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function k1k2k3
format long
clear all
clc
tspan = [0 1 2 3 4 5 6 7 8 9 10 ];
x0=[1 1 1 1 ];
k0 = [1 1 1 1 1 1 1 1 1 1 1 ]*1e-4;   
lb = [0 0 0 0 0 0 0 0 0 0 0];
ub = [1 1 1 1 1 1 1 1 1 1 1 ]*1e5;


data=[0.012,0.073,0.089,0.092,0.316,0.498,1.810,2.314,0.679,0.063,0.044;
    0.005,0.084,0.093,0.270,0.406,0.642,0.814,1.026,0.422,0.053,0.014;
    0.037,0.638,0.969,2.057,20.419,39.655,69.107,34.099,5.657,0.697,0.346;
   0.008,0.224,0.234,0.347,1.860,2.854,3.786,1.883,0.601,0.157,0.079;
   ]';
size(data);
yexp = data;

[k,resnorm,residual,exitflag,output,lambda,jacobian] =lsqnonlin(@ObjFunc,k0,lb,ub,[],tspan,x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\nʹÓú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
fprintf('\tk1 = %.16f \n',k(1))
fprintf('\tk2 = %.16f \n',k(2))
fprintf('\tk3 = %.16f \n',k(3))
fprintf('\tk4 = %.16f \n',k(4))
fprintf('\tk5 = %.16f \n',k(5))
fprintf('\tk5 = %.16f \n',k(6))
fprintf('\tk5 = %.16f \n',k(7))
fprintf('\tk5 = %.16f \n',k(8))
fprintf('\tk5 = %.16f \n',k(9))

ts=0:1:max(tspan);

[ts ys]=ode45(@KineticsEqs,ts,x0,[],k);
[ttt XXsim] = ode45(@KineticsEqs,tspan,x0,[],k);

figure(1),
plot(ts,ys(:,1),'b',tspan(2:end),yexp(:,1),'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','best');

figure(2),
plot(ts,ys(:,2),'b',tspan(2:end),yexp(:,2),'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','best');

figure(3),
plot(ts,ys(:,3),'b',tspan(2:end),yexp(:,3),'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','best');

figure(4),
plot(ts,ys(:,4),'b',tspan(2:end),yexp(:,4),'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','best');



function f = ObjFunc(k,tspan,x0,yexp)           % Ä¿±êº¯Êý
[t Xsim] = ode45(@KineticsEqs,tspan,x0,[],k);
Xsim1=Xsim(:,1);
Xsim2=Xsim(:,2);
Xsim3=Xsim(:,3);
Xsim4=Xsim(:,4);
ysim(:,1) = Xsim1(2:end);
ysim(:,2) = Xsim2(2:end);
ysim(:,3) = Xsim3(2:end);
ysim(:,4) = Xsim4(2:end);
size(ysim(:,1));
size(ysim(:,2));
size(ysim(:,3));
size(ysim(:,4));
size(yexp(:,1));
size(yexp(:,2));
size(yexp(:,3));
size(yexp(:,4));
f = [(ysim(:,1)-yexp(:,1)) (ysim(:,2)-yexp(:,2)) (ysim(:,3)-yexp(:,3))  (ysim(:,4)-yexp(:,4)) ];




function dEdt = KineticsEqs(t,C,k)   
% ODEÄ£ÐÍ·½³Ì %g(1)=k(4);g(2)=k(5);g(3)=k(6);m(1)=k(7);m(2)=k(8);m(3)=k(9);
CA=C(1);CB=C(2);CC=C(3);CD=C(4);
%dCAdt = k(1)*CA*(CB/2-1)-k(2)*CB+k(3)*CC;
%dCBdt=-g(1)*CA+g(2)*CB.*(1-CB/5)+g(3)*CC.*(1-CC/10);
%dCCdt=m(1)*CA.*(CA/2-1)-m(2)*CB-m(3)*CC;
dCAdt= -k(1)*CA-k(2)*CA;
dCBdt=k(1)*CA-k(3)*CB-k(4)*CB;
dCCdt=k(3)*CB-k(5)*CC;
dCDdt=k(2)*CA+k(4)*CB+k(5)*CC;
dEdt=[dCAdt;dCBdt;dCCdt;dCDdt];

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lf0612

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dS/dt=-k1*S-k2*S
dE/dt=k1*S-k3*E-k4*E
dI/dt=k3*E-k5*I
dR/dt=k2*S+-k4*E+k5*I
2Â¥2014-06-24 21:17:46
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CODE:
function k1k2k3k4k5
format long
clear all
clc
tspan = [0 1 2 3 4 5 6 7 8 9 10];
x0=[0.012 0.005 0.037 0.008];
%k0 = [-0.5 -0.8 -0.8 -1.5 2];  
k0 = [-0.87 -0.9 48.11 -47.80 -0.142];
lb = -[1 1 1 1 1]*1e9;
ub = [1 1 1 1 1]*1e5;


data=[0.073,0.089,0.092,0.316,0.498,1.810,2.314,0.679,0.063,0.044;
    0.084,0.093,0.270,0.406,0.642,0.814,1.026,0.422,0.053,0.014;
    0.638,0.969,2.057,20.419,39.655,69.107,34.099,5.657,0.697,0.346;
   0.224,0.234,0.347,1.860,2.854,3.786,1.883,0.601,0.157,0.079;
   ]';
size(data);
yexp = data;

[k,resnorm,residual,exitflag,output,lambda,jacobian] =lsqnonlin(@ObjFunc,k0,lb,ub,[],tspan,x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\nʹÓú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
fprintf('\tk1 = %.16f \n',k(1))
fprintf('\tk2 = %.16f \n',k(2))
fprintf('\tk3 = %.16f \n',k(3))
fprintf('\tk4 = %.16f \n',k(4))
fprintf('\tk5 = %.16f \n',k(5))

ts=0:1:max(tspan);

[ts ys]=ode45(@KineticsEqs,ts,x0,[],k);
[ttt XXsim] = ode45(@KineticsEqs,tspan,x0,[],k);

figure(1),
plot(ts,ys(:,1),'b',tspan(2:end),yexp(:,1),'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','best');

figure(2),
plot(ts,ys(:,2),'b',tspan(2:end),yexp(:,2),'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','best');

figure(3),
plot(ts,ys(:,3),'b',tspan(2:end),yexp(:,3),'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','best');

figure(4),
plot(ts,ys(:,4),'b',tspan(2:end),yexp(:,4),'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','best');



function f = ObjFunc(k,tspan,x0,yexp)           % Ä¿±êº¯Êý
[t Xsim] = ode45(@KineticsEqs,tspan,x0,[],k);
Xsim1=Xsim(:,1);
Xsim2=Xsim(:,2);
Xsim3=Xsim(:,3);
Xsim4=Xsim(:,4);
ysim(:,1) = Xsim1(2:end);
ysim(:,2) = Xsim2(2:end);
ysim(:,3) = Xsim3(2:end);
ysim(:,4) = Xsim4(2:end);
size(ysim(:,1));
size(ysim(:,2));
size(ysim(:,3));
size(ysim(:,4));
size(yexp(:,1));
size(yexp(:,2));
size(yexp(:,3));
size(yexp(:,4));
f = [(ysim(:,1)-yexp(:,1)) (ysim(:,2)-yexp(:,2)) (ysim(:,3)-yexp(:,3))  (ysim(:,4)-yexp(:,4)) ];




function dEdt = KineticsEqs(t,C,k)   
% ODEÄ£ÐÍ·½³Ì %g(1)=k(4);g(2)=k(5);g(3)=k(6);m(1)=k(7);m(2)=k(8);m(3)=k(9);
CA=C(1);CB=C(2);CC=C(3);CD=C(4);
%dCAdt = k(1)*CA*(CB/2-1)-k(2)*CB+k(3)*CC;
%dCBdt=-g(1)*CA+g(2)*CB.*(1-CB/5)+g(3)*CC.*(1-CC/10);
%dCCdt=m(1)*CA.*(CA/2-1)-m(2)*CB-m(3)*CC;
dCAdt= -k(1)*CA-k(2)*CA;
dCBdt=k(1)*CA-k(3)*CB-k(4)*CB;
dCCdt=k(3)*CB-k(5)*CC;
dCDdt=k(2)*CA+k(4)*CB+k(5)*CC;
dEdt=[dCAdt;dCBdt;dCCdt;dCDdt];

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5Â¥2014-06-25 09:55:08
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