How can I plot a curve with different ranges for x?

I would like to plot three ranges for x with three different functions in a same graph in matlab. The first range is 1<x<20. The second range is from 20<x<30 and the last range is 30<x<200. The y functions are Euler method but using different parameters. I have already typed the codes of Euler method but I don't know how to combine the graphs with different ranges for x.

[Mathieu NOE]

Hello

can you share your code ?

tx

[Sze Wing HO]

clear all; clc;

%% r = 1
tau_E = 3.69; % average time in the exposed state
gamma_1 = 1/tau_E;
tau_I = 3.48; % average time in the infected state
gamma_2 = 1/tau_I;
E0 = 10; I0 = 0; N0 = 6e7;
r1 = 1;p = 0.01;

f = @(u1, beta, gamma_1, gamma_2)...
    [-beta*u1(1)*u1(3),...
    beta*u1(1)*u1(3) - gamma_1*u1(2),...
    gamma_1*u1(2) - gamma_2*u1(3),...
    (1-p)*gamma_2*u1(3)];

dt = 0.01; Days = 30;
t1 = [20:1:Days]; %t = t';
u1 = zeros(Days+1,4);
u1(1,:) = [N0, E0, 0, 0];
N = N0; beta = r1*gamma_2/N;

for day = 1:Days
    day
    u1_old = u1(day,:);
    for k = 1:100
        u1_new = u1_old + dt*f(u1_old, beta, gamma_1, gamma_2);
        u1_old = u1_new;
    end
    u1(day+1,:) = u1_old(:);
end
%% r = 0.8
tau_E = 3.69; % average time in the exposed state
gamma_1 = 1/tau_E;
tau_I = 3.48; % average time in the infected state
gamma_2 = 1/tau_I;
E0 = 10; I0 = 0; N0 = 6e7;
r2 = 0.8;p = 0.01;

f = @(u2, beta, gamma_1, gamma_2)...
    [-beta*u2(1)*u2(3),...
    beta*u2(1)*u2(3) - gamma_1*u2(2),...
    gamma_1*u2(2) - gamma_2*u2(3),...
    (1-p)*gamma_2*u2(3)];

dt = 0.01; Days = 200;
t2 = [30:1:Days]; %t = t';
u2 = zeros(Days+1,4);
u2(1,:) = [N0, E0, 0, 0];
N = N0; beta2 = r2*gamma_2/N;

for day = 1:Days
    day
    u2_old = u2(day,:);
    for k = 1:100
        u2_new = u2_old + dt*f(u2_old, beta2, gamma_1, gamma_2);
        u2_old = u2_new;
    end
    u2(day+1,:) = u2_old(:);
end
%% r = 3
tau_E = 3.69; % average time in the exposed state
gamma_1 = 1/tau_E;
tau_I = 3.48; % average time in the infected state
gamma_2 = 1/tau_I;
E0 = 10; I0 = 0; N0 = 6e7;
r3 = 3;p = 0.01;

f = @(u3, beta, gamma_1, gamma_2)...
    [-beta*u3(1)*u3(3),...
    beta*u3(1)*u3(3) - gamma_1*u3(2),...
    gamma_1*u3(2) - gamma_2*u3(3),...
    (1-p)*gamma_2*u3(3)];

dt = 0.01; Days = 20;
t3 = [1:1:Days]; %t = t';
u3 = zeros(Days+1,4);
u3(1,:) = [N0, E0, 0, 0];
N = N0; beta3 = r3*gamma_2/N;

for day = 1:Days
    day
    u3_old = u3(day,:);
    for k = 1:100
        u3_new = u3_old + dt*f(u3_old, beta3, gamma_1, gamma_2);
        u3_old = u3_new;
    end
    u3(day+1,:) = u3_old(:);
end

[Mathieu NOE]

hello again

stated to look at your code and I have a few questions - some clarifications would be appreciated :

first I am not sure what the time vector is supposed to be as you have for example t1 and u1 , which have different size; same for t2 / u2 and t3 / u3

the results are computed on a daily basis , so time axis is days ?

I supposed the data you want to plot is u1 , u2 , u3 , all components or one in particular ?

I simply added this piece of code to plot the data and get an idea of the issue

Got these plots :

figure(1);
hold on
plot(u1(:,1))
plot(u2(:,1))
plot(u3(:,1))
xlabel('days');
legend('u1(:,1)','u2(:,1)','u3(:,1)');
hold off 

figure(2);
hold on
plot(u1(:,2))
plot(u2(:,2))
plot(u3(:,2))
xlabel('days');
legend('u1(:,2)','u2(:,2)','u3(:,2)');
hold off 

figure(3);
hold on
plot(u1(:,3))
plot(u2(:,3))
plot(u3(:,3))
xlabel('days');
legend('u1(:,3)','u2(:,3)','u3(:,3)');
hold off 

figure(4);
hold on
plot(u1(:,4))
plot(u2(:,4))
plot(u3(:,4))
xlabel('days');
legend('u1(:,4)','u2(:,4)','u3(:,4)');
hold off 

[Sze Wing HO]

Thank you for your response. I didn't stated clearly. I would like to have one curve only which is u(:,3). The u(:,1), u(:,2) and u(:,4) are unnecessary. The first part of the curve is 1<t<20 which t is the days. And the second part of the curve is 20<t<30 and 30<t<200 respectively. Their u(:,3) functions are different because of the different values of r. What I want is a parabolic curve. Thank you again for your help!!

[Mathieu NOE]

ok but I have a problem with your code

for each of the 3 runs you do a for loop going from 1 to Days and Days = 30 in the first run, Days = 200 in the second run, and Days = 20 in the third one

at the end if we do a concatenation of all results , I have a vector of length 253 , which is not coherent with your answer above (as far as I understand the total dat should then be of length 200 if time goes from 1 to 200)

so there is something wrong with my understanding ?

or do we have to take only a fraction of the length of each run (20 of the 31 samples of the first run for example ?

[Sze Wing HO]

Maybe my code is not correct as I am not sure how to separate the days into three parts(1<t<20 when r=3, 20<t<30 when r=1, 30<t<200 when r=0.8). What can I do if I want to separate them with same vector length?

[Mathieu NOE]

just to understand ... so there is an time order to follow , as I guess you want to have a simulation that is in this order : r = 3 then 1 then 0.8 (continuous decrease of r)

your code at this time seems to suggest you start with r = 1 then 0.8 then 3 , so I am a bit lost...

also I was supposing that when you go from first to second run, your new initial conditions are not zero again, but you would use the last iteration result from previous run ...

[Mathieu NOE]

As you said you were expecting a parabloa curve , I guessed what your intentions are and midified the code accordingly.

here the plot , I re-ordered the simutions so that the runs are coherent with R decreasing from 3 to 1 to 0.8 , which is not your original code

Plot looks then like that : is it what you wanted ?

updated Code is :

clear all; clc;

%% r = 3
tau_E = 3.69; % average time in the exposed state
gamma_1 = 1/tau_E;
tau_I = 3.48; % average time in the infected state
gamma_2 = 1/tau_I;
E0 = 10; I0 = 0; N0 = 6e7;
r3 = 3;p = 0.01;
f = @(u3, beta, gamma_1, gamma_2)...
    [-beta*u3(1)*u3(3),...
    beta*u3(1)*u3(3) - gamma_1*u3(2),...
    gamma_1*u3(2) - gamma_2*u3(3),...
    (1-p)*gamma_2*u3(3)];
dt = 0.01; 
Days = 20; %% time duration : day 1 to 20 
t3 = [1:1:Days]; %% time duration : day 1 to 20
u3 = zeros(Days,4); %% cor MN
u3(1,:) = [N0, E0, 0, 0];
N = N0; beta3 = r3*gamma_2/N;
for day = 1:Days-1  %% cor MN
    
    u3_old = u3(day,:);
    for k = 1:100
        u3_new = u3_old + dt*f(u3_old, beta3, gamma_1, gamma_2);
        u3_old = u3_new;
    end
    u3(day+1,:) = u3_old(:);
end


%% r = 1
tau_E = 3.69; % average time in the exposed state
gamma_1 = 1/tau_E;
tau_I = 3.48; % average time in the infected state
gamma_2 = 1/tau_I;
E0 = 10; I0 = 0; N0 = 6e7;
r1 = 1;p = 0.01;
f = @(u1, beta, gamma_1, gamma_2)...
    [-beta*u1(1)*u1(3),...
    beta*u1(1)*u1(3) - gamma_1*u1(2),...
    gamma_1*u1(2) - gamma_2*u1(3),...
    (1-p)*gamma_2*u1(3)];
dt = 0.01;
Days = 11; % time duration : day 20 to 30
% t1 = [20:1:Days]; %t = t';
t1 = [t3(end):1:t3(end)+Days-1]; % time duration : day 20 to 30
u1 = zeros(Days,4); %% cor MN
% u1(1,:) = [N0, E0, 0, 0];
u1(1,:) = u3(end,:); %% cor MN : use last run last sample as new initial conditions 

N = N0; beta = r1*gamma_2/N;

for day = 1:Days-1  %% cor MN
    
    u1_old = u1(day,:);
    for k = 1:100
        u1_new = u1_old + dt*f(u1_old, beta, gamma_1, gamma_2);
        u1_old = u1_new;
    end
    u1(day+1,:) = u1_old(:);
end



%% r = 0.8
tau_E = 3.69; % average time in the exposed state
gamma_1 = 1/tau_E;
tau_I = 3.48; % average time in the infected state
gamma_2 = 1/tau_I;
E0 = 10; I0 = 0; N0 = 6e7;
r2 = 0.8;p = 0.01;
f = @(u2, beta, gamma_1, gamma_2)...
    [-beta*u2(1)*u2(3),...
    beta*u2(1)*u2(3) - gamma_1*u2(2),...
    gamma_1*u2(2) - gamma_2*u2(3),...
    (1-p)*gamma_2*u2(3)];
dt = 0.01;
Days = 171; % time duration : day 30 to 200
% t2 = [30:1:Days]; %t = t'; 
t2 = [t1(end):1:t1(end)+Days-1]; % time duration : day 30 to 200
u2 = zeros(Days,4); %% cor MN
% u2(1,:) = [N0, E0, 0, 0];
u2(1,:) = u1(end,:); %% cor MN : use last run last sample as new initial conditions 

N = N0; beta2 = r2*gamma_2/N;

for day = 1:Days-1  %% cor MN
    
    u2_old = u2(day,:);
    for k = 1:100
        u2_new = u2_old + dt*f(u2_old, beta2, gamma_1, gamma_2);
        u2_old = u2_new;
    end
    u2(day+1,:) = u2_old(:);
end


figure(4);
hold on
plot(t3,u3(:,3))
plot(t1,u1(:,3))
plot(t2,u2(:,3))
title('R = 3 / 1 / 0.8');
xlabel('days');
% legend('u3(:,3)','u1(:,3)','u2(:,3)');
legend('R = 3','R = 1','R = 0.8');
hold off 
% 

[Sze Wing HO]

Yes, thank you. That's what I want.

[Mathieu NOE]

If you agree , I will post again the updated code in the answer section, so you can "accept" it if you're ok for it ?

Answer 1

[Mathieu NOE]

So basically , the updated code as guessed from your initial request

clear all; clc;
%% r = 3
tau_E = 3.69; % average time in the exposed state
gamma_1 = 1/tau_E;
tau_I = 3.48; % average time in the infected state
gamma_2 = 1/tau_I;
E0 = 10; I0 = 0; N0 = 6e7;
r3 = 3;p = 0.01;
f = @(u3, beta, gamma_1, gamma_2)...
    [-beta*u3(1)*u3(3),...
    beta*u3(1)*u3(3) - gamma_1*u3(2),...
    gamma_1*u3(2) - gamma_2*u3(3),...
    (1-p)*gamma_2*u3(3)];
dt = 0.01; 
Days = 20; %% time duration : day 1 to 20 
t3 = [1:1:Days]; %% time duration : day 1 to 20
u3 = zeros(Days,4); %% cor MN
u3(1,:) = [N0, E0, 0, 0];
N = N0; beta3 = r3*gamma_2/N;
for day = 1:Days-1  %% cor MN
    
    u3_old = u3(day,:);
    for k = 1:100
        u3_new = u3_old + dt*f(u3_old, beta3, gamma_1, gamma_2);
        u3_old = u3_new;
    end
    u3(day+1,:) = u3_old(:);
end
%% r = 1
tau_E = 3.69; % average time in the exposed state
gamma_1 = 1/tau_E;
tau_I = 3.48; % average time in the infected state
gamma_2 = 1/tau_I;
E0 = 10; I0 = 0; N0 = 6e7;
r1 = 1;p = 0.01;
f = @(u1, beta, gamma_1, gamma_2)...
    [-beta*u1(1)*u1(3),...
    beta*u1(1)*u1(3) - gamma_1*u1(2),...
    gamma_1*u1(2) - gamma_2*u1(3),...
    (1-p)*gamma_2*u1(3)];
dt = 0.01;
Days = 11; % time duration : day 20 to 30
% t1 = [20:1:Days]; %t = t';
t1 = [t3(end):1:t3(end)+Days-1]; % time duration : day 20 to 30
u1 = zeros(Days,4); %% cor MN
% u1(1,:) = [N0, E0, 0, 0];
u1(1,:) = u3(end,:); %% cor MN : use last run last sample as new initial conditions 
N = N0; beta = r1*gamma_2/N;
for day = 1:Days-1  %% cor MN
    
    u1_old = u1(day,:);
    for k = 1:100
        u1_new = u1_old + dt*f(u1_old, beta, gamma_1, gamma_2);
        u1_old = u1_new;
    end
    u1(day+1,:) = u1_old(:);
end
%% r = 0.8
tau_E = 3.69; % average time in the exposed state
gamma_1 = 1/tau_E;
tau_I = 3.48; % average time in the infected state
gamma_2 = 1/tau_I;
E0 = 10; I0 = 0; N0 = 6e7;
r2 = 0.8;p = 0.01;
f = @(u2, beta, gamma_1, gamma_2)...
    [-beta*u2(1)*u2(3),...
    beta*u2(1)*u2(3) - gamma_1*u2(2),...
    gamma_1*u2(2) - gamma_2*u2(3),...
    (1-p)*gamma_2*u2(3)];
dt = 0.01;
Days = 171; % time duration : day 30 to 200
% t2 = [30:1:Days]; %t = t'; 
t2 = [t1(end):1:t1(end)+Days-1]; % time duration : day 30 to 200
u2 = zeros(Days,4); %% cor MN
% u2(1,:) = [N0, E0, 0, 0];
u2(1,:) = u1(end,:); %% cor MN : use last run last sample as new initial conditions 
N = N0; beta2 = r2*gamma_2/N;
for day = 1:Days-1  %% cor MN
    
    u2_old = u2(day,:);
    for k = 1:100
        u2_new = u2_old + dt*f(u2_old, beta2, gamma_1, gamma_2);
        u2_old = u2_new;
    end
    u2(day+1,:) = u2_old(:);
end
figure(4);
hold on
plot(t3,u3(:,3))
plot(t1,u1(:,3))
plot(t2,u2(:,3))
title('R = 3 / 1 / 0.8');
xlabel('days');
% legend('u3(:,3)','u1(:,3)','u2(:,3)');
legend('R = 3','R = 1','R = 0.8');
hold off 
%