2e:null 2f:["$","title",null,{"children":"Clustering students to slow virus spread inside schools | Benjamin Schmidt | Observable"}] 34:Ta8e,md`# Clustering students to slow virus spread inside schools As many schools in the United States look to reopen despite high levels of coronavirus infection nationwide, one major consideration needs to be how coronavirus is likely to spread from classroom to classroom. My son's school-to-be has done a lot of good work around the physical plant, but I think there may be some room to improve distancing in the social networks within the school. Usually, parents have little control over what classroom their children are in; we don't prioritize joining friends or playmates, or may even actively dislike it. In normal circumstances, that's fine. But this year, we can significantly ameliorate the welfare of everyone at the schools--students, teachers, and families--with a few steps, **if** parents provide information on who their students see. The point of this notebook is to argue that 1. Schools *should* take children's social networks more into account than usual, to protect teachers and students, and that 2. Schools *can* can take children's networks into account; this notebook is proof-of concept for a private, in-browser program that could handle assignments from a spreadsheet of preferences. Here are the rules: 1. Children should be in the same classrooms as their frequent playmates and babysitting partners. Otherwise, outbreaks will spread rapidly among all the classrooms of the same grade. This is an easy call, I think. 2. Siblings need to be handled carefully to avoid outbreaks spreading between grades. In particular, **sibling clusters--cases where there are multiple families with, say, *both* a second- and a fourth-grader--should be consolidated together into the same classrooms**. This notebook shows what this looks like on a simulated school population, but it would also be possible to use the same code here to generate class assignments for a real population. This might be well worth the time--from what I've seen, schools are just using their same old classroom assignment methods--spreadsheets?--because it's too hard to manually take all the connections between people into effect. This is not the completely optimal classroom assignment, but algorithm used here--allocating students in an order based around traversing the network--could significantly reduce the risk to the rest of the community even if a student--or an entire classroom--gets sick. And it could certainly be improved. This notebook is based around an elementary school in New York City that is moving to 2-day-a-week instruction with about 12 9-person classes per grade (each centered on Wednesday, Thursday, or Friday), but the problems are similar at a variety of schools. `35:T7aa,chart = { classes; // Observable trick; rebuild when the class assignments change. const height = width * 0.5; const chosen_links = new Set(link_restrictions); const chosen_grades = new Set(display_grades); pop.make_links(); const data = make_data((x) => chosen_grades.has(x.grade)); const links = data.links.filter((d) => chosen_links.has(d.link_type)); //.map(d => Object.create(d)); const nodes = data.nodes; const simulation = d3 .forceSimulation(nodes) .force( "link", d3.forceLink(links).id((d) => d.id) ) .force("charge", d3.forceManyBody().strength(-4)) .force("center", d3.forceCenter(width / 2, height / 2)) .force("x", d3.forceX().strength(0.01)) .force("y", d3.forceY().strength(0.01)); const svg = d3.create("svg").attr("viewBox", [0, 0, width, height]); const link = svg .append("g") .attr("stroke", "#999") .attr("stroke-opacity", 0.6) .selectAll("line") .data(links) .join("line") .attr("stroke-width", (d) => Math.sqrt(d.value)); const node = svg .append("g") .attr("stroke", "#fff") .attr("stroke-width", 1.5) .selectAll("circle") .data(nodes) .join("circle") .attr("r", 5) .attr("fill", (d) => color(d[colorize])) .call(drag(simulation)); node.on("mouseover", (d) => { mutable current = d; }); node.append("title").text((d) => `${d.name}, grade ${d.grade}`); const x = d3.scaleLinear().range([10, width - 10]); const y = d3.scaleLinear().range([10, height - 10]); simulation.on("tick", () => { y.domain(d3.extent(nodes.map((d) => d.y))); x.domain(d3.extent(nodes.map((d) => d.x))); link .attr("x1", (d) => x(d.source.x)) .attr("y1", (d) => y(d.source.y)) .attr("x2", (d) => x(d.target.x)) .attr("y2", (d) => y(d.target.y)); node.attr("cx", (d) => x(d.x)).attr("cy", (d) => y(d.y)); }); invalidation.then(() => simulation.stop()); return svg; }36:T4f8,function* simulate_outbreak(probability = .1, draw = true) { pop.make_links() // structured as a generator. if (draw) { chart.selectAll("circle").style("fill", "grey") } d3.shuffle(pop.students) let infected_set = new Set([pop.students[0]]) const ever_infected = new Set([pop.students[0].id]) while (infected_set.size) { const new_infections = new Set() for (let student of infected_set) { // Note if a student interacts with someone in multiple contexts, they // have additional chances to catch it from them. for (let studentB of student.links) { if (Math.random() > probability) {continue} if (ever_infected.has(studentB.student.id)) { continue } ever_infected.add(studentB.student.id) new_infections.add(studentB.student) } } infected_set = new_infections if (draw) { // Waste time to slow animation. Yuck. for (let i of d3.range(6)) { yield ever_infected.size } chart.selectAll("circle") .transition() .style("fill", d => ever_infected.has(d.id) ? "red" : "lightgrey") .attr("r", d => new_infections.has(d) ? 10 : 5) } } yield ever_infected.size }37:T9a8,class Random_School_Population extends School_Population { constructor(grades = ["K", "1", "2", "3", "4", "5"], students = 720) { super() this.grades = grades for (let i of d3.range(students)) { d3.shuffle(grades) this.students.push(new Student(grades[0])) } this.give_students_random_links() this.n_classrooms = { "K": 4, "1": 4, "2": 3, "3": 4, "4": 3, "5": 3 } } get classrooms() { if (this._classrooms) {return this._classrooms} this._classrooms = [] for (let grade of this.grades) { for (let i of d3.range(this.n_classrooms[grade])) { for (let day of ["W", "Th", "Fr"]) { this._classrooms.push({ day: day, teacher_number: i, grade: grade, students: [], max_size: 9 }) } } } return this._classrooms } assign_learning_pods(fraction = SHARE_OF_STUDENTS_IN_PODS, sizes = [2, 3, 4, 5, 6, 7]) { for (let grade of this.grades) { const kids = this.get_grade(grade).filter(kids => kids.format != "remote") const pods = [[]] d3.shuffle(kids) d3.shuffle(sizes) let next_pod_size = sizes[0] for (let kid of kids) { if (Math.random() > fraction) { continue } if (pods[0].length == next_pod_size) { pods.unshift([]) next_pod_size = d3.shuffle(sizes)[0] } pods[0].unshift(kid) } for (let pod of pods) { this.groups.push(new Pod(pod)) } } } assign_siblings(sibshare = SHARE_OF_STUDENTS_WITH_SIBLINGS) { d3.shuffle(this.students) const families = this.students.reduceRight((full_list, next_student) => { // 1 in four times, a student is assumed to be related to the one // next to them; the rest of the time, they're a new family. if (Math.random() < sibshare) { full_list[0].unshift(next_student) } else { full_list.unshift([next_student]) } return full_list }, [[]]) families.filter(family => family.length > 1).map(family => { // For prettiness, give them all a last name. family.map(student => student.last = family[0].last) this.groups.push(new Family(family)) }) } give_students_random_links() { // Learning pods this.assign_learning_pods() this.assign_siblings() } }38:Te22,class School_Population { constructor() { this.students = [] this.groups = [] } make_links() { for (const student of this.students) { student.links = [] } for (const group of this.groups) { group.make_links() } } get_grade(grade) { return this.students.filter(student => student.grade == grade) } remove_all_classrooms() { this._classrooms = undefined this.groups = this.groups.filter(d => d.link_type != "classroom") this.students.forEach(student => { student.links = student.links.filter(d => d.link_type != "classroom") }) } set_classrooms(list_of_rooms) { this._classrooms = list_of_rooms for (let classroom of list_of_rooms) { this.groups.push(new Classroom(classroom.students)) } } build_classrooms(order = "random") { let students this.remove_all_classrooms() if (order === "random") { students = this.grades.map(grade => { const students_in_grade = this.get_grade(grade); d3.shuffle(students_in_grade); return students_in_grade }) } if (order === "network") { // Get the order from the current network. students = this.networked_groups } // Builds empty classrooms. const classrooms = this.classrooms; for (let set_of_students of students) { if (set_of_students === undefined) {continue} // Sort the classrooms by how filled they are. This sorting will persist through the currently // active group of students--for instance, a pod or something. Unless the classroom is filled. classrooms.sort((a, b) => a.students.length - b.students.length) for (let student of set_of_students) { const grade_classes = classrooms.filter(room => room.grade === student.grade) const unfilled_classes = grade_classes.filter(room => room.students.length < room.max_size) let destination_class; if (unfilled_classes.length > 0) { destination_class = unfilled_classes[0] } else { grade_classes.sort((a, b) => a.length - b.length); destination_class = grade_classes[0] } destination_class.students.push(student) } } this.set_classrooms(classrooms) return this._classrooms } get networked_groups() { let current_group = -1 const completed = new Set() // Approach in a random order. d3.shuffle(this.students) // Reset values. this.students.forEach(student => student._assigned_group = undefined) const queue = [...this.students] const groups = [] while (queue.length > 0) { // pop the first element off the queue. const kid = queue.shift() if (completed.has(kid.id)) { // We've already done the kid. continue } // All kids start unassigned; but students added // b/c of links will get added earlier. if (kid._assigned_group === undefined) { kid._assigned_group = current_group++ groups[current_group] = [] } for (const link of kid.links) { const {student, link_type} = link // Put the kid in this group; student._assigned_group = current_group; // move the kid to the top of the queue, so that all of // their linkages will be followed before we move on. queue.unshift(student) } completed.add(kid.id); if (groups[current_group] === undefined) { groups[current_group] = [] } groups[current_group].push(kid); } return groups } }39:[] 32:{"id":"867060e12c123493","slug":"clustering-students-to-slow-virus-spread-inside-schools","title":"Clustering students to slow virus spread inside schools","thumbnail":"ae8018fd326d8feae3bd3b075bc2de02035929ce51a2d67ef4d81b218f4c5c57","access_level":"public","create_time":"$D2020-08-05T22:20:53.767Z","update_time":"$D2022-09-02T21:00:58.909Z","view_time":null,"first_public_time":"$D2020-08-10T21:14:22.006Z","has_unpublished_edits":null,"fork":false,"stars":21,"starred":false,"owner":{"type":"team","id":"18bbeceb36c8f564","login":"bmschmidt","name":"Benjamin Schmidt","avatar_url":"https://avatars-next.observableusercontent.com/addc2adb5ec95cc72a64820e4a08488bad5d48d95a895eef85a45b136ed66792","tier":"starter_2024"},"version":1313,"publish_version":1313,"role":null,"authored":false,"authors":[{"type":"individual","id":"33354ca265b21f01","login":"bmschmidt","name":"Benjamin Schmidt","avatar_url":"https://avatars-next.observableusercontent.com/addc2adb5ec95cc72a64820e4a08488bad5d48d95a895eef85a45b136ed66792","tier":null}],"members":[{"type":"individual","id":"33354ca265b21f01","login":"bmschmidt","name":"Benjamin Schmidt","avatar_url":"https://avatars-next.observableusercontent.com/addc2adb5ec95cc72a64820e4a08488bad5d48d95a895eef85a45b136ed66792","tier":null,"role":"editor"}],"comments":[{"id":"e8ab2f356b1bb73a","reply_to_id":null,"content":"fix by locking to version 149\n> import { drag } from '@d3/force-directed-graph@149';","create_time":"$D2022-07-04T18:15:29.882Z","update_time":null,"resolved":true,"user":{"type":"individual","id":"45a379fcfcb14253","login":"fil","name":"Fil","avatar_url":"https://avatars-next.observableusercontent.com/d5b1777907117a2bdf2a07eb98600d7a9beb21639fde42b9753e95c88c7731a6","tier":null}},{"id":"65cd768a002f9c24","reply_to_id":"e8ab2f356b1bb73a","content":"Thanks!","create_time":"$D2022-07-05T13:02:19.903Z","update_time":null,"resolved":true,"user":{"type":"individual","id":"33354ca265b21f01","login":"bmschmidt","name":"Benjamin Schmidt","avatar_url":"https://avatars-next.observableusercontent.com/addc2adb5ec95cc72a64820e4a08488bad5d48d95a895eef85a45b136ed66792","tier":null}}],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":8,"collection":{"id":"e7cc41ec60819d92","slug":"coronavirus","title":"Coronavirus","owner":{"id":"f35c755083683fe5","login":"observablehq","name":"Observable"}},"type":"notebook","body":{"title":"Clustering students to slow virus spread inside schools","cells":[{"id":0,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":939,"value":"md`## Show only certain networks\n\nTo understand the connections between students, try checking and unchecking some of these boxes. Pod/playgroup connections can bind an entire grade closely together; while family connections bridge across different grades.\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":474,"value":"viewof link_restrictions = checkbox({\"title\": \"Show networks derived from\",\"options\": [\"pod\", \"family\", \"classroom\"], value: [\"pod\", \"family\", \"classroom\"]} )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":976,"value":"md`# Take student connections into account\n\nThe selector below changes from a random assignment to one that groups social networks together. This is the most important thing to change!\n\nWhen you do so, the network will re-arrange as classroom assignments shift.\n`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":673,"value":"viewof assign_students_to_classes = radio({\"title\": \"Method of student assignment into classrooms\", description: \"This is the consideration I'm most interested in. Students can be randomly assigned, or we can assign in an order that groups connected students together. Someone who knows more network theory than I could probably find yet a better way to break students into communities and then isolate them; a further option would be to allow schools to notify parents of especially high-risk interactions to the community.\", options: [\n {\"label\": \"Randomly\", value: \"random\"},\n {\"label\": \"Keeping social networks close to each other.\", value: \"network\"}],\n 'value': 'network'})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":343,"value":"{\n while (true) { // Runs once per animation frame.\n yield md`\n\n Mouseover (or tap) any point in the network to see who the student is.\n\n * Student: ${current.name}\n * Grade: ${current.grade}\n * Number of exposures: ${current.links ? current.links.map(d=>d.student.id).length : 0}`\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":698,"value":"display = chart.node()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":812,"value":"viewof single_simulation = html`

${Object.assign(html`

Grade ${d.grade} Teacher ${d.teacher_number}'s ${d.day} class

Classroom assignments