View source for Epidemiology: The SEIR model

<html>
<form><input type="button" value="clear and run a simulation of 100 days" onClick="clearturtle();run()">
<input type="button" value="stop" onClick="stop()">
<input type="button" value="continue" onClick="goOn()"></form>
</html>
<jsxgraph width="600" height="600" box="box">
var brd = JXG.JSXGraph.initBoard('box', {originX: 20, axis: true, originY: 300, unitX: 6, unitY: 250});

var S = brd.createElement('turtle',[],{strokeColor:'yellow',strokeWidth:3});
var E = brd.createElement('turtle',[],{strokeColor:'blue',strokeWidth:3});
var I = brd.createElement('turtle',[],{strokeColor:'red',strokeWidth:3});
var R = brd.createElement('turtle',[],{strokeColor:'green',strokeWidth:3});
            
var s = brd.createElement('slider', [[0,-0.3], [30,-0.3],[0,1.27E-6,1]], {name:'s'});
var beta = brd.createElement('slider', [[0,-0.4], [30,-0.4],[0,0.5,1]], {name:'&beta;'});
var gamma = brd.createElement('slider', [[0,-0.5], [30,-0.5],[0,0.3,1]], {name:'&gamma;'});
var mu = brd.createElement('slider', [[0,-0.6], [30,-0.6],[0,0.0,1]], {name:'&mu;'});
var a = brd.createElement('slider', [[0,-0.7], [30,-0.7],[0,0.0,1]], {name:'a'});

brd.createElement('text', [40,-0.3, "initially infected population rate (on load: I(0)=1.27E-6)"]);
brd.createElement('text', [40,-0.4, "&beta;: infection rate"]);
brd.createElement('text', [40,-0.5, "&gamma;: recovery rate = 1/(days of infection)"]);

var t = 0; // global

brd.createElement('text', [40,-0.2, 
        function() {return "Day "+t+": infected="+brd.round(7900000*I.pos[1],1)+" recovered="+brd.round(7900000*R.pos[1],1);}]);

/*            
S.hideTurtle();
E.hideTurtle();
I.hideTurtle();
R.hideTurtle();
*/
function clearturtle() {
  S.cs();
  E.cs();
  I.cs();
  R.cs();

  S.hideTurtle();
  E.hideTurtle();
  I.hideTurtle();
  R.hideTurtle();
}
            
function run() {
  S.setPos(0,1.0-s.Value());
  I.setPos(0,s.Value());
  R.setPos(0,0);
  E.setPos(0,0);
                
  delta = 1; // global
  t = 0;  // global
  loop();
}
             
function turtleMove(turtle,dx,dy) {
  turtle.MoveTo([dx+turtle.pos[0],dy+turtle.pos[1]]);
}
             
function loop() {
  var dS = /*mu.Value()*(1-S.pos[1])*/-beta*I.pos[1]*S.pos[1]; 
  var dE = beta*I.pos[1]*S.pos[1]-(mu.Value()+a.Value())*E.pos[1];
  var dI = /*a.Value()*E.pos[1]*/-(gamma.Value()+mu.Value())*I.pos[1];
  var dR = gamma.Value()*I.pos[1]/*-mu.Value()*R.pos[1]*/;
  turtleMove(S,delta,dS);
//  turtleMove(E,delta,dE);
  turtleMove(I,delta,dI);
  turtleMove(R,delta,dR);
                
  t += delta;
  if (t<100.0) {
    active = setTimeout(loop,10);
  }
}

function stop() {
  if (active) clearTimeout(active);
  active = null;
}
function goOn() {
   if (t>0) {
     if (active==null) {
       active = setTimeout(loop,10);
     }
   } else {
     run();
   }

}
</jsxgraph>