Logistic curve fitting in epidemiology: Difference between revisions
Logistic curve fitting in epidemiology (view source)
Revision as of 22:55, 8 April 2021
, 3 years agoAda version
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:;*[[https://www.zoology.ubc.ca/~bio310/Blank%20Page%204_files/DL%20R%20and%20r.htm Calculating r and R0]]
<br><br>
=={{header|Ada}}==
{{trans|C++}}
<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;</lang>
{{out}}
<pre>r = 0.1123022, R0 = 3.8482793</pre>
=={{header|C}}==
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