Comparación del modelo Gompertz y Richards, biotecnologia microbiana

Seminario Biotecnología Microbiana 2
Comparación del modelo Gompertz y Richards

clc
close all
clear all
load Ecoli
xdata=Ecoli(:,1);
N=Ecoli(:,2);
ydata=log10(N)-log10(N(1)); %log(N/N0)%Valores iniciales
b0(1)=max(ydata); % valor inicial de A
for i=1:length(ydata)-4
tg(i)=(ydata(i+4)-ydata(i))/(xdata(i+4)-xdata(i));
end
[v in]=max(tg);
b0(2)=v; %valor inicial de mub0(3)=(b0(2)*xdata(in)-ydata(in))/b0(2); %valor inicial de lambda
figure
plot(xdata,ydata,'o')
xlabel('t (horas)')
ylim([-1 max(ydata)+0.5])
%Opcionesoptions=statset('MaxIter',200,'TolFun',1e-12,'TolX',1e-12);
%Regresión no lineal
%gompertz
[b(1,:),r,J,COVB,mse(1)] = nlinfit(xdata,ydata,@gompertz,b0,options);
%richards
[br(1,:),r,J,COVB,mse(2)] = nlinfit(xdata,ydata,@richards,[b0 1],options);hold on
regresion(1,:)=gompertz(b(1,:),xdata);
regresion(2,:)=richards(br(1,:),xdata);
plot(xdata,regresion','-','LineWidth',2)
legend('Observaciones','gompertz','richards')
hold off
b
brgl(1)=size(ydata,1)-size(b,2); %grados de libertad gompertz
gl(2)=size(ydata,1)-size(br,2); %grados de libertad richards
sse=mse.*gl
f=((sse(1)-sse(2))/(gl(1)-gl(2)))/(sse(2)/gl(2)) %valor delestadístico
pvalor=1-fcdf(f,gl(1)-gl(2),gl(2)) %p-valor


b = 6.8246 0.9972 0.9384
br = 6.3644 1.0507 1.1783 0.6901
sse = 0.9304 0.8128
f = 1.8807
p-valor = 0.1935


Comparacióndel modelo Logístico y Gompertz

clc
close all
clear all
load Ecoli
xdata=Ecoli(:,1);
N=Ecoli(:,2);
ydata=log10(N)-log10(N(1)); %log(N/N0)
%Valores iniciales
b0(1)=max(ydata); % valor inicialde A
for i=1:length(ydata)-4
tg(i)=(ydata(i+4)-ydata(i))/(xdata(i+4)-xdata(i));
end
[v in]=max(tg);
b0(2)=v; %valor inicial de mu
b0(3)=(b0(2)*xdata(in)-ydata(in))/b0(2); %valor inicial delambda
figure
plot(xdata,ydata,'o')
xlabel('t (horas)')
ylim([-1 max(ydata)+0.5])
%Opciones
options=statset('MaxIter',200,'TolFun',1e-12,'TolX',1e-12);
%Regresión no lineal
[b,r,J,COVB,mse] =...