Hi, i am trying plot my thesis graph using dde23 but i keep on getting this error, derivative and history function have different lengths.. HELP PLEASE!

function Hassan

lags = 0.2;

tspan = [0,60];

sol = dde23(@ddehs, lags, @hshist, tspan);

time = sol.x;
S    = sol.y(1,:);
I    = sol.y(2,:);
V    = sol.y(3,:);


figure;
plot(time,S,'r')
xlabel('Time (Years)'); ylabel('Susceptible Human Population');
legend('S_h')

figure;
plot(time,I,'b')
xlabel('Time (Years'); ylabel('Infected Human Population');
legend('I_h')

figure;
plot(time,V,'b')
xlabel('Time (Years'); ylabel('Vaccinated Human Population');
legend('V_h')

end

function dydt = ddehs(~,y,z)

        Kh = 10000; muH = 0.0066;
        aH = 0.02;  Bh  = 0.3;
        muD = 0.08; tau = 0.2;
        wH = 1;

        ylag1 = z(:,1);
        

        dydt = [ muH*Kh - (muH + aH)*y(1) - Bh*y(1)*ylag1*exp(-muH*tau)
                 Bh*y(1)*ylag1*exp(-muD*tau) - (muH + wH)*y(2)
                 aH*y(1) - muH*y(3) ];

end

function s = hshist(~)
        
        s = ones(3,1);

end

Answer 1

[Torsten]

z(:,1) is a 3x1 vector with z(1,1) = y1(t-0.02), z(2,1) = y2(t-0.02) and z(3,1) = y3(t-0.02),

You have to decide which of the three delay terms you want to insert in dydx(1) and dydx(2).

[Musa Abdullahi]

Hi, thank you for your help.. how can i plot both equation on same graph??

[Torsten]

Why both ? You have three.

plot(sol.x,sol.y)

Or use

time = sol.x;
S    = sol.y(1,:);
I    = sol.y(2,:);
V    = sol.y(3,:);
hold on
plot(time,S,'r')
plot(time,I,'b')
plot(time,V,'g')
xlabel('Time (Years)');
legend('S_h','I_h','V_h')
hold off

[Musa Abdullahi]

Thank you so much.. How can i show the effect of one parameter on one population by varying the parameter values.. (like effects of varying delay values on infected humans populations)?

[Torsten]

Make a loop over the parameter values, call dde23 for each parameter value and save the results.

After you have exited the loop, plot the solution curves.

[Musa Abdullahi]

Hi, I have tried ploting my modified model equations but the graph is not displaying..

here is my code...

function Modified

lags = 0.2;

tspan = [0,60];

sol = dde23(@ddehs, lags, @hshist, tspan);

time = sol.x;
S    = sol.y(1,:);
I    = sol.y(2,:);
V    = sol.y(3,:);
T    = sol.y(4,:);
R    = sol.y(5,:);

hold on

plot(time,I,'b')
plot(time,S,'r')
plot(time,V,'g')
plot(time,T,'k')
plot(time,R,'y')

xlabel('Time (Years)');

legend('S_h','I_h','V_h','T_h','R_h')

hold off

end

function dydt = ddehs(~,y,z)

        Lh = 100000; muh = 0.06;
        uh = 0.09;  Bh  = 0.5;
        mud = 0.08; tau = 0.2;
        ah = 1; mh = 0.2; bh =0.5; rh = 0.5;
        dh = 0.21;

        ylag1 = z(3,1);
        

        dydt = [ Lh - Bh*y(1)*ylag1*exp(-mud*tau)-(muh + uh)*y(1) + bh*y(3) + dh*y(5)
                 Bh*y(1)*ylag1*exp(-mud*tau) - (muh + mh + ah)*y(2)
                 uh*y(1) - (bh + muh)*y(3)
                 ah*y(2) - (muh + rh)*y(4)
                 rh*y(4) - (muH + dh)*y(5) ];

end

function s = hshist(~)
        
         s = ones(3,1);

end

[Musa Abdullahi]

PLEASE HELP!! PLEASE

[Musa Abdullahi]

Can you please give me a hint on how to go about that loop?... trying to show the effect of one parameter on one population..

[Torsten]

lags = [0.2,2.0,6.0,12.0];
time = 0:0.1:60;
for i = 1:numel(lags)
  tspan = [0,60];
  sol = dde23(@ddehs, lags(i), @hshist, tspan);
  yint = deval(sol,time);
  S(i,:) = yint(1,:);
  I(i,:) = yint(2,:);
  V(i,:) = yint(3,:);
end
figure;
plot(time,S,'r')
xlabel('Time (Years)'); ylabel('Susceptible Human Population');
legend('S_h')

figure;
plot(time,I,'b')
xlabel('Time (Years)'); ylabel('Infected Human Population');
legend('I_h')

figure;
plot(time,V,'b')
xlabel('Time (Years)'); ylabel('Vaccinated Human Population');
legend('V_h')

function dydt = ddehs(~,y,z)
  Kh = 10000; muH = 0.0066;
  aH = 0.02;  Bh  = 0.3;
  muD = 0.08; tau = 0.2;
  wH = 1;
  ylag1 = z(2,1);

  dydt = [ muH*Kh - (muH + aH)*y(1) - Bh*y(1)*ylag1*exp(-muH*tau)
           Bh*y(1)*ylag1*exp(-muD*tau) - (muH + wH)*y(2)
           aH*y(1) - muH*y(3) ];
end

function s = hshist(~)
  s = ones(3,1);
end

[Musa Abdullahi]

THANK YOU!!

Answer 2

[Musa Abdullahi]

Hi, I have been trying to plot the graph of the equations from the existing journal i am working on.. but shape i am getting is not the same with what they have.. below is a screenshot of their graph and what i am obtaining from my code..

and this is what my plot

Can you please point out my error here? Thank you so much..