simulation of dde problem

Good evening sir i am trying to find simulation of dde model problem but i got error. I. request you sir please help me by resolving this error

beta = 1.9;
a1 = 0.3;
a2 = 0.2;
gamma1= 0.01;
gamma2= 0.01;
gamma3= 0.05;
mu= 0.05;
tau =14;
N=1;
d1 = 0.04;
d2 = 0.02;

ddeSEIQR = @(t,y,Z)[N-beta*y(1)*y(3)/N-mu*y(1);... 
    (beta*y(1)*y(3)/N)-beta*exp(-mu*tau)*Z(1,1)*Z(3,1)/N-a1*y(2)-gamma1*y(2)-mu*y(2);...
    beta*exp(-mu*tau)*Z(1,1)*Z(3,1)/N-a2*y(3)-gamma2*y(3)-d1*y(3)-mu*y(3);...
    a1*y(2)+a2*y(3)-d2*y(4)-gamma3*y(4)-mu*y(4);...
    gamma1*y(2)+gamma2*y(3)+gamma3*y(4)-mu*y(5)];

sol = dde23(ddeSEIQR,[14,1],[0.999,0,0.001,0,0],[0,200] ) ;     




figure;
plot(sol.x,sol.y(1,:))
hold on
plot(sol.x,sol.y(2,:),'-')
hold on
plot(sol.x,sol.y(3,:),'--')
hold on
plot(sol.x,sol.y(4,:),'--')
hold on
plot(sol.x,sol.y(5,:),'--')
hold off
title('Equilibrium points for SEAIQR Model');

label ('time(days)');

Unrecognized function or variable 'label'.

label('solution y');
legend('S', 'E','I', 'Q','R');

ERROR:

Error using vertcat

Dimensions of arrays being concatenated are not consistent.

Error in

SEIQR_dde>@(t,y,Z)[N-beta*y(1)*y(3)/N,-mu*y(1);(beta*y(1)*y(3)/N)-beta*exp(-mu*tau)*Z(1,1)*Z(3,1)/N-a1*y(2)-gamma1*y(2)-mu*y(2);beta*exp(-mu*tau)*Z(1,1)*Z(3,1)/N-a2*y(3)-gamma2*y(3)-d1*y(3)-mu*y(3);a1*y(2)+a2*y(3)-d2*y(4)-gamma3*y(4)-mu*y(4);gamma1*y(2)+gamma2*y(3)+gamma3*y(4)-mu*y(5)]

(line 15)

ddeSEIQR = @(t,y,Z)[N- beta*y(1)*y(3)/N -mu*y(1);

Error in dde23 (line 228)

f0 = feval(ddefun,t0,y0,Z0,varargin{:});

Error in SEIQR_dde (line 21)

sol = dde23(ddeSEIQR,[14,1],[0.999,0,0.001,0,0],[0,200] ) ;

[Torsten]

Error removed.

[mallela ankamma rao]

Thanks alot Mr.Torsten sir. i have one doubt sir

sol = dde23(ddeSEIQR,[14,1],[0.999,0,0.001,0,0],[0,200] ) ;

here ddeSEIQR is function,[0.999,0,0.001,0,0],

[0,200] is initial conditions,

[0,200] is tspan

what is [14,1] and how did i take ?

[Torsten]

what is [14,1] and how did i take ?

Did you read the documentation of dde23 ?

14 and 1 are the lags in your differential equations.

I wonder why you specified two lags because in your equations, you only refer to the first (14) with the terms

Z(1,1) (which means y1(t-14)) and

Z(3,1) (which means y3(t-14)).

[mallela ankamma rao]

Thank you very much sir Sir this is not my model code. I want to do a paper on delay differential equations.so while i am searching for code,i got this code. Sir if you dont mind,can you refer some codes on dde models

Answer 1

[Mr. Pavl M.]

% I've actually found the specific ammendment-corregendum-initial 
% enreachment and SOLVED it:

clc
clear all
close all


tol = 1e-07;

rand('state',1)

diary on

diary('PavW.txt')
disp(' ');

disp('  * * * * * * * * * * * *')

  * * * * * * * * * * * *

disp('  *      Start          *');

  *      Start          *

disp('  * * * * * * * * * * * *')

  * * * * * * * * * * * *

function h = history(t)
h = t;
end

function [position,isterminal,direction] = zeroEventsFcn(t,y,ydelay)
position = y(5);
isterminal = 1;
direction = 0;
end

beta = 1.9;
a1 = 0.3;
a2 = 0.2;
gamma1= 0.01;
gamma2= 0.01;
gamma3= 0.05;
mu= 0.05;
tau =14;
N=1;
d1 = 0.04;
d2 = 0.02;

ddeSEIQR = @(t,y,Z)[N-beta*y(1)*y(3)/N-mu*y(1);... 
    (beta*y(1)*y(3)/N)-beta*exp(-mu*tau)*Z(1,1)*Z(3,1)/N-a1*y(2)-gamma1*y(2)-mu*y(2);...
    beta*exp(-mu*tau)*Z(1,1)*Z(3,1)/N-a2*y(3)-gamma2*y(3)-d1*y(3)-mu*y(3);...
    a1*y(2)+a2*y(3)-d2*y(4)-gamma3*y(4)-mu*y(4);gamma1*y(2)+gamma2*y(3)+gamma3*y(4)-mu*y(5)];

delays1 = [14,1];
delays2 = 15;

%sol = dde23(@ddefun,delays,history,tspan);

opts = ddeset(Events=@zeroEventsFcn);
sol = dde23(ddeSEIQR,delays1,[0.999,0,0.001,0,0],[0 200],opts); 

figure;
plot(sol.x,sol.y(1,:))
hold on
plot(sol.x,sol.y(2,:),'-',sol.xe,sol.ye(2,:),"o")
hold on
plot(sol.x,sol.y(3,:),'--')
hold on
plot(sol.x,sol.y(4,:),'--')
hold on
plot(sol.x,sol.y(5,:),'--',sol.xe,sol.ye(5,:),"o")
hold off
title('Equilibrium points for SEAIQR Model with events');
xlabel('time [days]');
ylabel('solution y');
legend('S','E','I','Q','R');

diary off

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