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Logistic curve fitting in epidemiology: Difference between revisions

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Logistic curve fitting in epidemiology (view source)

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{{task|Probability and statistics}}
{{Draft Task}}
 
The least-squares method (see references below) in statistics is used to fit data
Line 12:
including the growth of epidemics, are curves akin to the logistic curve:
 
'''f <big><big><big><b> ƒ(x) = L / (1 + e<sup>-k(x-x<sub>0</sub>)</sup>)''' </b></big></big></big>
 
Though predictions based on fitting to such curves may errerror, especially if used to
extrapolate from incomplete data, curves similar to the logistic curve have had
good fits in population studies, including modeling the growth of past epidemics.
 
The task:
 
;Task
* Given the following daily world totals since December 31, 2019 for persons
who have become infected with the novel coronavirus Covid-19:
 
Given the following daily world totals since <tt> December 31, 2019 </tt> for persons who have become infected with the novel coronavirus Covid-19:
<pre>
Daily totals:
Line 38 ⟶ 34:
</pre>
 
* Use the following variant of the logistic curve as a formula:
 
Use the following variant of the logistic curve as a formula:
'''f(t) = n<sub>0</sub> e<sup>(r t)</sup> / ((1 + n<sub>0</sub> (e<sup>(r t)</sup> - 1) / K)'''
<big><big><big><b> ƒ(t) = n<sub>0</sub> e<sup>(r t)</sup> / ((1 + n<sub>0</sub> (e<sup>(r t)</sup> - 1) / K) </b></big></big></big>
 
Where:
Where r is the rate of growth of the infection in the population.
::* &nbsp; <big><b> r </b></big> &nbsp; is the rate of growth of the infection in the population.
::* &nbsp; <big><b> K </b></big> &nbsp; is the world population, about 7.8 billion.
::* &nbsp; <big><b> n<sub>0</sub> </b></big> &nbsp; is 27, the number of cases found in China at the start of the pandemic.
 
 
The R0 of an infection (different from r above) is a measure of how many
 
The &nbsp; <big><b> R0 </b></big> &nbsp; of an infection (different from &nbsp; <big><b>r</b></big> &nbsp; above) is a measure of how many
new individuals will become infected for every individual currently infected.
It is an important measure of how quickly an infectious disease may spread.
 
<big><b>R0</b></big> &nbsp; is related to the logistic curve's &nbsp; <big><b>r</b></big> &nbsp; parameter by the formula:
 
''' <big><big><big><b> r ≈ ln(R0) / G''' </b></big></big></big>
 
where &nbsp; <big><b> G, </b></big> &nbsp; the generation time, is roughly the sum of the incubation time, perhaps 5 days, and
the mean contagion period, perhaps 7 days, so, for covid-19, roughly we have:
 
<big><big><big><b> R0 ≈ e<sup>12r</sup> </b></big></big></big>
 
'''R0 ≈ e<sup>12r</sup>'''
 
Assume the following constants hold in the formula above:
* K is the world population, about 7.9 billion
* n0 is 27, the number of cases found in China at the start of the pandemic.
 
;Task:
* Demonstrate code that finds a least-squares fits of the curve to the data.
* Show the calculated &nbsp; <big><b> r </b></big> &nbsp; for the logistic curve.
* Show the final &nbsp; <big><b> R0 </b></big> &nbsp; parameter you calculate from the logistic curve &nbsp; <big><b> r </b></big> &nbsp; value parameter.
 
;See also
 
;See also
:;*[[https://en.wikipedia.org/wiki/Basic_reproduction_number Basic reproduction number]]
:;*[[https://en.wikipedia.org/wiki/Logistic_function Logistic functions]]
:;*[[https://en.wikipedia.org/wiki/Least_squares Least squares]]
:;*[[https://ourworldindata.org/coronavirus#all-charts-preview World covid-19 case tallies]]
:;*[[https://www.zoology.ubc.ca/~bio310/Blank%20Page%204_files/DL%20R%20and%20r.htm Calculating r and R0]]
<br><br>
 
=={{header|11l}}==
{{trans|C++}}
 
<syntaxhighlight lang="11l">-V K = 7.8e9
-V n0 = 27
-V actual = [
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023, 2820,
4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615, 24522, 28273,
31491, 34933, 37552, 40540, 43105, 45177, 60328, 64543, 67103,
69265, 71332, 73327, 75191, 75723, 76719, 77804, 78812, 79339,
80132, 80995, 82101, 83365, 85203, 87024, 89068, 90664, 93077,
95316, 98172, 102133, 105824, 109695, 114232, 118610, 125497,
133852, 143227, 151367, 167418, 180096, 194836, 213150, 242364,
271106, 305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054, 1174652
]
 
F f(Float r) -> Float
V sq = 0.0
L(act) :actual
V eri = exp(r * L.index)
V guess = (:n0 * eri) / (1 + :n0 * (eri - 1) / :K)
V diff = guess - act
sq += diff * diff
R sq
 
F solve(func, =guess = 0.5, epsilon = 0.0)
V delta = I guess != 0 {guess} E 1
V f0 = func(guess)
V factor = 2.0
L delta > epsilon & guess != guess - delta
V nf = func(guess - delta)
I nf < f0
f0 = nf
guess -= delta
E
nf = func(guess + delta)
I nf < f0
f0 = nf
guess += delta
E
factor = 0.5
delta *= factor
R guess
 
V r = solve(f)
V R0 = exp(12 * r)
print(‘r = #.6, R0 = #.6’.format(r, R0))</syntaxhighlight>
 
{{out}}
<pre>
r = 0.112302, R0 = 3.848279
</pre>
 
=={{header|Ada}}==
{{trans|C++}}
<syntaxhighlight lang="ada">with Ada.Text_Io;
with Ada.Numerics.Generic_Elementary_Functions;
 
procedure Curve_Fitting is
 
type Real is new Long_Float;
type Fuction_Access is access function (X : Real) return Real;
type Time_Type is new Natural; -- Days
 
package Real_Io is new Ada.Text_Io.Float_Io (Real);
package Math is new Ada.Numerics.Generic_Elementary_Functions (Real);
 
Actual : constant array (Time_Type range <>) of Integer :=
(27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023, 2820,
4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615, 24522, 28273,
31491, 34933, 37552, 40540, 43105, 45177, 60328, 64543, 67103,
69265, 71332, 73327, 75191, 75723, 76719, 77804, 78812, 79339,
80132, 80995, 82101, 83365, 85203, 87024, 89068, 90664, 93077,
95316, 98172, 102133, 105824, 109695, 114232, 118610, 125497,
133852, 143227, 151367, 167418, 180096, 194836, 213150, 242364,
271106, 305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054, 1174652);
 
N0 : constant Real := Real (Actual (Actual'First)); -- Initially infected
K : constant Real := 7.8e9; -- World population apx.
 
function Logistic_Curve_Function (R : Real) return Real is
sq : Real := 0.0;
begin
for I in Actual'range loop
declare
Eri : constant Real := Math.Exp (R * Real (I));
Guess : constant Real := (N0 * Eri) / (1.0 + N0 * (Eri - 1.0) / K);
Diff : constant Real := Guess - Real (Actual (I));
begin
Sq := Sq + Diff * Diff;
end;
end loop;
return sq;
end Logistic_Curve_Function;
 
procedure Solve (Func : Fuction_Access;
Guess : Real := 0.5;
Epsilon : Real := 0.0;
New_Guess : out Real)
is
Delt : Real := (if guess /= 0.0 then guess else 1.0);
f0 : Real := Func (Guess);
factor : Real := 2.0;
begin
New_Guess := Guess;
while
Delt > Epsilon and New_Guess /= New_Guess - Delt
loop
declare
nf : real := func (New_guess - delt);
begin
if nf < f0 then
f0 := nf;
New_guess := New_guess - delt;
else
nf := func (New_guess + delt);
if nf < f0 then
f0 := nf;
New_guess := New_guess + delt;
else
Factor := 0.5;
end if;
end if;
end;
Delt := Delt * factor;
end loop;
end Solve;
 
use Ada.Text_Io;
 
Incubation_Time : constant Real := 5.0; -- Days
Contagion_Period : constant Real := 7.0; -- Days
Generation_Time : constant Real := Incubation_Time + Contagion_Period;
 
R : Real; -- Rate
R0 : Real; -- Infection rate
begin
Solve (Logistic_Curve_Function'Access, New_Guess => R);
R0 := Math.Exp (Generation_Time * R);
 
Put ("r = "); Real_IO.Put (R, Exp => 0, Aft => 7);
Put (", R0 = "); Real_Io.Put (R0, Exp => 0, Aft => 7);
New_Line;
end Curve_Fitting;</syntaxhighlight>
{{out}}
<pre>r = 0.1123022, R0 = 3.8482793</pre>
 
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">K: 7.8e9
N0: 27
Actual: [
27.0, 27.0, 27.0, 44.0, 44.0, 59.0, 59.0,
59.0, 59.0, 59.0, 59.0, 59.0, 59.0, 60.0,
60.0, 61.0, 61.0, 66.0, 83.0, 219.0, 239.0,
392.0, 534.0, 631.0, 897.0, 1350.0, 2023.0, 2820.0,
4587.0, 6067.0, 7823.0, 9826.0, 11946.0, 14554.0, 17372.0,
20615.0, 24522.0, 28273.0, 31491.0, 34933.0, 37552.0, 40540.0,
43105.0, 45177.0, 60328.0, 64543.0, 67103.0, 69265.0, 71332.0,
73327.0, 75191.0, 75723.0, 76719.0, 77804.0, 78812.0, 79339.0,
80132.0, 80995.0, 82101.0, 83365.0, 85203.0, 87024.0, 89068.0,
90664.0, 93077.0, 95316.0, 98172.0, 102133.0, 105824.0, 109695.0,
114232.0, 118610.0, 125497.0, 133852.0, 143227.0, 151367.0, 167418.0,
180096.0, 194836.0, 213150.0, 242364.0, 271106.0, 305117.0, 338133.0,
377918.0, 416845.0, 468049.0, 527767.0, 591704.0, 656866.0, 715353.0,
777796.0, 851308.0, 928436.0, 1000249.0, 1082054.0, 1174652.0
]
 
f: function [r][
result: 0
loop 0..dec size Actual 'i [
eri: exp r * to :floating i
guess: (N0 * eri) // (1 + N0 * (eri - 1) // K)
diff: guess - Actual\[i]
result: result + diff * diff
]
return result
]
 
solve: function [fn][
guess: 0.5
eps: 0.0
result: guess
 
delta: guess
f0: call fn @[result]
factor: 2.0
 
while [and? -> delta > eps
-> result <> result - delta][
nf: call fn @[result-delta]
if? nf < f0 [
f0: nf
result: result - delta
]
else [
nf: call fn @[result+delta]
if? nf < f0 [
f0: nf
result: result + delta
]
else [
factor: 0.5
]
]
delta: delta * factor
]
return result
]
 
r: solve 'f
r0: exp 12 * r
 
print ["r =" r]
print ["R0 =" r0]</syntaxhighlight>
 
{{out}}
 
<pre>r = 0.11230217569755
R0 = 3.848279280916719</pre>
 
=={{header|C}}==
{{trans|C++}}
<syntaxhighlight lang="c">#include <math.h>
#include <stdio.h>
 
const double K = 7.8e9;
const int n0 = 27;
const double actual[] = {
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023, 2820,
4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615, 24522, 28273,
31491, 34933, 37552, 40540, 43105, 45177, 60328, 64543, 67103,
69265, 71332, 73327, 75191, 75723, 76719, 77804, 78812, 79339,
80132, 80995, 82101, 83365, 85203, 87024, 89068, 90664, 93077,
95316, 98172, 102133, 105824, 109695, 114232, 118610, 125497,
133852, 143227, 151367, 167418, 180096, 194836, 213150, 242364,
271106, 305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054, 1174652
};
const size_t actual_size = sizeof(actual) / sizeof(double);
 
double f(double r) {
double sq = 0;
size_t i;
for (i = 0; i < actual_size; ++i) {
double eri = exp(r * i);
double guess = (n0 * eri) / (1 + n0 * (eri - 1) / K);
double diff = guess - actual[i];
sq += diff * diff;
}
return sq;
}
 
double solve(double (*fn)(double), double guess, double epsilon) {
double delta, f0, factor;
for (delta = guess ? guess : 1, f0 = fn(guess), factor = 2;
delta > epsilon && guess != guess - delta;
delta *= factor) {
double nf = (*fn)(guess - delta);
if (nf < f0) {
f0 = nf;
guess -= delta;
} else {
nf = fn(guess + delta);
if (nf < f0) {
f0 = nf;
guess += delta;
} else {
factor = 0.5;
}
}
}
return guess;
}
 
double solve_default(double (*fn)(double)) {
return solve(fn, 0.5, 0);
}
 
int main() {
double r = solve_default(f);
double R0 = exp(12 * r);
printf("r = %f, R0 = %f\n", r, R0);
return 0;
}</syntaxhighlight>
{{out}}
<pre>r = 0.112302, R0 = 3.848279</pre>
 
=={{header|C++}}==
{{trans|Phix}}
<syntaxhighlight lang="cpp">#include <cmath>
#include <functional>
#include <iostream>
 
constexpr double K = 7.8e9;
constexpr int n0 = 27;
constexpr double actual[] = {
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023, 2820,
4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615, 24522, 28273,
31491, 34933, 37552, 40540, 43105, 45177, 60328, 64543, 67103,
69265, 71332, 73327, 75191, 75723, 76719, 77804, 78812, 79339,
80132, 80995, 82101, 83365, 85203, 87024, 89068, 90664, 93077,
95316, 98172, 102133, 105824, 109695, 114232, 118610, 125497,
133852, 143227, 151367, 167418, 180096, 194836, 213150, 242364,
271106, 305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054, 1174652
};
 
double f(double r) {
double sq = 0;
constexpr size_t len = std::size(actual);
for (size_t i = 0; i < len; ++i) {
double eri = std::exp(r * i);
double guess = (n0 * eri)/(1 + n0 * (eri - 1)/K);
double diff = guess - actual[i];
sq += diff * diff;
}
return sq;
}
 
double solve(std::function<double(double)> fn, double guess=0.5, double epsilon=0) {
for (double delta = guess ? guess : 1, f0 = fn(guess), factor = 2;
delta > epsilon && guess != guess - delta;
delta *= factor) {
double nf = fn(guess - delta);
if (nf < f0) {
f0 = nf;
guess -= delta;
} else {
nf = fn(guess + delta);
if (nf < f0) {
f0 = nf;
guess += delta;
} else
factor = 0.5;
}
}
return guess;
}
 
int main() {
double r = solve(f);
double R0 = std::exp(12 * r);
std::cout << "r = " << r << ", R0 = " << R0 << '\n';
return 0;
}</syntaxhighlight>
 
{{out}}
<pre>
r = 0.112302, R0 = 3.84828
</pre>
 
=={{header|D}}==
{{trans|C++}}
<syntaxhighlight lang="d">import std.math;
import std.stdio;
 
immutable K = 7.8e9;
immutable n0 = 27;
immutable actual = [
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023, 2820,
4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615, 24522, 28273,
31491, 34933, 37552, 40540, 43105, 45177, 60328, 64543, 67103,
69265, 71332, 73327, 75191, 75723, 76719, 77804, 78812, 79339,
80132, 80995, 82101, 83365, 85203, 87024, 89068, 90664, 93077,
95316, 98172, 102133, 105824, 109695, 114232, 118610, 125497,
133852, 143227, 151367, 167418, 180096, 194836, 213150, 242364,
271106, 305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054, 1174652
];
 
double f(double r) {
double sq = 0.0;
auto len = actual.length;
for (size_t i = 0; i < len; ++i) {
auto eri = exp(r * i);
auto guess = (n0 * eri) / (1 + n0 * (eri - 1) / K);
auto diff = guess - actual[i];
sq += diff * diff;
}
return sq;
}
 
double solve(double function(double) fn, double guess = 0.5, double epsilon = 0) {
for (double delta = guess ? guess : 1, f0 = fn(guess), factor = 2;
delta > epsilon && guess != guess - delta;
delta *= factor
) {
double nf = fn(guess - delta);
if (nf < f0) {
f0 = nf;
guess -= delta;
} else {
nf = fn(guess + delta);
if (nf < f0) {
f0 = nf;
guess += delta;
} else {
factor = 0.5;
}
}
}
return guess;
}
 
void main() {
double r = solve(&f);
double R0 = exp(12 * r);
writeln("r = ", r, ", R0 = ", R0);
}</syntaxhighlight>
{{out}}
<pre>r = 0.112302, R0 = 3.84828</pre>
 
 
=={{header|FreeBASIC}}==
{{trans|Phix}}
<syntaxhighlight lang="freebasic">Const K = 7.8e9 ' approx world population
Const n0 = 27 ' number of cases at day 0
Dim Shared As Integer actual(1 To ...) => { _
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60, _
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023, _
2820, 4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615, _
24522, 28273, 31491, 34933, 37552, 40540, 43105, 45177, _
60328, 64543, 67103, 69265, 71332, 73327, 75191, 75723, _
76719, 77804, 78812, 79339, 80132, 80995, 82101, 83365, _
85203, 87024, 89068, 90664, 93077, 95316, 98172, 102133, _
105824, 109695, 114232, 118610, 125497, 133852, 143227, _
151367, 167418, 180096, 194836, 213150, 242364, 271106, _
305117, 338133, 377918, 416845, 468049, 527767, 591704, _
656866, 715353, 777796, 851308, 928436, 1000249, 1082054, 1174652 }
 
Function f1(r As Double) As Double
Dim As Double sq = 0
For i As Integer = 1 To Ubound(actual)
Dim As Double eri = Exp(r*(i-1))
Dim As Double guess = (n0*eri) / (1+n0*(eri-1) / K)
Dim As Double diff = guess-actual(i)
sq += diff*diff
Next
Return sq
End Function
 
Function solve(f As Function (As Double) As Double, guess As Double = 0.5, epsilon As Double = 0.0) As Double
Dim As Double f0 = f(guess)
Dim As Double delta = Iif(guess, guess, 1)
Dim As Double factor = 2 ' double until f0 best then halve until delta <= epsilon
While delta > epsilon And guess <> guess-delta
Dim As Double nf = f(guess-delta)
If nf < f0 Then
f0 = nf
guess -= delta
Else
nf = f(guess+delta)
If nf < f0 Then
f0 = nf
guess += delta
Else
factor = 0.5
End If
End If
delta *= factor
Wend
Return guess
End Function
 
Dim As Double r = solve(@f1)
Dim As Double R0 = Exp(12 * r)
Print Using "r = #.##########, R0 = #.########"; r; R0
Sleep</syntaxhighlight>
{{out}}
<pre>r = 0.1123021757, R0 = 3.84827928</pre>
 
 
=={{header|Go}}==
{{libheader|lm}}
This uses the Levenberg-Marquardt method.
<syntaxhighlight lang="go">package main
 
import (
"fmt"
"github.com/maorshutman/lm"
"log"
"math"
)
 
const (
K = 7_800_000_000 // approx world population
n0 = 27 // number of cases at day 0
)
 
var y = []float64{
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023,
2820, 4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615,
24522, 28273, 31491, 34933, 37552, 40540, 43105, 45177,
60328, 64543, 67103, 69265, 71332, 73327, 75191, 75723,
76719, 77804, 78812, 79339, 80132, 80995, 82101, 83365,
85203, 87024, 89068, 90664, 93077, 95316, 98172, 102133,
105824, 109695, 114232, 118610, 125497, 133852, 143227,
151367, 167418, 180096, 194836, 213150, 242364, 271106,
305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054,
1174652,
}
 
func f(dst, p []float64) {
for i := 0; i < len(y); i++ {
t := float64(i)
dst[i] = (n0*math.Exp(p[0]*t))/(1+n0*(math.Exp(p[0]*t)-1)/K) - y[i]
}
}
 
func main() {
j := lm.NumJac{Func: f}
prob := lm.LMProblem{
Dim: 1,
Size: len(y),
Func: f,
Jac: j.Jac,
InitParams: []float64{0.5},
Tau: 1e-6,
Eps1: 1e-8,
Eps2: 1e-8,
}
res, err := lm.LM(prob, &lm.Settings{Iterations: 100, ObjectiveTol: 1e-16})
if err != nil {
log.Fatal(err)
}
r := res.X[0]
fmt.Printf("The logistic curve r for the world data is %.8f\n", r)
fmt.Printf("R0 is then approximately equal to %.7f\n", math.Exp(12*r))
}</syntaxhighlight>
 
{{out}}
<pre>
The logistic curve r for the world data is 0.11230218
R0 is then approximately equal to 3.8482793
</pre>
 
=={{header|Java}}==
{{trans|Kotlin}}
<syntaxhighlight lang="java">import java.util.List;
import java.util.function.Function;
 
public class LogisticCurveFitting {
private static final double K = 7.8e9;
private static final int N0 = 27;
 
private static final List<Double> ACTUAL = List.of(
27.0, 27.0, 27.0, 44.0, 44.0, 59.0, 59.0, 59.0, 59.0, 59.0, 59.0, 59.0, 59.0, 60.0, 60.0,
61.0, 61.0, 66.0, 83.0, 219.0, 239.0, 392.0, 534.0, 631.0, 897.0, 1350.0, 2023.0, 2820.0,
4587.0, 6067.0, 7823.0, 9826.0, 11946.0, 14554.0, 17372.0, 20615.0, 24522.0, 28273.0,
31491.0, 34933.0, 37552.0, 40540.0, 43105.0, 45177.0, 60328.0, 64543.0, 67103.0,
69265.0, 71332.0, 73327.0, 75191.0, 75723.0, 76719.0, 77804.0, 78812.0, 79339.0,
80132.0, 80995.0, 82101.0, 83365.0, 85203.0, 87024.0, 89068.0, 90664.0, 93077.0,
95316.0, 98172.0, 102133.0, 105824.0, 109695.0, 114232.0, 118610.0, 125497.0,
133852.0, 143227.0, 151367.0, 167418.0, 180096.0, 194836.0, 213150.0, 242364.0,
271106.0, 305117.0, 338133.0, 377918.0, 416845.0, 468049.0, 527767.0, 591704.0,
656866.0, 715353.0, 777796.0, 851308.0, 928436.0, 1000249.0, 1082054.0, 1174652.0
);
 
private static double f(double r) {
var sq = 0.0;
var len = ACTUAL.size();
for (int i = 0; i < len; i++) {
var eri = Math.exp(r * i);
var guess = (N0 * eri) / (1.0 + N0 * (eri - 1.0) / K);
var diff = guess - ACTUAL.get(i);
sq += diff * diff;
}
return sq;
}
 
private static double solve(Function<Double, Double> fn) {
return solve(fn, 0.5, 0.0);
}
 
private static double solve(Function<Double, Double> fn, double guess, double epsilon) {
double delta;
if (guess != 0.0) {
delta = guess;
} else {
delta = 1.0;
}
 
var f0 = fn.apply(guess);
var factor = 2.0;
 
while (delta > epsilon && guess != guess - delta) {
var nf = fn.apply(guess - delta);
if (nf < f0) {
f0 = nf;
guess -= delta;
} else {
nf = fn.apply(guess + delta);
if (nf < f0) {
f0 = nf;
guess += delta;
} else {
factor = 0.5;
}
}
 
delta *= factor;
}
 
return guess;
}
 
public static void main(String[] args) {
var r = solve(LogisticCurveFitting::f);
var r0 = Math.exp(12.0 * r);
System.out.printf("r = %.16f, R0 = %.16f\n", r, r0);
}
}</syntaxhighlight>
{{out}}
<pre>r = 0.1123021756975501, R0 = 3.8482792809167194</pre>
 
=={{header|jq}}==
{{trans|Wren}}
 
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
<syntaxhighlight lang="jq">def K: 7800000000; # approx world population
def n0: 27; # number of cases at day 0
def y: [
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023,
2820, 4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615,
24522, 28273, 31491, 34933, 37552, 40540, 43105, 45177,
60328, 64543, 67103, 69265, 71332, 73327, 75191, 75723,
76719, 77804, 78812, 79339, 80132, 80995, 82101, 83365,
85203, 87024, 89068, 90664, 93077, 95316, 98172, 102133,
105824, 109695, 114232, 118610, 125497, 133852, 143227,
151367, 167418, 180096, 194836, 213150, 242364, 271106,
305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054,
1174652
];
def f:
. as $r
| reduce range(0; y|length) as $i (0;
(($r*$i)|exp) as $eri
| ((n0*$eri)/(1+n0*($eri-1)/K) - y[$i]) as $dst
| . + $dst * $dst);
def solve(f; $guess; $epsilon):
{ f0: ($guess|f),
delta: $guess,
factor: 2,
$guess}
# double until f0 best, then halve until delta <= epsilon
| until(.delta <= $epsilon;
.nf = ((.guess - .delta)|f)
| if .nf < .f0
then .f0 = .nf
| .guess = .guess - .delta
else .nf = ((.guess + .delta)|f)
| if .nf < .f0
then .f0 = .nf
| .guess = .guess + .delta
else .factor = 0.5
end
end
| .delta = .delta * .factor )
| .guess;
 
((solve(f; 0.5; 0) * 1e10)|round / 1e10 ) as $r
| ((((12 * $r)|exp) * 1e8)|round / 1e8) as $R0
| "r = \($r), R0 = \($R0)"</syntaxhighlight>
{{out}}
<pre>
r = 0.1123021757, R0 = 3.84827928
</pre>
 
 
 
=={{header|Julia}}==
<syntaxhighlight lang="julia">using LsqFit
 
const K = 7_800_000_000 # approximate world population
const n0 = 27 # starting at day 0 with 27 Chinese cases
 
""" The model for logistic regression with a given r """
@. model(t, r) = (n0 * exp(r * t)) / (( 1 + n0 * (exp(r * t) - 1) / K))
 
# Daily world totals of covid cases, all countries
ydata = [
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023,
2820, 4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615,
24522, 28273, 31491, 34933, 37552, 40540, 43105, 45177,
60328, 64543, 67103, 69265, 71332, 73327, 75191, 75723,
76719, 77804, 78812, 79339, 80132, 80995, 82101, 83365,
85203, 87024, 89068, 90664, 93077, 95316, 98172, 102133,
105824, 109695, 114232, 118610, 125497, 133852, 143227,
151367, 167418, 180096, 194836, 213150, 242364, 271106,
305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054,
1174652,
]
tdata = collect(LinRange(0.0, 96, 97))
 
# starting approximation for r of 1/2
rparam = [0.5]
 
fit = curve_fit(model, tdata, ydata, rparam)
 
# Our answer for r given the world data and simplistic model
r = fit.param
println("The logistic curve r for the world data is: ", r)
println("The confidence interval at 5% significance is: ",
confidence_interval(fit, 0.05))
println("Since R0 ≈ exp(G * r), and G ≈ 12 days, R0 ≈ ", exp(12r[1]))
</syntaxhighlight>{{out}}
<pre>
The logistic curve r for the world data is: [0.11230217572265622]
The confidence interval at 5% significance is: [(0.11199074156706985, 0.11261360987824258)]
Since R0 ≈ exp(G * r), and G ≈ 12 days, R0 ≈ 3.8482792820761063
</pre>
 
=={{header|Kotlin}}==
{{trans|D}}
<syntaxhighlight lang="scala">import kotlin.math.exp
 
const val K = 7.8e9
const val n0 = 27
val actual = arrayOf(
27.0, 27.0, 27.0, 44.0, 44.0, 59.0, 59.0, 59.0, 59.0, 59.0, 59.0, 59.0, 59.0, 60.0, 60.0,
61.0, 61.0, 66.0, 83.0, 219.0, 239.0, 392.0, 534.0, 631.0, 897.0, 1350.0, 2023.0, 2820.0,
4587.0, 6067.0, 7823.0, 9826.0, 11946.0, 14554.0, 17372.0, 20615.0, 24522.0, 28273.0,
31491.0, 34933.0, 37552.0, 40540.0, 43105.0, 45177.0, 60328.0, 64543.0, 67103.0,
69265.0, 71332.0, 73327.0, 75191.0, 75723.0, 76719.0, 77804.0, 78812.0, 79339.0,
80132.0, 80995.0, 82101.0, 83365.0, 85203.0, 87024.0, 89068.0, 90664.0, 93077.0,
95316.0, 98172.0, 102133.0, 105824.0, 109695.0, 114232.0, 118610.0, 125497.0,
133852.0, 143227.0, 151367.0, 167418.0, 180096.0, 194836.0, 213150.0, 242364.0,
271106.0, 305117.0, 338133.0, 377918.0, 416845.0, 468049.0, 527767.0, 591704.0,
656866.0, 715353.0, 777796.0, 851308.0, 928436.0, 1000249.0, 1082054.0, 1174652.0
)
 
fun f(r: Double): Double {
var sq = 0.0
val len = actual.size
for (i in 0 until len) {
val eri = exp(r * i)
val guess = (n0 * eri) / (1.0 + n0 * (eri - 1.0) / K)
val diff = guess - actual[i]
sq += diff * diff
}
return sq
}
 
fun solve(fn: (Double) -> Double, guess: Double = 0.5, epsilon: Double = 0.0): Double {
var guess2 = guess
 
var delta = if (guess2 != 0.0) guess2 else 1.0
var f0 = fn(guess2)
var factor = 2.0
 
while (delta > epsilon && guess2 != guess2 - delta) {
var nf = fn(guess2 - delta)
if (nf < f0) {
f0 = nf
guess2 -= delta
} else {
nf = fn(guess2 + delta)
if (nf < f0) {
f0 = nf
guess2 += delta
} else {
factor = 0.5
}
}
 
delta *= factor
}
 
return guess2
}
 
fun main() {
val r = solve(::f)
val r0 = exp(12.0 * r)
println("r = $r, R0 = $r0")
}</syntaxhighlight>
{{out}}
<pre>r = 0.11230217569755005, R0 = 3.8482792809167194</pre>
 
 
=={{header|Nim}}==
{{trans|Kotlin}}
<syntaxhighlight lang="nim">import math, sugar
 
const
K = 7.8e9
N0 = 27
Actual = [ 27.0, 27.0, 27.0, 44.0, 44.0, 59.0, 59.0,
59.0, 59.0, 59.0, 59.0, 59.0, 59.0, 60.0,
60.0, 61.0, 61.0, 66.0, 83.0, 219.0, 239.0,
392.0, 534.0, 631.0, 897.0, 1350.0, 2023.0, 2820.0,
4587.0, 6067.0, 7823.0, 9826.0, 11946.0, 14554.0, 17372.0,
20615.0, 24522.0, 28273.0, 31491.0, 34933.0, 37552.0, 40540.0,
43105.0, 45177.0, 60328.0, 64543.0, 67103.0, 69265.0, 71332.0,
73327.0, 75191.0, 75723.0, 76719.0, 77804.0, 78812.0, 79339.0,
80132.0, 80995.0, 82101.0, 83365.0, 85203.0, 87024.0, 89068.0,
90664.0, 93077.0, 95316.0, 98172.0, 102133.0, 105824.0, 109695.0,
114232.0, 118610.0, 125497.0, 133852.0, 143227.0, 151367.0, 167418.0,
180096.0, 194836.0, 213150.0, 242364.0, 271106.0, 305117.0, 338133.0,
377918.0, 416845.0, 468049.0, 527767.0, 591704.0, 656866.0, 715353.0,
777796.0, 851308.0, 928436.0, 1000249.0, 1082054.0, 1174652.0]
 
type Func = (float) -> float
 
func f(r: float): float =
for i in 0..Actual.high:
let
eri = exp(r * i.toFloat)
guess = (N0 * eri) / (1 + N0 * (eri - 1) / K)
diff = guess - Actual[i]
result += diff * diff
 
 
func solve(fn: Func; guess = 0.5, epsilon = 0.0): float =
result = guess
var delta = if result != 0: result else: 1.0
var f0 = fn(result)
var factor = 2.0
 
while delta > epsilon and result != result - delta:
var nf = fn(result - delta)
if nf < f0:
f0 = nf
result -= delta
else:
nf = fn(result + delta)
if nf < f0:
f0 = nf
result += delta
else:
factor = 0.5
delta *= factor
 
 
let r = f.solve()
let r0 = exp(12 * r)
echo "r = ", r, ", R0 = ", r0</syntaxhighlight>
 
{{out}}
<pre>r = 0.11230217569755, R0 = 3.848279280916719</pre>
 
=={{header|Perl}}==
{{trans|Phix}}
<syntaxhighlight lang="perl">use strict;
use warnings;
 
my $K = 7_800_000_000; # population
my $n0 = 27; # cases @ day 0
 
my @y = (
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59,
60, 60, 61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350,
2023, 2820, 4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615, 24522, 28273, 31491,
34933, 37552, 40540, 43105, 45177, 60328, 64543, 67103, 69265, 71332, 73327, 75191, 75723,
76719, 77804, 78812, 79339, 80132, 80995, 82101, 83365, 85203, 87024, 89068, 90664, 93077,
95316, 98172, 102133, 105824, 109695, 114232, 118610, 125497, 133852, 143227, 151367, 167418, 180096,
194836, 213150, 242364, 271106, 305117, 338133, 377918, 416845, 468049, 527767, 591704, 656866, 715353,
777796, 851308, 928436,1000249,1082054,1174652
);
 
sub logistic_func {
my($r) = @_;
my $sq = 0;
for my $i (0 .. @y-1) {
my $eri = exp($r * $i);
my $dst = ($n0 * $eri) / (1 + $n0 * ($eri-1) / $K) - $y[$i];
$sq = $sq + $dst**2;
}
$sq
}
 
sub solve {
my($fn, $guess, $epsilon) = @_;
my($nfm,$nfp);
my $f0 = &$fn($guess);
my $delta = $guess;
my $factor = 2;
while ($delta > $epsilon) {
($nfm = &$fn($guess - $delta)) < $f0 ?
($f0 = $nfm, $guess -= $delta, $delta *= $factor)
:
($nfp = &$fn($guess + $delta)) < $f0 ?
($f0 = $nfp, $guess += $delta, $delta *= $factor)
:
$delta /= $factor
}
$guess
}
 
my $r = solve(\&logistic_func, 0.5, 0);
my $R0 = exp(12 * $r);
printf "r = %%(%.3f), R0 = %%(%.3f)\n", $r, $R0;</syntaxhighlight>
{{out}}
<pre>r = %(0.112), R0 = %(3.848)</pre>
 
=={{header|Phix}}==
Simplified, my interpretation of shift-cutting (from [[wp:Non-linear_least_squares]])
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #000080;font-style:italic;">-- demo\rosetta\Curve_fit.exw</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">K</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">7_800_000_000</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- approx world population</span>
<span style="color: #000000;">n0</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">27</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- number of cases at day 0</span>
<span style="color: #000000;">actual</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span>
<span style="color: #000000;">27</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">27</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">27</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">44</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">44</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">59</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">59</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">59</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">59</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">59</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">59</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">59</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">59</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">60</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">60</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">61</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">61</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">66</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">83</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">219</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">239</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">392</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">534</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">631</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">897</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1350</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2023</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">2820</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4587</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6067</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7823</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9826</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">11946</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">14554</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17372</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20615</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">24522</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">28273</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">31491</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">34933</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">37552</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">40540</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">43105</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">45177</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">60328</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">64543</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">67103</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">69265</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">71332</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">73327</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">75191</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">75723</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">76719</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">77804</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">78812</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">79339</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">80132</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">80995</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">82101</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">83365</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">85203</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">87024</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">89068</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">90664</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">93077</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">95316</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">98172</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">102133</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">105824</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">109695</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">114232</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">118610</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">125497</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">133852</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">143227</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">151367</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">167418</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">180096</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">194836</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">213150</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">242364</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">271106</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">305117</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">338133</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">377918</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">416845</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">468049</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">527767</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">591704</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">656866</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">715353</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">777796</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">851308</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">928436</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1000249</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1082054</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">1174652</span> <span style="color: #0000FF;">}</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">sq</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">actual</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">eri</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)),</span>
<span style="color: #000000;">guess</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">n0</span><span style="color: #0000FF;">*</span><span style="color: #000000;">eri</span><span style="color: #0000FF;">)/(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">n0</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">eri</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">K</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">diff</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">guess</span><span style="color: #0000FF;">-</span><span style="color: #000000;">actual</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">sq</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">diff</span><span style="color: #0000FF;">*</span><span style="color: #000000;">diff</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">sq</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">guess</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">epsilon</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">f0</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">guess</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">delta</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">guess</span><span style="color: #0000FF;">?</span><span style="color: #000000;">guess</span><span style="color: #0000FF;">:</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">factor</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span> <span style="color: #000080;font-style:italic;">-- double until f0 best, then
-- halve until delta&lt;=epsilon
-- or we hit precision limit</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">delta</span><span style="color: #0000FF;">></span><span style="color: #000000;">epsilon</span> <span style="color: #000080;font-style:italic;">-- (predefined limit)</span>
<span style="color: #008080;">and</span> <span style="color: #000000;">guess</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">guess</span><span style="color: #0000FF;">-</span><span style="color: #000000;">delta</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (precision limit)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">nf</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">guess</span><span style="color: #0000FF;">-</span><span style="color: #000000;">delta</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nf</span><span style="color: #0000FF;"><</span><span style="color: #000000;">f0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">f0</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nf</span>
<span style="color: #000000;">guess</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">delta</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">nf</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">guess</span><span style="color: #0000FF;">+</span><span style="color: #000000;">delta</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nf</span><span style="color: #0000FF;"><</span><span style="color: #000000;">f0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">f0</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nf</span>
<span style="color: #000000;">guess</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">delta</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">factor</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.5</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">delta</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">factor</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">guess</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">R0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">12</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"r = %.10f, R0 = %.8f\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">R0</span><span style="color: #0000FF;">})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
r = 0.1123021757, R0 = 3.84827928
</pre>
 
=={{header|Python}}==
Uses NumPy/SciPy's optimize package.
<langsyntaxhighlight lang="python">import numpy as np
import scipy.optimize as opt
 
n0, K = 27, 7_800_000_000
 
def f(t, r0r):
return (n0 * np.exp(r0r * t)) / (( 1 + n0 * (np.exp(r0r * t) - 1) / K))
 
y = [
Line 105 ⟶ 1,085:
", with covariance of", cov)
print("The calculated R0 is then", np.exp(12 * r))
</langsyntaxhighlight>{{out}}
<pre>
The r for the world Covid-19 data is: [0.11230218] , with covariance of [[2.46164331e-08]]
The calculated R0 is then [3.8482793]
</pre>
 
=={{header|R}}==
<syntaxhighlight lang="r">
library(minpack.lm)
 
K <- 7800000000 # approximate world population
n0 <- 27 # starting at day 0 with 27 Chinese cases
 
x <- seq(from=0.0, 96.0, length=97)
 
# The model for logistic regression with a given r0
getPred <- function(par, xx) (n0 * exp(par$r * xx)) / (( 1 + n0 * (exp(par$r * xx) - 1) / K))
 
residFun <- function(p, observed, xx) observed - getPred(p, xx)
 
parStart <- list(r=0.5)
 
# Daily world totals of covid cases, all countries
observed <- c(
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023,
2820, 4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615,
24522, 28273, 31491, 34933, 37552, 40540, 43105, 45177,
60328, 64543, 67103, 69265, 71332, 73327, 75191, 75723,
76719, 77804, 78812, 79339, 80132, 80995, 82101, 83365,
85203, 87024, 89068, 90664, 93077, 95316, 98172, 102133,
105824, 109695, 114232, 118610, 125497, 133852, 143227,
151367, 167418, 180096, 194836, 213150, 242364, 271106,
305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054,
1174652)
 
nls.out <- nls.lm(par=parStart, fn=residFun, observed=observed, xx = x)
 
cat("The r for the model is: ", coef(nls.out), "\n")
 
cat("Therefore, R0 is approximately: ", exp(12 * coef(nls.out)))
</syntaxhighlight>{{out}}
<pre>
The r for the model is: 0.1123022
Therefore, R0 is approximately: 3.848279
</pre>
 
=={{header|Raku}}==
{{works with|Rakudo|2020.05}}
{{trans|Perl}}
 
Original task numbers of cases per day as of April 05 plus updated, as of today, May 11 numbers.
 
<syntaxhighlight lang="raku" line>my $K = 7_800_000_000; # population
my $n0 = 27; # cases @ day 0
 
my @Apr05 = <
27 27 27 44 44 59 59 59 59 59
59 59 59 60 60 61 61 66 83 219
239 392 534 631 897 1350 2023 2820 4587 6067
7823 9826 11946 14554 17372 20615 24522 28273 31491 34933
37552 40540 43105 45177 60328 64543 67103 69265 71332 73327
75191 75723 76719 77804 78812 79339 80132 80995 82101 83365
85203 87024 89068 90664 93077 95316 98172 102133 105824 109695
114232 118610 125497 133852 143227 151367 167418 180096 194836 213150
242364 271106 305117 338133 377918 416845 468049 527767 591704 656866
715353 777796 851308 928436 1000249 1082054 1174652
>;
 
my @May11 = <
27 27 27 44 44 59 59 59 59 59
59 59 59 60 60 61 61 66 83 219
239 392 534 631 897 1350 2023 2820 4587 6067
7823 9826 11946 14554 17372 20615 24522 28273 31491 34933
37552 40540 43105 45177 60328 64543 67103 69265 71332 73327
75191 75723 76719 77804 78812 79339 80132 80995 82101 83365
85203 87026 89068 90865 93077 95316 98172 102133 105824 109695
114235 118613 125497 133853 143259 154774 167418 180094 194843 213149
242374 271116 305235 338235 377968 416881 468092 527839 591796 656834
715377 777187 851587 928491 1006063 1087822 1174306 1245601 1316988 1391881
1476792 1563819 1653160 1734868 1807256 1873639 1953786 2033745 2117297 2199460
2278484 2350993 2427353 2513399 2579823 2657910 2731217 2832750 2915977 2981542
3054404 3131487 3216467 3308341 3389459 3468047 3545486 3624789 3714816 3809262
3899379 3986931 4063525
>;
 
sub logistic-func ($rate, @y) {
my $sq = 0;
for ^@y -> $time {
my $ert = exp($rate * $time);
my $δt = ($n0 * $ert) / (1 + $n0 * ($ert-1) / $K) - @y[$time];
$sq += $δt²;
}
$sq
}
 
sub solve (&f, $guess, \ε, @y) {
my $fₙ-minus;
my $fₙ-plus;
my $rate = $guess;
my $fₙ = f $rate, @y;
my $Δ = $rate;
my $factor = 2;
while $Δ > ε {
($fₙ-minus = f $rate - $Δ, @y) < $fₙ ??
do {
$fₙ = $fₙ-minus;
$rate -= $Δ;
$Δ *= $factor;
} !!
($fₙ-plus = f $rate + $Δ, @y) < $fₙ ??
do {
$fₙ = $fₙ-plus;
$rate += $Δ;
$Δ *= $factor;
} !!
$Δ /= $factor
}
$rate
}
 
for @Apr05, 'Dec 31 - Apr 5',
@May11, 'Dec 31 - May 11' -> @y, $period {
my $rate = solve(&logistic-func, 0.5, 0, @y);
my $R0 = exp(12 * $rate);
say "\nFor period: $period";
say "Instantaneous rate of growth: r = " , $rate.fmt('%08f');
say "Reproductive rate: R0 = ", $R0.fmt('%08f');
}
</syntaxhighlight>
{{out}}
<pre>For period: Dec 31 - Apr 5
Instantaneous rate of growth: r = 0.112302
Reproductive rate: R0 = 3.848279
 
For period: Dec 31 - May 11
Instantaneous rate of growth: r = 0.093328
Reproductive rate: R0 = 3.064672</pre>
 
=={{header|Ruby}}==
{{trans|C++}}
<syntaxhighlight lang="ruby">K = 7.9e9
N0 = 27
ACTUAL = [
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023, 2820,
4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615, 24522, 28273,
31491, 34933, 37552, 40540, 43105, 45177, 60328, 64543, 67103,
69265, 71332, 73327, 75191, 75723, 76719, 77804, 78812, 79339,
80132, 80995, 82101, 83365, 85203, 87024, 89068, 90664, 93077,
95316, 98172, 102133, 105824, 109695, 114232, 118610, 125497,
133852, 143227, 151367, 167418, 180096, 194836, 213150, 242364,
271106, 305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054, 1174652
]
 
def f(r)
sq = 0.0
len = ACTUAL.length
for i in 1 .. len
j = i - 1
eri = Math.exp(r * j)
guess = (N0 * eri) / (1 + N0 * (eri - 1.0) / K)
diff = guess - ACTUAL[j]
sq += diff * diff
end
return sq
end
 
def solve(fn, guess=0.5, epsilon=0.0)
delta = guess ? guess : 1.0
f0 = send(fn, guess)
factor = 2.0
while delta > epsilon and guess != guess - delta
nf = send(fn, guess - delta)
if nf < f0 then
f0 = nf
guess -= delta
else
nf = send(fn, guess + delta)
if nf < f0 then
f0 = nf
guess += delta
else
factor = 0.5
end
end
 
delta *= factor
end
return guess
end
 
def main
r = solve(:f)
r0 = Math.exp(12.0 * r)
print "r = ", r, ", R0 = ", r0, "\n"
end
 
main()</syntaxhighlight>
{{out}}
<pre>r = 0.11230215850810021, R0 = 3.8482784871191575</pre>
 
=={{header|V (Vlang)}}==
{{trans|wren}}
<syntaxhighlight lang="v (vlang)">import math
const (
k = 7800000000 // approx world population
n0 = 27 // number of cases at day 0
y = [
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023,
2820, 4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615,
24522, 28273, 31491, 34933, 37552, 40540, 43105, 45177,
60328, 64543, 67103, 69265, 71332, 73327, 75191, 75723,
76719, 77804, 78812, 79339, 80132, 80995, 82101, 83365,
85203, 87024, 89068, 90664, 93077, 95316, 98172, 102133,
105824, 109695, 114232, 118610, 125497, 133852, 143227,
151367, 167418, 180096, 194836, 213150, 242364, 271106,
305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054,
1174652
]
)
fn f(r f64) f64 {
mut sq := 0.0
for i in 0..y.len {
eri := math.exp(r * i)
dst := (n0 * eri) / (1 + n0 * (eri - 1) / k) -y[i]
sq = sq + dst * dst
}
return sq
}
fn solve(fu fn(f64)f64, g f64, epsilon int) f64 {
mut guess := g
mut f0 := fu(guess)
mut delta := guess
mut factor := 2.0
for delta > epsilon {
mut nf := fu(guess - delta)
if nf < f0 {
f0 = nf
guess -= delta
} else {
nf = fu(guess + delta)
if nf < f0 {
f0 = nf
guess += delta
} else {
factor = 0.5
}
}
delta *= factor
}
return guess
}
fn main() {
r := math.round(solve(f, 0.5, 0) * 1e10) / 1e10
r0 := math.round(math.exp(12 * r) * 1e8) / 1e8
println("r = $r, R0 = $r0")
}</syntaxhighlight>
{{out}}
<pre>r = 0.1123021757, R0 = 3.84827928</pre>
 
=={{header|Wren}}==
{{trans|Phix}}
<syntaxhighlight lang="wren">var K = 7800000000 // approx world population
var n0 = 27 // number of cases at day 0
 
var y = [
27, 27, 27, 44, 44, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60,
61, 61, 66, 83, 219, 239, 392, 534, 631, 897, 1350, 2023,
2820, 4587, 6067, 7823, 9826, 11946, 14554, 17372, 20615,
24522, 28273, 31491, 34933, 37552, 40540, 43105, 45177,
60328, 64543, 67103, 69265, 71332, 73327, 75191, 75723,
76719, 77804, 78812, 79339, 80132, 80995, 82101, 83365,
85203, 87024, 89068, 90664, 93077, 95316, 98172, 102133,
105824, 109695, 114232, 118610, 125497, 133852, 143227,
151367, 167418, 180096, 194836, 213150, 242364, 271106,
305117, 338133, 377918, 416845, 468049, 527767, 591704,
656866, 715353, 777796, 851308, 928436, 1000249, 1082054,
1174652
]
 
var f = Fn.new { |r|
var sq = 0
for (i in 0...y.count) {
var eri = (r*i).exp
var dst = (n0*eri)/(1+n0*(eri-1)/K) - y[i]
sq = sq + dst * dst
}
return sq
}
 
var solve = Fn.new { |f, guess, epsilon|
var f0 = f.call(guess)
var delta = guess
var factor = 2 // double until f0 best then halve until delta <= epsilon
while (delta > epsilon) {
var nf = f.call(guess - delta)
if (nf < f0) {
f0 = nf
guess = guess - delta
} else {
nf = f.call(guess + delta)
if (nf < f0) {
f0 = nf
guess = guess + delta
} else {
factor = 0.5
}
}
delta = delta * factor
}
return guess
}
 
var r = (solve.call(f, 0.5, 0) * 1e10).round / 1e10
var R0 = ((12 * r).exp * 1e8).round / 1e8
System.print("r = %(r), R0 = %(R0)")</syntaxhighlight>
 
{{out}}
<pre>
r = 0.1123021757, R0 = 3.84827928
</pre>
 
=={{header|XPL0}}==
{{trans|C}}
<syntaxhighlight lang "XPL0">def K = 7.8e9;
def N0 = 27.;
real Actual;
int ActualSize;
 
func real Func(R);
real R;
real Sq, Eri, Guess, Diff;
int I;
[Sq:= 0.;
for I:= 0 to ActualSize-1 do
[Eri:= Exp(R * float(I));
Guess:= N0 * Eri / (1. + N0 * (Eri-1.) / K);
Diff:= Guess - Actual(I);
Sq:= Sq + Diff*Diff;
];
return Sq;
];
 
func real Solve(Guess, Epsilon);
real Guess, Epsilon;
real Delta, F0, Factor, NF;
[Delta:= if Guess # 0. then Guess else 1.;
F0:= Func(Guess);
Factor:= 2.;
while Delta > Epsilon and Guess # Guess-Delta do
[NF:= Func(Guess - Delta);
if NF < F0 then
[F0:= NF;
Guess:= Guess - Delta;
]
else
[NF:= Func(Guess + Delta);
if NF < F0 then
[F0:= NF;
Guess:= Guess + Delta;
]
else Factor:= 0.5;
];
Delta:= Delta * Factor;
];
return Guess;
];
 
real R, R0;
[Actual:= [
27., 27., 27., 44., 44., 59., 59., 59., 59., 59., 59., 59., 59., 60., 60.,
61., 61., 66., 83., 219., 239., 392., 534., 631., 897., 1350., 2023., 2820.,
4587., 6067., 7823., 9826., 11946., 14554., 17372., 20615., 24522., 28273.,
31491., 34933., 37552., 40540., 43105., 45177., 60328., 64543., 67103.,
69265., 71332., 73327., 75191., 75723., 76719., 77804., 78812., 79339.,
80132., 80995., 82101., 83365., 85203., 87024., 89068., 90664., 93077.,
95316., 98172., 102133., 105824., 109695., 114232., 118610., 125497.,
133852., 143227., 151367., 167418., 180096., 194836., 213150., 242364.,
271106., 305117., 338133., 377918., 416845., 468049., 527767., 591704.,
656866., 715353., 777796., 851308., 928436., 1000249., 1082054., 1174652.];
ActualSize:= 97;
R:= Solve(0.5, 0.0);
R0:= Exp(12.*R);
Text(0, "R = "); RlOut(0, R); CrLf(0);
Text(0, "R0 = "); RlOut(0, R0); CrLf(0);
]</syntaxhighlight>
{{out}}
<pre>
R = 0.11230
R0 = 3.84828
</pre>
PureFox
9,476

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/299636...354163"