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');