I understand that you want to integrate and plot S against t using MATLAB.
The given differential equation is: 
Let 
which rearranges the equation to 
which rearranges the equation to Below is the MATLAB code to solve and plot S over time using "ode45" solver:
% Assuming constants(Change accordingly)
q = 1; V = 1; S0 = 10; k = 1; E = 1; Km = 1; Ki = 1;
% Define parameters
a = q/V;
b = k*E/q;
% Define ODE as a function handle
dSdt = @(t, S) a * (S0 - S - (b*S) / (Km + S + Ki*S^2));
% Set time span
tspan = [0 10]; % Adjust as needed
S_initial = 1; % Initial condition for S
% Solve ODE using ode45
[t, S] = ode45(dSdt, tspan, S_initial);
% Plot the results
figure;
plot(t, S, 'b-', 'LineWidth', 2);
xlabel('Time (t)');
ylabel('S');
title('S vs Time');
grid on;
Ensure you update the values of 
based on your data.
based on your data.For more details on using "ode45", refer to the MATLAB documentation: https://www.mathworks.com/help/matlab/ref/ode45.html
Hope this helps!
