ODE model
%define the function file
% a general growth model where the cocentration of nutrient does not have any influence on the bacterial growth
function vdot = growth(t,v)
vdot = f*v;
% simulate the growth of volume of a bacterial cell depending on a constant growth rate.
%calling the function
[t, v] = ode45('growth', [0, 5], 1);
%the analytical solution
v_true = exp(k*t);
IN A NEW M-FILE
% simulate the growth of volume of a bacterial cell depending on a constant growth rate.
clear all;
%declare the time range
k=1;
%concentration of nutrient
nutrient = 21;
n = 0.8;
Ka = 10.5;
theta = (nutrient^n) / (((Ka)^n) + (nutrient^n));
t=[0.01:0.01:10];
%create graph
v1=exp(k*t);
v=exp((theta)*t);
subplot(2,1,1);
plot(t,v); grid on;
xlabel('time'); ylabel('volume of the cell');
title('An ODE model for the growth of the cell volume depending on a constant growth rate');
subplot(2,1,2);
plot(t,v1); grid on;
xlabel('time'); ylabel('volume of the cell');
title('An ODE model for the growth of the cell volume incorporating the hill function');