info += ' \n';

info += ' kll: yes it has to do with the corona virus epidemiology \n';

info += ' i try to find / learn some math, first only use:\n';

info += ' https://stackoverflow.com/questions/41195063/general-smoothstep-equation \n';

info += ' here try Pascal Triangle solution from Tushar Ghosh answer\n';

info += ' \n';

info += ' you are in the edit window and can press the (>) RUN button \n';

info += ' or go to present view https://editor.p5js.org/kll/present/kKdj9HDS1  \n\n';

info += ' operation: change slider to see day details ( white ) or adjust other settings numbers.\n\n';

info += ' copyleft: KLL engineering ( CC BY SA )\n';

info += ' more: http://kll.engineering-news.org/kllfusion01/articles.php?article_id=168 \n';

//________________________________________________________ VARIABLES

var x = 0;

var xmax = 100; //______ x axis 0 .. 100 ( timeline like in DAYs )

var xstart = 10; //_____ start step function at day

var xstop = 70; //______ stop step function at day

var xs = 0.0; //________ 0.0 .. 1.0 for the graph function

​

var dxss = 100.0 / (xstop - xstart) / xmax; // stepsize in the smooth window 

var xss = 0; //_________ 0.0 .. 1.0 for the smooth step range calc function

​

var y = 0;

var ymax = 100.0; //____ y axis 0 .. 100.0% / like of

var yreal = 331092264; // people in a country 69808350 THAILAND / 83783942 GERMANY / 331092264 USA

var yzoom = 2; //_______ right axis range for "R" https://en.wikipedia.org/wiki/Basic_reproduction_number

var ystart = 0; //______ start step from population %

var ystop = 80; //______ stop step at population ( assume epidemic level where infection stops alone )

var ys = 0.0; //________ 0.0 .. 1.0 for the calc function

var ydt = 18; //________ after 18 days of infection you are dead or ?healed?immune?

var ymt = 7.0; //_______ pct of infected die ( USA 19.7 https://www.worldometers.info/coronavirus/country/us/ )

var astep = 3.0; //_____ for generalSmoothStep(a, x)

​

// init data arrays

var xi = [100]; //_______ 0 .. 100 x ( 6 pix ) in graph area ( days )

var yi = [100]; //_______ 0 .. 100.0 y step function ( total infections )

var ydi = [100]; //______ numeric derivative of y data ( new infections )

var yti = [100]; //______ timespaned (ydt) infected ( active cases )

var ymd = [100]; //______ mortal cases that day ( not show in graph )

var ymi = [100]; //______ mortal cases

var yRi = [100]; //______ R reproduction rate

​

// garph area settings

var gx0 = 130;

var gy0 = 400;

var gxw = 600;

var gyh = 300;

​

let sSlider; //___________________________________________ day select slider

let ss = 0; //____________________________________________ select slider setpoint

let inp1,inp2,inp3,inp4,inp5,inp6,inp7,inp8;

​

//________________________________________________________ SETUP

function setup() {

  createCanvas(800, 520+120); // add operation menu

  console.log(info);

  create_DOM();

  // test_print();

  calc_list(); //_________________________________________ fill data arrays xi,yi ( and print )

}

​

function create_DOM() {

  sSlider = createSlider(0, 99, ss, 1);

  sSlider.size(gxw);

  sSlider.position(gx0, 530); 

​

  inp1 = createInput(str(xstart));

  inp1.changed(myInputXSTART);

  inp1.position(50,520+50);

  inp1.size(40);

​

  inp2 = createInput(str(xstop));

  inp2.changed(myInputXSTOP);

  inp2.position(150,520+50);

  inp2.size(40);

​

  inp3 = createInput(str(ystart));

  inp3.changed(myInputYSTART);

  inp3.position(250,520+50);

  inp3.size(40);

​

  inp4 = createInput(str(ystop));

  inp4.changed(myInputYSTOP);

  inp4.position(350,520+50);

  inp4.size(40);

​

  inp5 = createInput(str(astep));

  inp5.changed(myInputASTEP);

  inp5.position(450,520+50);

  inp5.size(40);

​

  inp6 = createInput(str(ydt));

  inp6.changed(myInputYDT);

  inp6.position(50,520+90);

  inp6.size(40);

​

  inp7 = createInput(str(ymt));

  inp7.changed(myInputYMT);

  inp7.position(150,520+90);

  inp7.size(40);

​

  inp8 = createInput(str(yreal));

  inp8.changed(myInputYREAL);

  inp8.position(250,520+90);

  inp8.size(80);

​

}

// change number and press ENTER to get that going

function myInputXSTART() {

  xstart = int(this.value());

  calc_list();

  console.log('xstart: ', xstart);

}

function myInputXSTOP() {

  xstop = int(this.value());

  calc_list();

  console.log('xstop: ', xstop);

}

function myInputYSTART() {

  ystart = int(this.value());

  calc_list();

  console.log('ystart: ', ystart);

}

function myInputYSTOP() {

  ystop = int(this.value());

  calc_list();

  console.log('ystop: ', ystop);

}

function myInputASTEP() {

  astep = float(this.value());

  calc_list();

  console.log('slope: ', astep);

}

function myInputYDT() {

  ydt = int(this.value());

  calc_list();

  console.log('sick days: ', ydt);

}

function myInputYMT() {

  ymt = float(this.value());

  calc_list();

  console.log('mortality : ', ymt,'%' );

}

function myInputYREAL() {

  yreal = int(this.value());

  calc_list();

  console.log('population: ', yreal );

}

//________________________________________________________ DRAW

function draw() {

  background(150, 150, 0);

  ss = sSlider.value();

  draw_graph();

}

​

//________________________________________________________ GRAPH

function draw_axis(ls = 10) {

  textSize(12);

  for (var i = 0; i <= ls; i++) {

    stroke(0,0, 80);

    line(gx0 - 20, gy0 - i * gyh / ls, gx0 - 10, gy0 - i * gyh / ls);

    noStroke();

    text(nf(i * ymax / ls, 3, 0), gx0 - 50, gy0 - i * gyh / ls + 4);

    text('pct', gx0 - 45, gy0 - gyh - 15);

​

    text(nf(i * yreal / ls, 8, 0), gx0 - 115, gy0 - i * gyh / ls + 4);

    text('people', gx0 - 115, gy0 - gyh - 15);

​

    text(nf(i * yzoom / ls, 0, 1), gx0 + gxw + 10, gy0 - i * gyh / ls + 4);

    text('R', gx0 + gxw + 10, gy0 - gyh - 15);

​

    stroke(0.0, 80);

    line(gx0 + i * gxw / ls, gy0 + 10, gx0 + i * gxw / ls, gy0 + 20);

    noStroke();

    text(nf(i * xmax / ls, 0, 0), gx0 + i * gxw / ls - 3, gy0 + 35);

    text('days', gx0 + gxw - 10, gy0 + 50);

  }

  strokeWeight(6); //_____________________________________ Make the points n pixels in size    

  stroke('purple'); //____________________________________ total infections

  point(gx0, gy0 + 55);

  noStroke();

  fill(0);

  text('total infection / '+nf(xstart,0,0)+'..'+nf(xstop,0,0)+' days '+nf(ystart,0,0)+'..'+nf(ystop,0,0)+' %', gx0 + 15, gy0 + 60);

  fill('white');

  text(nf(yi[ss],0,1)+' % '+nf(yi[ss]*yreal/100,0,0),gx0 + 220, gy0 + 60);

​

  stroke('red'); //______________________________________ step derivative new infections

  //noFill();

  fill(0, 70, 80);

  strokeWeight(1);

  circle(gx0, gy0 + 70, 5);

  noStroke();

  fill(0);

  text('new infections per day', gx0 + 15, gy0 + 75);

  fill('white');

  text(nf(ydi[ss],0,1)+' % '+nf(ydi[ss]*yreal/100,0,0),gx0 + 220, gy0 + 75);

​

  //noFill();

  fill(0, 70, 80);

  stroke('cyan'); //______________________________________ active cases

  rectMode(RADIUS);

  strokeWeight(0.5);

  rect(gx0, gy0 + 85, 3, 3);

  noStroke();

  fill(0);

  text('active cases ( avg ' + nf(ydt, 0, 0) + ' days sick )', gx0 + 15, gy0 + 90);

  fill('white');

  text(nf(yti[ss],0,1)+' % '+nf(yti[ss]*yreal/100,0,0),gx0 + 220, gy0 + 90);

​

  stroke('black'); //_____________________________________ dead

  noFill();

  circle(gx0, gy0 + 100, 5);

  fill(0);

  noStroke();

  //text('+',gx0-3, gy0 + 100+5);

  noStroke();

  fill(0);

  text('fatal cases ( avg ' + nf(ymt, 0, 1) + ' pct mortality)', gx0 + 15, gy0 + 105);

  fill('white');

  text(nf(ymi[ss],0,1)+' % '+nf(ymi[ss]*yreal/100,0,0),gx0 + 220, gy0 + 105);

​

  noFill(); //____________________________________________ R value ( right Y axis )

  stroke(200, 0, 0);

  strokeWeight(3);

  point(gx0 + gxw - 220, gy0 + 70);

  noStroke();

  fill(0);

  text('R value ( last 4 day / prev 4 day )', gx0 + gxw - 205, gy0 + 75);

  fill('white');

  text(nf(yRi[ss],0,2),gx0 +gxw -20, gy0 + 75);

​

  strokeWeight(1); //_____________________________________ slider position

  stroke('white');

  line(gx0+ss*gxw/100,gy0,gx0+ss*gxw/100,gy0-gyh-10);

  line(0,520,800,520);

  fill('white');

  noStroke();

  text('select day: '+nf(ss,0,0),gx0-80,530+15);

  text('Operation',10,520+15);

​

  text('infection simulation (Smooth Step Parameter)',10,520+45);

  text('xstart',10,520+65);

  text('xstop',110,520+65);

  text('ystart',210,520+65);

  text('ystop',310,520+65);

  text('slope',410,520+65);

​

  text('epidemiologic Parameter:',10,520+85);

  text('sickday',10,520+105);

  text('mortal',110,520+105);

  text('people',210,520+105);

​

}

​

function draw_graph() {

  fill(0, 80, 0);

  stroke(100, 0, 0);

  strokeWeight(2);

  textSize(30);

  text("simple epidemiological math", 30, 30);

​

  fill(0, 70, 80);

  stroke(0, 200, 0);

  rectMode(CORNER);

  rect(gx0 - 3, gy0 + 3, gxw + 6, -gyh - 6); //___________ graph background 6 pix bigger

  draw_axis(10);

  rectMode(RADIUS);

  for (var s = 0; s < 100; s++) {

    strokeWeight(6); //_____________________________________ total infections ( from smooth step function )   

    stroke('purple');

    point(gx0 + xi[s] * gxw / 100.0, gy0 - yi[s] * gyh / 100.0); // use array data in plot window

​

    stroke('red'); //_______________________________________ new infections

    noFill();

    strokeWeight(1);

    circle(gx0 + xi[s] * gxw / 100.0, gy0 - ydi[s] * gyh / 100.0, 6); // use array data in plot window

​

    noFill(); //____________________________________________ R value

    stroke('red');

    strokeWeight(3);

    if ( yRi[s] > 0.0 && yRi[s] < 2.0 )

      point(gx0 + xi[s] * gxw / 100.0, gy0 - yRi[s] * gyh / 2.0);

​

    stroke('cyan'); //______________________________________ active cases

    strokeWeight(0.5);

    rect(gx0 + xi[s] * gxw / 100.0, gy0 - yti[s] * gyh / 100.0, 3, 3); // use array data in plot window

​

    //fill(0); //_____________________________________________ fatal cases

    //noStroke();

    //text('+',gx0 + xi[s] * gxw / 100.0 -3, gy0 - ymi[s] * gyh / 100.0 +5);

    stroke('black'); //_______________________________________ new infections

    noFill();

    strokeWeight(1);

    circle(gx0 + xi[s] * gxw / 100.0, gy0 - ymi[s] * gyh / 100.0, 6); // use array data in plot window

​

  }

}

​

function calc_list() {

  // new version allow recalc after change of settings

  x = 0;

  xs = 0.0;

  xss = 0;

  ys = 0;

  y = 0;

  var yd = 0.0;

  dxss = 100.0 / (xstop - xstart) / xmax;

  for (var s = 0; s < 100; s++) {

    xs = s * 0.01;

    x = xs * 100;

    if (xs > xstart / xmax && xs <= xstop / xmax) {

      xss += dxss;

      ys = generalSmoothStep(astep, xss); //________________ 0.0 .. 1.0 over x 0.0 .. 1.0

    }

    y = ystart + ys * (ystop - ystart); //__________________ in y limited range

    xi[s]=x;

    yi[s]=y; //__________________________________________ total infections

    if (s > 0) yd = y - yi[s - 1];

    else yd = 0.0;

    ydi[s]=yd; //________________________________________ new cases

    yti[s]=0; //_________________________________________ init empty / calc later in a second run

    ymd[s]=0; //_________________________________________ init empty / calc later in a second run

    ymi[s]=0; //_________________________________________ init empty / calc later in a second run

    yRi[s]=0; //_________________________________________ init empty / calc later in a second run

    //console.log('s', s + 1, 'xs', nf(xs, 0, 2), 'x', nf(x, 0, 2), 'xss', nf(xss, 0, 3), 'ys', nf(ys, 0, 3), 'y', nf(y, 0, 2), 'yd', nf(yd, 0, 2));

  }

  // second run to calculate active cases

  for (s = ydt; s < 100; s++)

    for (var si = s - ydt; si <= s; si++) // accumulate all not older as ydt days

      yti[s] += ydi[si];

  // third run to calculate Deaths per day

  for (s = 0; s < 100; s++)

    if (s > ydt) ymd[s + ydt] = ydi[s] * ymt / 100.0;

  // 4th run to calculate accumulated Deaths

  for (s = 1; s < 100; s++) {

    ymi[s] = ymi[s - 1] + ymd[s]; // total deaths

  }

  // 5th run calc R

  for (s = 7; s < 100; s++) {

    var last4 = ydi[s - 3] + ydi[s - 2] + ydi[s - 1] + ydi[s];

    var prev4 = ydi[s - 7] + ydi[s - 6] + ydi[s - 5] + ydi[s - 4];

    if ( prev4 > 0 ) yRi[s] = last4 / prev4;

  }

}

​

//________________________________________________________ MATH

function generalSmoothStep(a, x) { //_____________________ Generalized smoothstep

  var result = 0;

  for (var n = 0; n <= a - 1; n++)

    result += pascalTriangle(-a, n) * pascalTriangle(2 * a - 1, a - n - 1) * Math.pow(x, a + n);

​

  return result;

}

​

function pascalTriangle(a, b) {

  var result = 1;

  for (var i = 1; i <= b; i++)

    result *= ((a - (i - 1)) / i);

​

  return result;

}

​

// unused

​

function smoothStep(x) { //_______________________________ Normal smoothstep

  return -2 * Math.pow(x, 3) + 3 * Math.pow(x, 2);

}

​

function test_print() {

  console.log("smoothStep(0.3) = " + smoothStep(0.3));

  console.log("generalSmoothStep(2, 0.3) = " + generalSmoothStep(2, 0.3));

}