while fitting my model data to experimental data the resultant curve is shooting very high and is not matching with experimental time points, even on changing ub and lb

% Experimental data
t1=[0 6 12 18 36 48];  % time points 
nfe2=[0.9 1.57 2.87 3.9 5.16 4.25];  %level of protein
t=1:1:48;  %simulation time
% ODE equation

ode_eqn = @(x, t)integrate_a(x, t);  %ODE equation to fit
x0 = [0.04 0.055];  % Initial guess for the parameters

% Least squares curve fitting using lsqcurvefit
x_fit = lsqcurvefit(ode_eqn, x0, t1, nfe2);

Local minimum possible.

lsqcurvefit stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.

disp("Fitted parameters using lsqcurvefit:")

Fitted parameters using lsqcurvefit:

disp(x_fit)

    1.1792    0.0282

% Nonlinear programming using fmincon
options = optimoptions('fmincon', 'Algorithm', 'interior-point');
x_fit_constrained = fmincon(@(x) sum((ode_eqn(x, t1) - nfe2).^2), x0,[],[],[],[],[0 0],[10 10],[],options);

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

disp("Fitted parameters using fmincon:")

Fitted parameters using fmincon:

disp(x_fit_constrained)

    1.1792    0.0282

% Plotting results
t_fit = linspace(1, max(t1),49);  % Time points for plotting fitted curve

figure;
plot(t1, nfe2, 'bo', 'MarkerSize', 8, 'LineWidth', 1.5);  % Plot experimental data
hold on;
plot(t_fit, ode_eqn(x_fit, t_fit), 'r-', 'LineWidth', 2);  % Plot fitted curve using lsqcurvefit
plot(t_fit, ode_eqn(x_fit_constrained, t_fit), 'g--', 'LineWidth', 2);  % Plot fitted curve using fmincon
hold off;

legend('Experimental Data', 'lsqcurvefit', 'fmincon');
xlabel('Time');
ylabel('Data');
title('Fitting Experimental Data to ODE Equation');

%%

function ifn = integrate_a(x, t)
%nf=[0.9 3.3 6.8 5.7 4.02 ];
%f=[100 98.31 35.5 12.85 4.68];
ifn=zeros(size(t));

for i=1:numel(t)
    if t(i)<6.48
        cd(i)=1;
    else
        cd(i)=(1- 0.0683)*exp(-0.0240*(t(i) - 6.48)) + 0.0683;
    end
    c=cd;
    if t(i)<4
        inf(i)=0.9;
    else      
        inf(i) = inf(i-1)+ (cd(i).*x(1)- inf(i-1).*x(2));
    end
    ifn=inf;
end
end

[Matt J]

the resultant curve is shooting very high and is not matching with experimental time points

That's nothing we can diagnose for you. It's possible your model is just unsuitable to the data.

Answer 1

[Image Analyst]

Are you just trying to fit this equation:

cd(i) = (1- 0.0683) * exp(-0.0240*(t(i) - 6.48)) + 0.0683;

If so use fitnlm. I'm attaching some demos. Adjust the equation/formula as needed.

[SWAPNAVA]

No I am trying to fit inf(i) = inf(i-1)+ (cd(i).*x(1)- inf(i-1).*x(2));

please check whether my waty is correct.

[Image Analyst]

I don't know what a "waty" is.

Also inf is a contant in MATLAB. It means "infinity". So I'm not sure what your equation means. Usually operations using infinity end up giving infinity again. For example inf(5) will give a 5x5 array of infinity values

i = 5;
a = inf(i)

a = 5×5

Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf

So you can't have inf(i) on the left hand side of the equation.

[SWAPNAVA]

no "inf" is a variable. i have changed to "infron" still I am getting the model output curve but it is reaching till 25 along y xis where experimental data is till 5 only maximum along y axis.