MATLAB: How to divide different graphs

MATLABode45

Is there anyway to divide this function up, and have the first 4 equations (dSdt(1) to dSdt(4)) computed into one graph and the remaining last 3 equations computed on a separate graph? This is a mathematical modelling question, with dSdt(1) to dSdt(4) representing the one population and dSdt(5) to dSdt(7) representing another population. to = 0; tf = 100; tspan = [to tf]; y0 = [5535002 50 50 0 0 0 0 ]; [t,S] = ode45(@denguefeverODE, tspan, y0); plot(t,S) title('Human Population Without Control') xlabel('Time') ylabel('Susceptible, Exposed, Infected, Recovered') legend('Susceptible', 'Exposed', 'Infected', 'Recovered') function dSdt = denguefeverODE(t,S) Nh = 5535002; Nm = 33210012; uh = 0.0045; um = 0.02941; Pmh = 0.375; Phm = 0.750; beta = 1; nu_h = 0.1666; epsilon_m = 0.1; tau_h = 0.1176; f = 6; dSdt = zeros(7,1); dSdt(1) = uh*Nh – (beta*Pmh*(S(7)/Nh)+uh)*S(1); dSdt(2) = beta*Pmh*(S(7)/Nh)*S(1) – (tau_h+uh)*S(2); dSdt(3) = tau_h*S(2)-(nu_h+uh)*S(3); dSdt(4) = nu_h*S(3)-uh*S(4); dSdt(5) = um*Nm – (beta*Phm*(S(3)/Nh)+um)*S(5); dSdt(6) = beta*Phm*(S(3)/Nh)*S(5); dSdt(7) = epsilon_m*S(6) – um*S(7);

Thank you!

Best Answer

I ran your code and tested this (it works). Your figure becomes two figures, each plotting the columns of ‘S’ you want:

figure(1)
plot(t,S(:,1:4))
title('Human Population Without Control')
xlabel('Time')
ylabel('Susceptible, Exposed, Infected, Recovered')
legend('Susceptible', 'Exposed', 'Infected', 'Recovered')
figure(2)
plot(t,S(:,5:7))
title('Human Population Without Control')
xlabel('Time')
ylabel('Susceptible, Exposed, Infected, Recovered')
legend('Susceptible', 'Exposed', 'Infected', 'Recovered')

Related Solutions

MATLAB: The mathematics behind modelling

You have a system of 7 coupled ODEs. You will need to code the equations into a function, define the initial conditions and interval for integration, then use an ODE solver such as ODE45 to solve the equations numerically. I got you started on your function, but you'll need to fill in the gaps and double check it:

function dSdt = denguefeverODE(t,S)
% Define parameters
Nh = 
Nm = 
uh = 
um = 
Pmh = 
Phm = 
beta = 
nu_h = 
epsilon_m = 
tau_h = 
f = 
% Define the equations. Each element in the output contains the answer for
% one equation, so there are 7 components. For ex. S(1) is Sh while dSdt(1)
% is dSh/dt, and S(7) is Im while dSdt(7) is dIm/dt.
dSdt = zeros(7,1);
dSdt(1) = uh*Nh - (beta*Pmh*(S(7)/Nh)+uh)*S(1);
dSdt(2) = beta*Pmh*(S(7)/Nh)*S(1) - (tau_h+uh)*S(2);
.
.
.
dSdt(7) = epsilon_m*S(6) - um*S(7);

Once you are ready to solve, the solver syntax is

tspan = [t0 tf];        % Change to initial and final times
y0 = [a b c d e f g];   % Need 7 initial conditions, 1 for each variable
[t,y] = ode45(@denguefeverODE, tspan, y0)

Then you can see all of the solution components with

plot(t,y)

More information here: http://www.mathworks.com/help/matlab/ordinary-differential-equations.html

MATLAB: Implementing a code from Berkley Madonna into Matlab

Just for fun (and because I’m interested in biochemistry), I decided to code this as best I could. It gives interesting results, but certainly not out of character for some biochemical systems. (I copied the equations directly from your code, pasted them into the function, and did a ‘Search - Replace’ with the Editor.)

K1 = 0.005;
K2 = 0.005;
K3 = 0.005;
K4 = 0.005;
Kc = 0.5;
Kd = 0.02;
kdd = 0.01;
V2 = 1.5;
V4 = 0.5;
vd = 0.25;
VM1 = 3;
VM3 = 1.;
Synth = 0.025;
% Original Equations: 
% PhsKnsKnt = [Synth-vd*X*(C/(Kd+C)) - kdd*C;    M*VM3*((1-X)/(K3+(1-X))) - V4*(X/(K4+X));    VM1*(C/(Kc+C))*((1-M)/(K1+(1-M))) - V2*(M/(K2+M))];
% Anonymous Function with substitutions: 
PhsKnsKnt = @(T, P)  [Synth - vd*P(2)*(P(1)/(Kd+P(1))) - kdd*P(1);    P(3)*VM3*((1-P(2))/(K3+(1-P(2)))) - V4*(P(2)/(K4+P(2)));    VM1*(P(1)/(Kc+P(1)))*((1-P(3))/(K1+(1-P(3)))) - V2*(P(3)/(K2+P(3)))];
[T P] = ode45(PhsKnsKnt, [0  100],  [0.01;  0.01;  0.01]);
C = P(:,1);
X = P(:,2);
M = P(:,3);
figure(1)
plot(T, P)
legend('[C] (µ\itM\rm)',  '[X] (µ\itM\rm)',  '[M] (µ\itM\rm)', 'Location','NorthWest')
xlabel('Time (s)')
ylabel('Concentration')
grid

Just out of curiosity, what biochemical system is this?

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