeStyle = "white"; }; const color_node = sim_results.status == "finished" ? color_node_after_sim : color_node_while_sim; // Make canvas look good on high res screens canvas.style.width = `${width}px`; canvas.style.height = `${height}px`; context.scale(2,2); // Clear previous content context.clearRect(0, 0, width, height); // Draw edges sim.edges.forEach(({source, target}) => { context.beginPath(); context.strokeStyle = target.infected && source.infected ? colors.inactive_edge : target.infected && !source.infected || source.infected && !target.infected ? colors.danger_edge : colors.safe_edge ; context.moveTo(source.x, source.y); context.lineTo(target.x, target.y); context.stroke(); }); // Draw nodes sim.nodes.forEach(node => { context.beginPath(); let radius = node.radius; let border_width = 1; color_node(node); context.lineWidth = border_width; context.moveTo(node.x + radius, node.y); context.arc(node.x, node.y, radius, 0, 2 * Math.PI); context.fill(); context.stroke(); }); d3.select(canvas).on("click", function(){ const node = sim.node_quadtree.find(...d3.mouse(this)); node.infected = !node.infected; mutable initial_infections = node.infected ? insert_el(initial_infections, node.id) : remove_el(initial_infections, node.id); }); function color_edge(source, target){ return target.infected && source.infected ? colors.inactive_edge : target.infected && !source.infected || source.infected && !target.infected ? colors.danger_edge : colors.safe_edge } return canvas; }34:Tae1,parameter_grid = { const data_sliders = {}; for (const parameter_id in data_gen_parameters){ const parameter_settings = { id: parameter_id, ...(data_gen_parameters[parameter_id]), on_update: update_data_button}; data_sliders[parameter_id] = inline_slider(parameter_settings); } const sim_sliders = {}; for (const parameter_id in simulation_parameters){ const parameter_settings = { id: parameter_id, ...(simulation_parameters[parameter_id]), on_update: update_sim_button}; sim_sliders[parameter_id] = inline_slider(parameter_settings); } const container = md` ## All Model Parameters Just want to tweak the parameters quickly? You can do that here. ### Data Parameters: __Number of nodes:__ ${data_sliders.num_nodes}. __Average number of edges per node:__ ${data_sliders.avg_num_edges} __Average number of edges for "popular" nodes: __ ${data_sliders.avg_num_edges_pop}. __Percentage of the nodes that are "popular":__ ${data_sliders.prop_popular_nodes}. --- ### Simulation Parameters: __Probability of infection:__ ${sim_sliders.prob_of_infect}. __Probability of random exposure:__ ${sim_sliders.prob_of_long_edge}. __Contagious period length:__ ${sim_sliders.contagious_period}. --- `; const new_data_button = container.querySelector("#new_data"); function update_data_button(){ new_data_button.style.background = colors.newly_infected; new_data_button.innerHTML = "Generate network with new parameters"; } function reset_data_button(){ new_data_button.innerHTML = "Generate a new network"; } new_data_button.addEventListener("click", () => { const new_params = {}; for(let param_id in data_sliders) { new_params[param_id] = { ...data_gen_parameters[param_id], val: data_sliders[param_id].value }; } mutable data_gen_parameters = new_params; reset_data_button(); }); const new_sim_button = container.querySelector("#new_sim"); function update_sim_button(){ new_sim_button.style.background = colors.newly_infected; new_sim_button.innerHTML = "Reset simulation with new parameters"; } function reset_sim_button(){ new_sim_button.innerHTML = "Restart simulation"; } new_sim_button.addEventListener("click", () => { const new_params = {}; for(let param_id in sim_sliders) { new_params[param_id] = { ...simulation_parameters[param_id], val: sim_sliders[param_id].value }; } mutable simulation_parameters = new_params; reset_sim_button(); }); reset_data_button(); reset_sim_button(); return container; }35:T1344,function setup_infection_sim_full(data_params){ // Generate network data const {nodes, edges, node_quadtree} = generate_network_data( data_params.num_nodes.val, build_poisson_mixture([ {mean: data_params.avg_num_edges.val, size: 1 - data_params.prop_popular_nodes.val}, {mean: data_params.avg_num_edges_pop.val, size: data_params.prop_popular_nodes.val} ]) ); function* run_simulation(sim_params, initial_infections = [], sim_speed = 1){ let time = 1; const hist = [{ total_infections: initial_infections.length, new_infections: initial_infections, n_new: initial_infections.length, potential_infectors: initial_infections.length, time: time++ }]; // Reset all nodes before starting nodes.forEach(node => { node.infected = false; node.inactive = false; node.time_infected = -1; node.uninfected_neighbors = [...node.neighbors]; }); // Setup the initial infecting nodes initial_infections.forEach(id => { const node = nodes[id]; node.infected = true; node.time_infected = time; // Create an array of potential neighbors to infect, make sure to not include already infected nodes node.uninfected_neighbors = node.neighbors.filter(n => !(initial_infections.includes(n.id))); }); // State vectors that keep track of what nodes are in what states const potential_infectors = new Set(initial_infections); const infections = new Set(initial_infections); while(potential_infectors.size > 0 && infections.size < nodes.length) { const no_longer_infecting = []; const new_infections = new Set(); const expose_node = node => { const was_infected = Math.random() < sim_params.prob_of_infect.val; if(was_infected) new_infections.add(node.id); }; potential_infectors.forEach(id => { const node = nodes[id]; // Exposes all the node's neighbors node.uninfected_neighbors.forEach(expose_node); // Does this node randomly expose a "long edge"? const has_long_edge = Math.random() < sim_params.prob_of_long_edge.val; if (has_long_edge){ const random_node = nodes[Math.floor(Math.random() * nodes.length)]; const is_infectable = !(random_node.id === node.id || random_node.infected); if(is_infectable) expose_node(random_node); } // Will node no longer be infections at the next time point? if(time >= node.time_infected + sim_params.contagious_period.val) no_longer_infecting.push(id); }); const set_inactive = id => { nodes[id].inactive = true; potential_infectors.delete(id); } // Remove nodes neighbors infected or have been infected for time period from potential infectors no_longer_infecting.forEach(set_inactive); // Run through newly infected nodes and set to infected new_infections.forEach( id => { infections.add(id); const node = nodes[id]; node.infected = true; node.time_infected = time; // Create an array of potential neighbors to infect, make sure to not include already infected nodes node.uninfected_neighbors = node.neighbors.filter(n => !(n.infected || new_infections.has(n.id))); // Node can only infect others if it has neighbors that are not already infected if(node.uninfected_neighbors.length !== 0) potential_infectors.add(id); // Go to all of this node's neighbors and remove itself from their list of nodes they could infect node.neighbors.forEach(neighbor => { neighbor.uninfected_neighbors = neighbor.uninfected_neighbors.filter(n => n.id !== id); if(neighbor.uninfected_neighbors.length == 0) set_inactive(neighbor.id); }); }); // Update state history hist.push({total_infections: infections.size, new_infections: [...new_infections], n_new: new_infections.size, potential_infectors: potential_infectors.size, time: time}); yield Promises.tick(sim_speed, {ids: [...infections], history: hist, timestep: time++, running: true, settings: sim_params, status: "running"}); } yield Promises.tick(sim_speed, {ids: [...infections], history: hist, timestep: hist.length, settings: sim_params, status: hist.length == 1 ? "waiting": "finished"}); } return {nodes, edges, node_quadtree, run_simulation, settings: data_params}; }36:T6c6,function generate_network_data(n, degree_distribution_fn){ const nodes = d3.range(n) .map((i) => ({id : i, x : Math.random()*w + margins.left, y : Math.random()*h + margins.top, neighbors: [] })); let node_quadtree = d3.quadtree() .extent([ [0, 0], [width, height] ]) .x(d => d.x) .y(d => d.y) .addAll(nodes); // We will have repeat edges so let's try and avoid them by using a set const u_edges = new Set(); let sum_K = 0; nodes.forEach(node => { const K = Math.max(degree_distribution_fn(), 1); sum_K += K; // first remove node from quadtree so find method doesn't return it node_quadtree.remove(node); // An array to hold the nearest nodes node.neighbors = []; while(node.neighbors.length < K) { const next_nearest = node_quadtree.find(node.x, node.y); // place this node in neighbors array node.neighbors.push(next_nearest); // Add edges between nodes to edge array in order u_edges.add(node.id < next_nearest.id ? {source: node, target: next_nearest} : {source: next_nearest, target: node}); // remove from quadtree node_quadtree.remove(next_nearest); } // Add back the nodes that were just removed to quadtree node.neighbors.forEach(n => node_quadtree.add(n)); // Add back current node as well node_quadtree.add(node); }); const avg_K = sum_K/nodes.length; nodes.forEach(node => { node.radius = average_node_r*node.neighbors.length/avg_K }) let edges = [...u_edges]; return {nodes, edges, node_quadtree}; }37:T492,function inline_slider({min = 0, max = 1, val = 0.5, step = 0.1, precision = 3, int = false, percent = false, on_update = () => {}, }){ min = min/step; max = max/step; val = val/step; const format_val = val => { let val_formatted = int ? Math.round(val) : val.toPrecision(precision); if(percent){ val_formatted = `${val_formatted*100}%`; } return val_formatted; } const div = html` ${format_val(val*step)} `; const range = div.querySelector("[type=range]"); const value_disp = div.querySelector('span'); div.value = range.valueAsNumber*step; range.addEventListener("input", () => { const newValue = range.valueAsNumber*step; div.value = newValue; value_disp.innerHTML = format_val(newValue); on_update(); }); return div; }38:Tb1c,html` Expand to see CSS declarations `39:[] 2f:{"id":"5027d4f150df638d","slug":"a-graphical-experiment-of-exponential-spread","title":"A graphical experiment of exponential spread","thumbnail":"cc98b9226a66d9d99ebdef77eb13342ae81386330d7633b5d4c55f1e3e9447b7","access_level":"public","create_time":"$D2020-03-22T01:42:34.481Z","update_time":"$D2020-05-11T16:51:09.288Z","view_time":null,"first_public_time":"$D2020-03-23T20:43:09.938Z","fork":false,"stars":59,"starred":false,"owner":{"type":"team","id":"c7ceaaf194433370","login":"nstrayer","name":"Nick Strayer","avatar_url":"https://avatars-next.observableusercontent.com/56ce9e43c9ae8d967575f2641fd299251ce5e022874e0c8fe8d04becea060719","tier":"starter_2024"},"version":2658,"publish_version":2658,"role":null,"authored":false,"authors":[{"type":"individual","id":"e253fe2c017ea3f1","login":"nstrayer","name":"Nick Strayer","avatar_url":"https://avatars-next.observableusercontent.com/56ce9e43c9ae8d967575f2641fd299251ce5e022874e0c8fe8d04becea060719","tier":null}],"members":[{"type":"individual","id":"e253fe2c017ea3f1","login":"nstrayer","name":"Nick Strayer","avatar_url":"https://avatars-next.observableusercontent.com/56ce9e43c9ae8d967575f2641fd299251ce5e022874e0c8fe8d04becea060719","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":33,"collection":{"id":"fcb6942d5a2c4d51","slug":"simulations","title":"simulations","owner":{"id":"c7ceaaf194433370","login":"nstrayer","name":"Nick Strayer"}},"type":"notebook","body":{"title":"A graphical experiment of exponential spread","cells":[{"id":1896,"value":"title = md`# A graphical experiment of exponential spread`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1665,"value":"notes = md`\n_Note: I am in no way an expert on disease spread. This is simply a little experiment I put together to allow me to think intuitively about spread in networks._\n\n_Update 1: Thanks a ton to [Duane Barlow](https://observablehq.com/@duaneatat) for a PR adding the ability to toggle how long a node is contagious for!_ \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1980,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1759,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1310,"value":"legend = {\n if(sim_results.status == \"finished\") {\n return md`### Node infected at time: ${legend_circ(colors.early_infection)} ${tex`t = 1`} ${tex`\\to`} ${legend_circ(colors.late_infection)} ${tex` t = ${sim_results.timestep}`}`\n }\n else {\n return md`### Node States\n\n${legend_circ(colors.healthy)} Healthy ${tex`\\to`} ${legend_circ(colors.newly_infected)} newly infected ${tex`\\to`} ${legend_circ(colors.infected)} spreading disease ${tex`\\to`}${legend_circ(colors.inactive)} all neighbors infected `\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":620,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":551,"value":"total_num_infections_viz = vegalite({\n title: \"Total number of infections\",\n data: {values: sim_results.history},\n width: width*0.9,\n height: chart_heights,\n mark: \"bar\",\n encoding: {\n x: {field: \"time\", type: \"ordinal\", title: \"\"},\n y: {field: \"total_infections\", type: \"quantitative\", title: \"infections\"},\n color: {value: colors.infected}\n },\n}); ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":570,"value":"num_new_infections_viz = vegalite({\n title: \"Number of new infections\", \n data: {values: sim_results.history},\n width: width*0.9,\n height: chart_heights,\n mark: \"bar\",\n encoding: {\n x: {field: \"time\", type: \"ordinal\", title: \"Time\"},\n y: {field: \"n_new\", type: \"quantitative\", title: \"infections\"},\n color: {value: colors.infected}\n }\n}); ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1545,"value":"log_log_viz = vegalite({\n title: \"Log-Log plot of total infections\", \n data: {values: sim_results.history},\n width: width*0.9,\n height: chart_heights,\n mark: {type: \"line\", point: true},\n encoding: {\n x: {field: \"time\", \n scale: {type: \"log\"},\n type: \"quantitative\", \n title: \"Time\"},\n y: {field: \"total_infections\", \n scale: {type: \"log\"},\n type: \"quantitative\", \n title: \"# infections\"},\n color: {value: colors.infected}\n },\n}); ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1907,"value":"degree_dist = vegalite({\n width,\n title: `Degree distribution of network w/ ${sim.nodes.length} nodes and ${sim.edges.length} edges`,\n data: {values: node_degree_dist},\n mark: \"bar\",\n encoding: {\n x: {\n field: \"degree\",\n title: \"degree\",\n type: \"ordinal\"\n },\n y: {\n field: \"count\",\n title: \"# of nodes\",\n type: \"quantitative\"\n }\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1352,"value":"ideas = md`\n## Things to try:\n\n- Run the simulation a few times with different infection rates, is the impact of the rate more or less than you would expect on the duration of the spread?\n- Around what average number of neighbors does the network start fragmenting into isolated sections?\n- Does reducing the number of connections make the spread last longer? Does it reduce the average number of new infections per day?\n- Try different contagious period lengths.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2246,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2230,"value":"sim_speed_text = md`\n__Simulation Speed:__\nWant to slow the simulation down? Raise the value below to your liking. This is the length of the pause between iterations so higher = slower.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1649,"value":"viewof sim_speed = inline_slider({min: 1, max: 1000, start:1, int: true})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1671,"value":"current_algorithm = md`\n## Current Algorithm\n\n1. Generate \\`N\\` uniform random points on a plane\n2. For each point:\n 1. Draw from a Poisson distribution to determine how many neighbors that point is connected to (\\`n_neighbors\\`)\n 2. Connect that node to the \\`n_neighbors\\` closest points to it\n3. Choose a random node to be the first infected and add to a \\`potential_infectors\\` list\n4. For each time point\n 1. For every node in \\`potential_infectors\\`:\n 1. Loop through all neighbors and add to \\`newly_infected\\` list with probability \\`p_infect\\`\n 2. If all neighbors of a node are infected or a certain number of iterations have passed since first infection, take node out of \\`potential_infectors\\`\n 2. Mark all nodes in \\`newly_infected\\` as infected and add to \\`potential_infectors\\`\n5. Repeat step 4 until no more nodes are left in \\`potential_infectors\\`\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2477,"value":"md`## Things I'd like to add\n\n- A node can either be a presenter (look sick) or no symptoms\n - Let nodes to avoid others if they \"look sick\"\n- Ability for nodes to either die or recover\n - Nodes that recover have a small chance of re-catching virus \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2295,"value":"md`## Contagion Simulation Code`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2605,"value":"sim","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2374,"value":"sim_results = sim.run_simulation(simulation_parameters, initial_infections)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2525,"value":"sim = setup_infection_sim_full(data_gen_parameters)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2520,"value":"$35","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2292,"value":"md`## Initial Values and Constants`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":981,"value":"colors = {\n const early_infection = \"#990000\";\n const late_infection = \"#fc8d59\";\n const infected = \"#e41a1c\";\n const healthy = \"#377eb8\";\n const safe_edge = \"#d9d9d9\";\n const interactive = \"#2690ce\";\n const inactive = change_brightness(infected, -1);\n const newly_infected = change_brightness(infected, 1);\n const danger_edge = d3.interpolateHslLong(safe_edge, infected)(0.5);\n const inactive_edge = d3.interpolateHslLong(safe_edge, inactive)(0.1); \n \n return {infected, \n inactive, \n newly_infected, \n healthy, \n safe_edge, \n inactive_edge, \n danger_edge,\n interactive,\n early_infection,\n late_infection};\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2430,"value":"md`__Slider Settings:__ \n\nThese control the range of allowed values and steps for each parameter in model.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2619,"value":"mutable data_gen_parameters = ({\n num_nodes: {\n val: 3000,\n min: 1000, \n max: 15001, \n step: 100, \n int: true,\n },\n avg_num_edges: {\n val: 8,\n min: 1, \n max: 25, \n step: 0.1,\n },\n avg_num_edges_pop: { \n val: 25,\n min: 10, \n max: 100,\n step: 0.1,\n },\n prop_popular_nodes: {\n val: 0.2,\n min: 0, \n max: 1, \n step: 0.01,\n percent: true,\n }\n});","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2418,"value":"mutable simulation_parameters = ({\n prob_of_infect: {\n val: 0.15,\n min: 0.01, \n max: 0.99, \n start: 0.15, \n step: 0.01,\n },\n prob_of_long_edge:\n { \n val: 0,\n min: 0, \n max: 0.2, \n start: 0, \n step: 0.005,\n },\n contagious_period: {\n val: 10,\n min: 1, \n max: 30, \n start: 10, \n step: 1, \n int: true,\n }\n});","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2289,"value":"md`\n## Data Generation Functions\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1965,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2314,"value":"md`## Node Degree Distribution`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1974,"value":"function build_poisson_mixture(degree_dists){\n\n let total_size = degree_dists.reduce((size, dist) => size + dist.size, 0);\n\n const dist_selection_probs = degree_dists\n .reduce((P, dist, i) => [\n ...P, (P[i-1] || 0) + (dist.size / total_size)\n ], []);\n\n return () => {\n const rval = Math.random();\n let dist_i;\n for(dist_i = 0; dist_i < degree_dists.length; dist_i++){\n if(rval < dist_selection_probs[dist_i]) break;\n }\n return gen_pois(degree_dists[dist_i].mean);\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":31,"value":"function gen_pois(lambda, max_its = 1000){ \n let i = -1, cum_sum = 0;\n while(cum_sum < 1 && i < max_its){\n i++;\n cum_sum += -Math.log(1-Math.random())/lambda; // Or use gen_expon()\n }\n return i;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1936,"value":"node_degree_dist = {\n const degree_map = sim.nodes.reduce((d_counts, n) => {\n const degree = n.neighbors.length;\n d_counts[degree] = (d_counts[degree]||0) + 1;\n return d_counts;\n }, {});\n \n return Object.keys(degree_map).map(d => ({degree: +d, count: degree_map[d]}));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2317,"value":"md`## State Variables`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":421,"value":"mutable initial_infections = {\n data_gen_parameters;\n simulation_parameters;\n sim.nodes.forEach(n => n.infected = false);\n return []\n};","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2300,"value":"md`## Visualization Sizing`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1891,"value":"average_node_r = Math.min(Math.max(width/320, 1), 7);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":10,"value":"height = 500;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":577,"value":"chart_heights = 130;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":969,"value":"h = height - margins.top - margins.bottom;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":971,"value":"w = width - margins.left - margins.right;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":962,"value":"margins = ({left: 20, right: 20, top: 10, bottom: 10});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2305,"value":"md`## Misc helper functions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1866,"value":"function insert_el(arr, el) {\n \n if(!arr.includes(el)){\n arr.push(el);\n }\n \n return arr;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":430,"value":"function remove_el(arr, el){\n return arr.filter(d => d != el);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":949,"value":"function last(arr) {\n return arr[arr.length - 1];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1092,"value":"function change_brightness(color, k = 1) {\n const {l, c, h} = d3.lch(color);\n return d3.lch(l + 18 * k, c, h);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1307,"value":"function legend_circ(color, radius = 9) {\n return d3.select(DOM.svg(2*radius, 2*radius))\n .call(svg => svg.append(\"circle\")\n .attr(\"cx\", radius)\n .attr(\"cy\", radius)\n .attr(\"r\", radius)\n .attr(\"fill\", color))\n .node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1133,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":2329,"value":"md`## Libraries`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":4,"value":"d3 = require(\"d3@5\", \"d3-array\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":552,"value":"vegalite = require(\"@observablehq/vega-lite@0.1\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1229,"value":"$38","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W39","stdlib":"1","titling":"auto"}} 30:"$2f:body"