How can i vary the value of one parameter and plot them on same graph?

Hi there!

function idtry
%
r = 1.3;
tspan = [0:20:40];
%
sol = dde23(@ddems,r,@ddemshist,tspan);
time = sol.x;
SD    = sol.y(1,:);
ID    = sol.y(2,:);
VD    = sol.y(3,:);
hold on 
plot(time,SD,'b','LineWidth',2)
plot(time,VD,'g','LineWidth',2)
hold off

plot(time,ID,'--r','LineWidth',2)
xlabel('Time(days)');
ylabel('Infected Dogs Population');
legend('I_d')

grid on
grid minor

function s = ddemshist(t)
% Constant history function for DDEX1.
s = [40 0 0]';
% --------------------------------------------------------------------------

function dydt = ddems(t,y,Z)
Ad = 15; mud = 0.2; k = 2.9; cd = 0.01; 
Bd = 0.4; r = 0.2; md = 0.02; 
% Differential equations function for DDEX1.
ylag1 = Z(:,1);
dydt = [ Ad-Bd*y(1)*ylag1(1)*exp(-mud*r)-(mud+k)*y(1)+cd*y(3)
    Bd*y(1)*ylag1(1)*exp(-mud*r)-(mud+md)*y(2)
    k*y(1)-(cd+mud)*y(3)
    ];

I want to vary the value of k to be [0.8, 1.6, 2.4, 2.9] and plot on the same graph.. how can i do that please?

Answer 1

[Voss]

One way is to make the function ddems nested inside the function idtry and make k a variable in idtry's workspace; then k will be available in ddems's workspace as well because it's a nested function. Then you can loop over the values of k in idtry.

https://www.mathworks.com/help/matlab/matlab_prog/nested-functions.html

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html

idtry

function idtry
%
rr = 1.3;
tspan = [0:20:40];
%
hold on 
k_all = [0.8, 1.6, 2.4, 2.9];
for ii = 1:numel(k_all)
    k = k_all(ii);
    sol = dde23(@ddems,rr,@ddemshist,tspan);
    time = sol.x;
%     SD    = sol.y(1,:);
    ID    = sol.y(2,:);
%     VD    = sol.y(3,:);
%     hold on 
%     plot(time,SD,'b','LineWidth',2) % why plot these at all? they're just going to 
%     plot(time,VD,'g','LineWidth',2) % be replaced by the next plot() after "hold off"
%     hold off
    plot(time,ID,'--','LineWidth',2,'DisplayName',sprintf('I_d k=%.1f',k));
end
xlabel('Time(days)');
ylabel('Infected Dogs Population');
% legend('I_d')
legend()
grid on
grid minor

    
    function s = ddemshist(t)
    % Constant history function for DDEX1.
    s = [40 0 0]';
    end


    % --------------------------------------------------------------------------
    function dydt = ddems(t,y,Z)
    Ad = 15; mud = 0.2; %k = 2.9;
    cd = 0.01; 
    Bd = 0.4; r = 0.2; md = 0.02; 
    % Differential equations function for DDEX1.
    ylag1 = Z(:,1);
    dydt = [ Ad-Bd*y(1)*ylag1(1)*exp(-mud*r)-(mud+k)*y(1)+cd*y(3)
             Bd*y(1)*ylag1(1)*exp(-mud*r)-(mud+md)*y(2)
             k*y(1)-(cd+mud)*y(3)
           ];
    end


end

[Abdullahi]

Hi there, thank you so much for your help.. why is it that the shape of my plot is getting attached to y-axis? how can i get the plot away from y-axis?

[Voss]

Do you mean, why are the curves nearly vertical near x = 0? All I can say is, because that's what dde23 gave you.

Maybe set the axes XScale to 'log' to see that region better.

idtry

function idtry
%
rr = 1.3;
tspan = [0:20:40];
%
hold on 
k_all = [0.8, 1.6, 2.4, 2.9];
for ii = 1:numel(k_all)
    k = k_all(ii);
    sol = dde23(@ddems,rr,@ddemshist,tspan);
    time = sol.x;
%     SD    = sol.y(1,:);
    ID    = sol.y(2,:);
%     VD    = sol.y(3,:);
%     hold on 
%     plot(time,SD,'b','LineWidth',2) % why plot these at all? they're just going to 
%     plot(time,VD,'g','LineWidth',2) % be replaced by the next plot() after "hold off"
%     hold off
    plot(time,ID,'--','LineWidth',2,'DisplayName',sprintf('I_d k=%.1f',k));
end
set(gca(),'XScale','log');
xlabel('Time(days)');
ylabel('Infected Dogs Population');
% legend('I_d')
legend('Location','Northwest')
grid on
grid minor
    
    function s = ddemshist(t)
    % Constant history function for DDEX1.
    s = [40 0 0]';
    end
    % --------------------------------------------------------------------------
    function dydt = ddems(t,y,Z)
    Ad = 15; mud = 0.2; %k = 2.9;
    cd = 0.01; 
    Bd = 0.4; r = 0.2; md = 0.02; 
    % Differential equations function for DDEX1.
    ylag1 = Z(:,1);
    dydt = [ Ad-Bd*y(1)*ylag1(1)*exp(-mud*r)-(mud+k)*y(1)+cd*y(3)
             Bd*y(1)*ylag1(1)*exp(-mud*r)-(mud+md)*y(2)
             k*y(1)-(cd+mud)*y(3)
           ];
    end
end

[Abdullahi]

Ok.. that works well, but can we get the curves to rise at 10^-6? so we can study the behaviour of the curves

[Voss]

We can set the x-limits of the axes to start at 1e-6 (see below), but changing the curves themselves requires changing the equations and/or parameters, which would mean you'd be solving a different problem than the problem this code solves.

idtry

function idtry
%
rr = 1.3;
tspan = [0:20:40];
%
hold on 
k_all = [0.8, 1.6, 2.4, 2.9];
for ii = 1:numel(k_all)
    k = k_all(ii);
    sol = dde23(@ddems,rr,@ddemshist,tspan);
    time = sol.x;
%     SD    = sol.y(1,:);
    ID    = sol.y(2,:);
%     VD    = sol.y(3,:);
%     hold on 
%     plot(time,SD,'b','LineWidth',2) % why plot these at all? they're just going to 
%     plot(time,VD,'g','LineWidth',2) % be replaced by the next plot() after "hold off"
%     hold off
    plot(time,ID,'--','LineWidth',2,'DisplayName',sprintf('I_d k=%.1f',k));
end
xl = xlim();
set(gca(), ...
    'XScale','log', ...
    'XLim',[1e-6 xl(2)]);
xlabel('Time(days)');
ylabel('Infected Dogs Population');
% legend('I_d')
legend('Location','Northwest')
grid on
grid minor
    
    function s = ddemshist(t)
    % Constant history function for DDEX1.
    s = [40 0 0]';
    end
    % --------------------------------------------------------------------------
    function dydt = ddems(t,y,Z)
    Ad = 15; mud = 0.2; %k = 2.9;
    cd = 0.01; 
    Bd = 0.4; r = 0.2; md = 0.02; 
    % Differential equations function for DDEX1.
    ylag1 = Z(:,1);
    dydt = [ Ad-Bd*y(1)*ylag1(1)*exp(-mud*r)-(mud+k)*y(1)+cd*y(3)
             Bd*y(1)*ylag1(1)*exp(-mud*r)-(mud+md)*y(2)
             k*y(1)-(cd+mud)*y(3)
           ];
    end
end

[Abdullahi]

Ok. Thank you so much

[Voss]

You're welcome!

[Abdullahi]

Hi, i tried to vary a different parameter (ah) this time using same approach as above but it is producing only one plot. what's is the problem?

function ihplot

%

r = 0.4;

tspan = [0:20:40];

%

hold on

ah_all = [0.8, 1.2, 1.6, 2.0];

for ii = 1:numel(ah_all)

ah = ah_all(ii);

sol = dde23(@ddems,r,@ddemshist,tspan);

time = sol.x;

IH = sol.y(2,:);

plot(time,IH,'-','LineWidth',2.5,'DisplayName',sprintf('I_h ah=%.1f',ah));

end

xlabel('Time(days)');

ylabel('Infected Humans Population');

% legend('I_d')

legend('ah=0.8','ah=1.2','ah=1.6','ah=2.0')

grid on

grid minor

function s = ddemshist(t)

% Constant history function for DDEX1.

s = [500 100 0 0 0]';

end

% --------------------------------------------------------------------------

function dydt = ddems(t,y,Z)

Ah = 300; muh = 0.2; mud = 0.03; Kd = 1000;

ah = 0.6; ad = 1; vh = 0.8; k = 0.2;

Bh = 0.4; Bd = 0.5; r = 0.4; dh = 0.4; d = 0.1;

mh = 0.02; rh = 0.2;

% Differential equations function for DDEX1.

ylag1 = Z(:,1);

dydt = [ Ah-Bh*y(1)*ylag1(1)*exp(-mud*r)-(muh+vh)*y(1)+dh*y(3)+d*y(5)

Bh*y(1)*ylag1(1)*exp(-mud*r)-(muh+mh+ah)*y(2)

vh*y(1)-(dh+muh)*y(3)

ah*y(2)-(muh+rh)*y(4)

rh*y(4)-(muh+d)*y(5)

];

end

end

[Voss]

'ah' is still being set in ddems(). You have to remove that in order for the 'ah' in ihplot() to be used. (Notice that I commented out the line setting 'k' in ddems() in my answer - same thing.)

[Abdullahi]

work great.. Thank you so much

[Voss]

You're welcome!

[Abdullahi]

can i vary the lags (r) in the same way?

[Voss]

Yes, but since there is a variable 'r' in both the function idtry and the function ddems, one of them has to be changed to something else. Actually, I should've changed one of them when I made ddems a nested function, but I didn't notice it until now. Now I have edited the code in my answer and comments so that one of the r's is called rr. Notice the curves have changed slightly.

Once you have changed one of the 'r's to something else, you can loop over r values like you've done before with k and ah. However, notice in the case of r (what I call rr in my updated code), it is used only as an input to dde23 and is not used in ddems, unlike k and ah.

[Abdullahi]

the two r's are same, i renamed the lag (i.e. tau) in the original equations to be r.. (see equations below).

[Voss]

If the two r's are the same, then remove the one defined in ddems and just use the one defined in idtry/ihplot. Loop over r values in idtry/ihplot, like you did with k and ah.

[Abdullahi]

ok.. let me try that