感染症の伝播と集団免疫効果を視覚化する。

先日、たまたま見つけて購入した「Nature in Code」に掲載されていた、感染症シミュレーション(SIRモデル)が面白そうだったので作成してみた。

白いセルが感染可能者（感染する前の健康な人）、赤いセルが感染者、緑のセルが隔離者（死亡、もしくは快復して免疫を獲得した人）となる。

参考書のコードを少しカスタマイズして、感染率や隔離率を調整できるようにした。
感染率が高いと早く広範囲に感染が広がり、隔離率が高いと早く収束する。
数値は、「初期感染者」以外は、０〜１の値で割合を示す。例えば、感染率が1の場合、隣接する感染可能者は100%感染する。

初期免疫保持者率は、感染が広がる前に免疫を獲得している人（灰色）の割合。
初期免疫保持者が多いと、拡散せずに早期に収束する。（集団免疫効果）

このシミュレーターだと初期隔離者がランダムに配置されるため、集団免疫率は入力した数値より低くなる。
（重複したセルに配置されることがあるので、1を入力しても100%にならない)

改良の余地が多いけど、数値をいろいろ調整して試してみると、なかなか楽しい。

サンプルコード

!(function(){
    "use strict";
    
    var width = 600;
    var height = 600;
    var svg = d3.select('svg')
          .attr('width', width)
          .attr('height', height);
        
        
    var grid_length = 100;
    var grid = [];
    var temp_grid = [];
    var point = 3
    var touch = 0.75;
    var beta = 0.1;
    var gamma = 0.05;
    var timer;    
    var flag = true;
    
    init();
    
    d3.select("#point").on("change", init);
    d3.select("#touch").on("change", init);
    
    d3.select("#start").on("click", function(){
        beta = d3.select("#beta").node().value;
        gamma = d3.select("#gamma").node().value;
        
        function simulate_and_visualize() {        
            run_time_step();
            update_grid(grid,["S","white","I","red","R","green", "W", "gray"]);
        }
        if(flag) timer = setInterval(simulate_and_visualize, 50);
        
        flag = false;
    });
    
    d3.select("#stop").on("click", function(){
        clearInterval(timer);
        flag = true;
    });
    
    d3.select("#reset").on("click", function(){
        clearInterval(timer);
        init_grid();
        update_grid(grid,["S","white","I","red","R","green", "W", "gray"]);
        flag = true;
    });
    
    
    function init() {
        clearInterval(timer);
        point = d3.select("#point").node().value;
        touch = d3.select("#touch").node().value;
        init_grid();
        update_grid(grid,["S","white","I","red","R","green", "W", "gray"]);    
    }
    
    
    function get_random_int(min, max) {
        return Math.floor(Math.random()*(max - min + 1)) + min;
    }
    
    function init_grid() {
        for(var i=0; i < grid_length; i = i + 1){
            grid[i] = [];
            for (var ii = 0; ii < grid_length; ii = ii + 1){
                grid[i][ii] = "S";
            }
        }
        for (var i = 0; i < (grid_length*grid_length) * (1 - touch ) ; i++) {
            grid[get_random_int(0, grid_length-1)][get_random_int(0, grid_length-1)] = "W";
        }
        for (var i = 0; i < point ; i++) {
            grid[get_random_int(0, grid_length-1)][get_random_int(0, grid_length-1)] = "I";
        }
    }
    
    
    function run_time_step() {
        for(var i=0; i < grid_length; i = i + 1){
            temp_grid[i] = [];
            for (var ii = 0; ii < grid_length; ii = ii + 1){
                temp_grid[i][ii] = grid[i][ii];
            }
        }
        for (i=0; i < grid_length; i = i+1){
            for(ii = 0; ii < grid_length; ii = ii + 1){
                if (grid[i][ii] == "I"){
                    expose_neighbors(i, ii);
                    tray_recovery(i, ii);
                }
            }
        }
        for (i=0; i < grid_length; i = i+1){
            for(ii = 0; ii < grid_length; ii = ii + 1){
                grid[i][ii] = temp_grid[i][ii];
            }
        }
    }
    
    function expose_neighbors(i, ii) {
        for(var n_i = i-1; n_i <= i+1; n_i = n_i + 1){
            for(var n_ii = ii-1; n_ii <= ii+1; n_ii = n_ii + 1){
                if (n_i == i && n_ii == ii){
                    continue;                
                }
                try_infection(get_bounded_index(n_i), get_bounded_index(n_ii));
            }
        }
    }
    
    function try_infection(i, ii) {
        if (grid[i][ii] == "S"){
            if (Math.random() < beta){
                temp_grid[i][ii] = "I"
            }
        }
    }
    
    function tray_recovery(i, ii) {
        if (grid[i][ii] == "I"){
            if (Math.random() < gamma){
                temp_grid[i][ii] = "R"
            }
        }
        
    }
    
    function get_bounded_index(index){
        var bounded_index = index;
        if (index < 0){
            bounded_index = index + grid_length;
        }
        if (index >= grid_length){
            bounded_index = index - grid_length;
        }
        
        return bounded_index;
    }
    
    function update_grid(data,colors) {
        var grid_length = data.length;
    
        var rw = Math.floor(width/grid_length);
        var rh = Math.floor(height/grid_length);
    
        var g = svg.selectAll('g').data(data)
                
        var newG = g.enter().append('g')
                .attr('transform', function (d, i) {
                  return 'translate(0, ' + (width/grid_length) * i + ')';
                });
    
        var rect = g.merge(newG).selectAll('rect')
                .data(function (d) {
                  return d;
                })
                
        var newRect = rect.enter().append('rect')
                .attr('x', function (d, i) {
                  return (width/grid_length) * i;
                })
                .attr('width', rw)
                .attr('height', rh)
            
                
        rect.merge(newRect).attr('class',function(d) {
                  return d;
                });
        
        for (var i = 0; i < colors.length; i = i + 2) {
            d3.selectAll("."+colors[i]).style("fill",colors[i+1]);	
        }
    }
    
    
}());

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!(function(){

"use strict";

var width = 600;

var height = 600;

var svg = d3.select('svg')

.attr('width', width)

.attr('height', height);

var grid_length = 100;

var grid = [];

var temp_grid = [];

var point = 3

var touch = 0.75;

var beta = 0.1;

var gamma = 0.05;

var timer;

var flag = true;

init();

d3.select("#point").on("change", init);

d3.select("#touch").on("change", init);

d3.select("#start").on("click", function(){

beta = d3.select("#beta").node().value;

gamma = d3.select("#gamma").node().value;

function simulate_and_visualize() {

run_time_step();

update_grid(grid,["S","white","I","red","R","green", "W", "gray"]);

}

if(flag) timer = setInterval(simulate_and_visualize, 50);

flag = false;

});

d3.select("#stop").on("click", function(){

clearInterval(timer);

flag = true;

});

d3.select("#reset").on("click", function(){

clearInterval(timer);

init_grid();

update_grid(grid,["S","white","I","red","R","green", "W", "gray"]);

flag = true;

});

function init() {

clearInterval(timer);

point = d3.select("#point").node().value;

touch = d3.select("#touch").node().value;

init_grid();

update_grid(grid,["S","white","I","red","R","green", "W", "gray"]);

}

function get_random_int(min, max) {

return Math.floor(Math.random()*(max - min + 1)) + min;

}

function init_grid() {

for(var i=0; i < grid_length; i = i + 1){

grid[i] = [];

for (var ii = 0; ii < grid_length; ii = ii + 1){

grid[i][ii] = "S";

}

for (var i = 0; i < (grid_length*grid_length) * (1 - touch ) ; i++) {

grid[get_random_int(0, grid_length-1)][get_random_int(0, grid_length-1)] = "W";

}

for (var i = 0; i < point ; i++) {

grid[get_random_int(0, grid_length-1)][get_random_int(0, grid_length-1)] = "I";

}

function run_time_step() {

for(var i=0; i < grid_length; i = i + 1){

temp_grid[i] = [];

for (var ii = 0; ii < grid_length; ii = ii + 1){

temp_grid[i][ii] = grid[i][ii];

}

for (i=0; i < grid_length; i = i+1){

for(ii = 0; ii < grid_length; ii = ii + 1){

if (grid[i][ii] == "I"){

expose_neighbors(i, ii);

tray_recovery(i, ii);

}

for (i=0; i < grid_length; i = i+1){

for(ii = 0; ii < grid_length; ii = ii + 1){

grid[i][ii] = temp_grid[i][ii];

}

function expose_neighbors(i, ii) {

for(var n_i = i-1; n_i <= i+1; n_i = n_i + 1){

for(var n_ii = ii-1; n_ii <= ii+1; n_ii = n_ii + 1){

if (n_i == i && n_ii == ii){

continue;

}

try_infection(get_bounded_index(n_i), get_bounded_index(n_ii));

}

function try_infection(i, ii) {

if (grid[i][ii] == "S"){

if (Math.random() < beta){

temp_grid[i][ii] = "I"

}

function tray_recovery(i, ii) {

if (grid[i][ii] == "I"){

if (Math.random() < gamma){

temp_grid[i][ii] = "R"

}

function get_bounded_index(index){

var bounded_index = index;

if (index < 0){

bounded_index = index + grid_length;

}

if (index >= grid_length){

bounded_index = index - grid_length;

}

return bounded_index;

}

function update_grid(data,colors) {

var grid_length = data.length;

var rw = Math.floor(width/grid_length);

var rh = Math.floor(height/grid_length);

var g = svg.selectAll('g').data(data)

var newG = g.enter().append('g')

.attr('transform', function (d, i) {

return 'translate(0, ' + (width/grid_length) * i + ')';

});

var rect = g.merge(newG).selectAll('rect')

.data(function (d) {

return d;

})

var newRect = rect.enter().append('rect')

.attr('x', function (d, i) {

return (width/grid_length) * i;

})

.attr('width', rw)

.attr('height', rh)

rect.merge(newRect).attr('class',function(d) {

return d;

});

for (var i = 0; i < colors.length; i = i + 2) {

d3.selectAll("."+colors[i]).style("fill",colors[i+1]);

}

}());

サンプルコード

投稿者: shimizu