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Spatial SIR model of Zombie outbreak
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README.md

Spatial SIR model of a zombie outbreak in France

This simple SIR model simulates a zombie outbreak in France, inspired by the scenario described in When zombies attack!: Mathematical modeling of an outbreak of zombie infection.

Here the model is extended spatially to allow neighboring grid cells to interact with one another (each cell can interact with its 8 adjacent cells) so infection can spread from cell to cell, and the global zombie outbreak can be visually appreciated (who doesn't want to see a nice zombie wave!).

The patient zero (there must be one ...) is placed somewhere between Lyon and Nimes. You can also add more foci infection by clicking on the map.

The two line charts on the right show the current state of the population for each iteration of the model:

  • Blue: living people (on the map) and remaining percentage of living population (bottom line chart)
  • Green: zombie wave (on the map) and percentage of living population that is infected (top line chart)
  • Red: dead people (on the map) and percentage of living population that died from the zombie outbreak (bottom line chart)

The France population density image is created from the published 2011 Europe Population grid data (see the formatData function in this repository for the details of how the data were transformed to the grid format).

Raw
france-dataGrid.json
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Raw
index.html
<!DOCTYPE html>
<meta charset="utf-8">
<style>
.pathSusceptible {
fill: none;
stroke: #1FBAD6;
stroke-width: 2;
}
.pathDeath {
fill: none;
stroke: #F25754;
stroke-width: 2;
}
.pathInfection {
fill: none;
stroke: #66FF00;
stroke-width: 2;
}
.daysCount {
position: absolute;
left: 380px;
top: 20px;
font-size: 1.5em;
color: white;
}
.instructionText {
width: 200px;
position: absolute;
left: 600px;
top: 10px;
font-size: 1.5em;
color: black;
}
text {
font-family: sans-serif;
}
</style>
<canvas style="position: absolute; left: 0; top: 0" onclick="storeGuess(event)"></canvas>
<svg id="infectionGraph" style="position: absolute; left: 545; top: 80"></svg>
<svg id="deathGraph" style="position: absolute; left: 545; top: 280"></svg>
<div class="instructionText">Click on the map to add more Zombies</div>
<div class="daysCount">
Days: <span id="daysCounter"></span>
</div>
<script src="https://d3js.org/d3.v4.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.4/lodash.js"></script>
<script>
const margin = {top: 10, right: 10, bottom: 10, left: 75},
width = 400 - margin.left - margin.right,
height = 200 - margin.top - margin.bottom
//two svg for the real time data
const svgInfection = d3.select("#infectionGraph")
.attr("width", width + margin.left + margin.right)
.attr("height", height + margin.top + margin.bottom)
.append("g")
.attr("transform", `translate(${margin.left}, ${margin.top})`)
.attr("width", width)
.attr("height", height)
const svgDeadAlive = d3.select("#deathGraph")
.attr("width", width + margin.left + margin.right)
.attr("height", height + margin.top + margin.bottom)
.append("g")
.attr("transform", `translate(${margin.left}, ${margin.top})`)
.attr("width", width)
.attr("height", height)
const pathInfection = svgInfection
.append('path')
.attr("class", "pathInfection")
const pathDeath = svgDeadAlive
.append('path')
.attr("class", "pathDeath")
const pathSusceptible = svgDeadAlive
.append('path')
.attr("class", "pathSusceptible")
const infectionAxis = svgInfection
.append("g")
.attr("class", "yAxis")
.attr("transform", `translate(${-3}, 0)`)
const deadAliveAxis = svgDeadAlive
.append("g")
.attr("class", "yAxis")
.attr("transform", `translate(${-3}, 0)`)
//svg for days counter text
const svgCounter = d3.select("#daysCounter")
.attr("width", 50)
.attr("height", 50)
const line = d3.line()
.curve(d3.curveCatmullRom.alpha(0.5))
const yScaleInfection = d3.scaleLinear()
.range([+svgInfection.attr("height"), 0])
const yScaleDeadAlive = d3.scaleLinear()
.range([+svgDeadAlive.attr("height"), 0])
let dataGrid;
const imWidth = 538;
const imHeight = 553;
d3.text("france-dataGrid.json", (error, data) => {
if (error) console.log(error)
const dataRaw = data.split(",").map(d => parseInt(d))
//create dataGrid that will be used to create an image
dataGrid = new Uint8ClampedArray(imWidth * imHeight * 4);//reserving enough bytes
dataRaw.map((d, i) => {
dataGrid[i*4 ] = 0; // red layer [0, 255]
dataGrid[i*4+1] = 0; // green layer
dataGrid[i*4+2] = d; // blue layer
dataGrid[i*4+3] = 255; // alpha layer
})
//initial image
let imageData = createImageURL(dataGrid, imWidth, imHeight)
loadImage(imageData, imWidth, imHeight);
//SIR Model parameters
const beta = 0.01 //how transmittable the disease is. One bite is all it takes!
const gamma = 3 //how fast you go from zombie to dead. Sort of average of how fast our zombie hunters are working and natural death ... 3 time iterations in this case
//Let's put patient 0 somewhere between Lyon and Nimes
const posI_0 = 410205
dataGrid[posI_0] = 1
//Initial state of susceptibles/infected/dead people
let nInfected = [],
nRemoved = [],
nSusceptible = [],
ct = 0;//for rolling window if too much iterations
let [pInfected, pRemoved, pSusceptible] = storeState(dataGrid, imWidth, imHeight)
//pInfected as percentage of living population
pInfected = pInfected/(pSusceptible+pInfected)
nInfected.push(pInfected)
nRemoved.push(pRemoved)
nSusceptible.push(pSusceptible)
const deadAliveAxisLeft = d3.axisLeft()
.scale(yScaleDeadAlive)
.tickFormat(d3.format(".0%"))
const infectionAxisLeft = d3.axisLeft()
.scale(yScaleInfection)
.tickFormat(d3.format(".2%"))
svgInfection
.append("g")
.attr("transform", `translate(${-63}, ${height/2})`)
.append("text")
.attr("transform", "rotate(-90)")
.attr("text-anchor", "middle")
.html("Current")
svgInfection
.append("g")
.attr("transform", `translate(${-50}, ${height/2})`)
.append("text")
.attr("transform", "rotate(-90)")
.attr("text-anchor", "middle")
.html("infected population")
svgDeadAlive
.append("g")
.attr("transform", `translate(${-40}, ${height/2})`)
.append("text")
.attr("transform", "rotate(-90)")
.attr("text-anchor", "middle")
.html("Dead/Alive")
deadAliveAxis
.call(deadAliveAxisLeft)
infectionAxis
.call(infectionAxisLeft)
//Run the simulation for iterMax iterations
let iter = 0;
const iterMax = 500;
let daysCount = d3.select("#daysCounter")
.html(iter)
const timer = d3.timer(function() {
//euler method to calculate new state
dataGrid = euler(dataGrid, beta, gamma, imWidth, imHeight);
//generate new image from the latest simulation data
imageData = createImageURL(dataGrid, imWidth, imHeight)
updateImageData(imageData, imWidth, imHeight)
//store current susceptibles/infected/dead state
let [pInfected, pRemoved, pSusceptible] = storeState(dataGrid, imWidth, imHeight)
//pInfected as percentage of living population
pInfected = pInfected/(pSusceptible+pInfected)
if (ct++ > width) { //rolling window
nInfected.shift();
nRemoved.shift();
nSusceptible.shift();
}
nInfected.push(pInfected)
nRemoved.push(pRemoved)
nSusceptible.push(pSusceptible)
yScaleInfection
.domain([0, d3.max(nInfected)]);
yScaleDeadAlive
.domain([0, d3.max(d3.merge([nRemoved, nSusceptible]))])
infectionAxisLeft
.scale(yScaleInfection)
infectionAxis
.transition()
.duration(100)
.call(infectionAxisLeft)
pathInfection
.attr('d', line(nInfected.map((d,i) => {
return [i, yScaleInfection(d)];
})));
pathDeath
.attr('d', line(nRemoved.map((d,i) => {
return [i, yScaleDeadAlive(d)];
})));
pathSusceptible
.attr('d', line(nSusceptible.map((d,i) => {
return [i, yScaleDeadAlive(d)];
})));
iter += 1
daysCount
.html(iter)
if (iter >= iterMax) timer.stop()
});//d3.timer
})//d3.text
function storeState(dataGrid, imWidth, imHeight){
let pI = 0,
pR = 0,
pS = 0
for (let y = 0; y < imHeight; y++) {
for (let x = 0; x < imWidth; x++) {
let pos = (y * imWidth + x) * 4 + 0; // position in buffer based
pI += dataGrid[pos+1]
pR += dataGrid[pos]
pS += dataGrid[pos+2]
}
}
return [pI, pR, pS]
}//storeState
function createImageURL(dataBuffer, imWidth, imHeight) {
// create off-screen canvas element to create image
const canvas = document.createElement('canvas'),
ctx = canvas.getContext('2d');
canvas.width = imWidth;
canvas.height = imHeight;
// create imageData object
let imData = ctx.createImageData(imWidth, imHeight);
// set our data as source
imData.data.set(dataBuffer);
// update off-screen canvas with new data
ctx.putImageData(imData, 0, 0);
const dataURL = canvas.toDataURL();//produces a PNG file
return dataURL
}//createImageURL
function loadImage(dataImage, imWidth, imHeight){
const img = new Image()
const canvas = d3.select('canvas')
.attr("width", imWidth)
.attr("height", imHeight)
const ctx = canvas.node().getContext('2d')
img.src = dataImage
img.onload = function() {
//flip image vertically
ctx.scale(1,-1);
ctx.translate(0,-imHeight);
ctx.drawImage(img, 0, 0, imWidth, imHeight)
}
}//loadImage
function updateImageData(dataImage, imWidth, imHeight){
const img = new Image()
const canvas = d3.select('canvas')
const ctx = canvas.node().getContext('2d')
img.src = dataImage
img.onload = function() {
ctx.drawImage(img, 0, 0, imWidth, imHeight)
}
}//updateImageData
function euler(imData, beta, gamma, imWidth, imHeight){
let newData = []
//start by y since data grouped by latitude first
for (let y = 0; y < imHeight; y++) {
for (let x = 0; x < imWidth; x++) {
const posS = (y * imWidth + x) * 4 + 2; //blue layer
const posI = (y * imWidth + x) * 4 + 1;
const posR = (y * imWidth + x) * 4 + 0; // position in buffer based on x and y
const posAlpha = (y * imWidth + x) * 4 + 3; // position in buffer based on x and y
newData[posAlpha] = 255 //alpha channel
const posS_a = ((y-1) * imWidth + x) * 4 + 2;
const posI_a = ((y-1) * imWidth + x) * 4 + 1;
const posS_b = ((y+1) * imWidth + x) * 4 + 2;
const posI_b = ((y+1) * imWidth + x) * 4 + 1;
//new infection
let newInfection = (beta * (
//line above
imData[posS_a ] * imData[posI_a ] * 0.75 +
imData[posS_a-4] * imData[posI_a-4] * 0.25 + //less influcenced by diagonales corners
imData[posS_a+4] * imData[posI_a+4] * 0.25 + //less influcenced by diagonales
//same line
imData[posS ] * imData[posI ] +
imData[posS-4] * imData[posI-4] * 0.75 +
imData[posS+4] * imData[posI+4] * 0.75 +
//line below
imData[posS_b ] * imData[posI_b ] * 0.75 +
imData[posS_b-4] * imData[posI_b-4] * 0.25 + //less influcenced by diagonales
imData[posS_b+4] * imData[posI_b+4] * 0.25 //less influcenced by diagonales
)
) | 0
//infected people dying
let newDead = gamma * imData[posI] | 0
//if infection is not greater than people in cell
if (newInfection <= imData[posS]){
newData[posS] = imData[posS] - newInfection
//if not all the infected people are dead
if (imData[posI] + newInfection >= newDead) {
newData[posI] = imData[posI] + newInfection - newDead
newData[posR] = imData[posR] + newDead
}
else {
newData[posI] = 0
newData[posR] = imData[posR] + imData[posI]
}
}
//if more infection than susceptible
else {
//if possible new death is possible
if (imData[posI] + imData[posS] >= newDead) {
newData[posS] = 0 //no susceptible left
newData[posI] = imData[posI] + imData[posS] - newDead
newData[posR] = imData[posR] + newDead
}
else {
newData[posS] = 0
newData[posI] = 0
newData[posR] = imData[posR] + imData[posS] + imData[posI]
}
}
}
}
return newData
}//euler
function storeGuess(event){
const x = event.offsetX;
const y = event.offsetY;
const posI = ((imHeight-y) * imWidth + x) * 4 + 1;
dataGrid[posI] = 1
}
</script>
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