2e:null 2f:["$","title",null,{"children":"SIR Model | Chathura Jayalath | Observable"}] 34:[] 32:{"id":"d3c61b848509c138","slug":"sir-models","title":"SIR Model","thumbnail":"456d2bab9060e40d813b088cdc0a8399b2386189545ac28979a274e18fffb9f1","access_level":"public","create_time":"$D2020-09-08T03:56:38.943Z","update_time":"$D2020-09-13T01:12:14.501Z","view_time":null,"first_public_time":"$D2020-09-08T04:37:13.719Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"faa67bfd1359f951","login":"deamonpog","name":"Chathura Jayalath","avatar_url":"https://avatars-next.observableusercontent.com/1bc13a0724d43e94c26de301357a2897d22e5c4e01e7f160ea8fba232ef861f1","tier":"starter_2024"},"version":219,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"5fe81dea2f61079a","login":"deamonpog","name":"Chathura Jayalath","avatar_url":"https://avatars-next.observableusercontent.com/1bc13a0724d43e94c26de301357a2897d22e5c4e01e7f160ea8fba232ef861f1","tier":null}],"members":[{"type":"individual","id":"5fe81dea2f61079a","login":"deamonpog","name":"Chathura Jayalath","avatar_url":"https://avatars-next.observableusercontent.com/1bc13a0724d43e94c26de301357a2897d22e5c4e01e7f160ea8fba232ef861f1","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"SIR Model","cells":[{"id":0,"value":"md`# SIR Model`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":215,"value":"md`https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SIR_model_without_vital_dynamics`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":152,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":156,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":200,"value":"md`## Initial Conditions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"viewof N0 = {\n const form = html``;\n form.i.oninput = () => form.o.value = `${(form.value = form.i.valueAsNumber).toFixed(0)} Population Count`;\n form.i.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":172,"value":"viewof InitSusFract = {\n const form = html``;\n form.i.oninput = () => form.o.value = `${(form.value = form.i.valueAsNumber).toFixed(3)} Initial Susceptible Fraction`;\n form.i.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":169,"value":"viewof InitInfFract = {\n const form = html``;\n form.i.oninput = () => form.o.value = `${(form.value = form.i.valueAsNumber).toFixed(3)} Initial Infected Fraction`;\n form.i.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"S0 = Math.round(InitSusFract * N0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"I0 = Math.round(InitInfFract * N0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":194,"value":"R0 = getR(N0, S0, I0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":203,"value":"md`## Model Parameters`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":58,"value":"viewof inTicks = {\n const form = html``;\n form.i.oninput = () => form.o.value = `${(form.value = form.i.valueAsNumber).toFixed(0)} ticks`;\n form.i.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"viewof inBeta = {\n const form = html``;\n form.i.oninput = () => form.o.value = `${(form.value = form.i.valueAsNumber).toFixed(4)} beta`;\n form.i.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":129,"value":"viewof inGamma = {\n const form = html``;\n form.i.oninput = () => form.o.value = `${(form.value = form.i.valueAsNumber).toFixed(4)} gamma`;\n form.i.oninput();\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":95,"value":"{\n let ticks = Math.round(inTicks)\n let beta = inBeta\n let gamma = inGamma\n let data = runModel(ticks, beta, gamma)\n let traceS = {\n x : Array.from(Array(ticks).keys()),\n y : data[0],\n name : 'S.',\n type : 'scatter'\n };\n let traceI = {\n x : Array.from(Array(ticks).keys()),\n y : data[1],\n name : 'I.',\n type : 'scatter'\n };\n let traceR = {\n x : Array.from(Array(ticks).keys()),\n y : data[2],\n name : 'R.',\n type : 'scatter'\n };\n const div = DOM.element('div');\n Plotly.newPlot(div, [traceS,traceI,traceR])\n return div\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":50,"value":"function getR(N, S, I){\n return N - (S + I);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"function nextS(N, S, I , R, beta, gamma){\n return S - (beta * I * S / N)\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"function nextI(N, S, I , R, beta, gamma){\n return I + ((beta * I * S / N) - gamma * I )\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"function nextR(N, S, I , R, beta, gamma){\n return R + (gamma * I);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":82,"value":"function runModel(ticks, beta, gamma) {\n let tsS = Array.from(Array(ticks).keys()).map(x => (x == 0)? S0 : -1)\n let tsI = Array.from(Array(ticks).keys()).map(x => (x == 0)? I0 : -1)\n let tsR = Array.from(Array(ticks).keys()).map(x => (x == 0)? getR(N0, S0, I0) : -1)\n for(let i=1; i < ticks; i++){\n tsS[i] = nextS(N0, tsS[i-1], tsI[i-1], tsR[i-1], beta, gamma)\n tsI[i] = nextI(N0, tsS[i-1], tsI[i-1], tsR[i-1], beta, gamma)\n tsR[i] = nextR(N0, tsS[i-1], tsI[i-1], tsR[i-1], beta, gamma)\n }\n return [tsS, tsI, tsR]\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":103,"value":"md`## Importing Libraries`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":99,"value":"Plotly = require(\"https://cdn.plot.ly/plotly-latest.min.js\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":101,"value":"d3 = require(\"d3\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"1","titling":"auto"}} 33:"$32:body"