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Highlights from
Tutorial on solving DDEs with DDE23

  • exam1
  • exam1
  • exam2
  • exam2
  • exam3
  • exam3
  • exam4
  • exam4
  • exam5
  • exam5
  • exam6 This is a demonstration problem for CTMS/BD in
  • exam6 This is a demonstration problem for CTMS/BD in
  • exam7 An example from C. Marriott and C. DeLisle, Effects
  • exam7 An example from C. Marriott and C. DeLisle, Effects
  • exam8 This is the suitcase problem from Suherman, et al.,
  • exam8 This is the suitcase problem from Suherman, et al.,
  • exer1 Example 1 of K.W. Neves, Automatic integration
  • exer1 Example 1 of K.W. Neves, Automatic integration
  • exer2 Example of J.D. Farmer, Chaotic Attractors of an
  • exer2 Example of J.D. Farmer, Chaotic Attractors of an
  • exer3 Wheldon's model of chronic granuloctic leukemia
  • exer3 Wheldon's model of chronic granuloctic leukemia
  • exer5
  • exer5
  • exer6 Sample problem of ARCHI manual. The absolute error
  • exer6 Sample problem of ARCHI manual. The absolute error
  • exer7 Marchuk immunology model of E. Hairer, S.P. Norsett, and
  • exer7 Marchuk immunology model of E. Hairer, S.P. Norsett, and
  • prob1 This system of ODE's is taken from 'An Introduction to Nuermcial Methods
  • prob1 This system of ODE's is taken from 'An Introduction to Nuermcial Methods
  • prob2 This problem considers a cardiovascular model, which can be found in
  • prob2 This problem considers a cardiovascular model, which can be found in
  • prob2b This problem considers a cardiovascular model, which can be found in
  • prob2b This problem considers a cardiovascular model, which can be found in
  • prob3 This problem is epidemic model due to Cooke, more information can be
  • prob3 This problem is epidemic model due to Cooke, more information can be
  • prob4 This problem is an epidemic model due to Cooke et alia, more information
  • prob4 This problem is an epidemic model due to Cooke et alia, more information
  • prob5 This problem population growth model due to Cooke et alia, more information
  • prob5 This problem population growth model due to Cooke et alia, more information
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Tutorial on solving DDEs with DDE23

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22 Aug 2003 (Updated )

Solving delay differential equations with DDE23. Tutorial + Examples.

prob4
function sol = prob4
%  This problem is an epidemic model due to Cooke et alia, more information
%  can be found in 'Interaction of maturation delay and nonlinear birth in
%  population and epidemic models' J. Math. Biol., 39 (1999) 332-352.
%  (This is reference 3 of the tutorial).

% Copyright 2004, The MathWorks, Inc.

  % Problem parameters, visible in nested functions.
  T = 0.2;
  lambda = 12;

  sol = dde23(@prob4f,T,[2; 3.5],[0, 25]);

  figure
  plot(sol.x,sol.y)
  legend('I(t)','N(t)',0)
  title(['Problem 4. Cooke et al. Epidemic Model with ' ...
         ' \lambda = ',num2str(lambda),'.'])
  xlabel('time t')

  %-----------------------------------------------------------------------
  % Nested function
  %
  
  function yp = prob4f(t,y,Z)
  %PROB4F  The derivative function for Problem 4 of the DDE Tutorial.
    a  = 1;
    b  = 80;
    d  = 1;
    d1 = 1;
    e  = 10;
    gamma = 0.5;

    I = y(1);
    N = y(2);
    Nlag = Z(2,1);
    dIdt = lambda*(N - I)*(I/N) - ( d + e + gamma)*I;
    dNdt = b*exp(-a*Nlag)*Nlag*exp(-d1*T) - d*N - e*I;
    yp = [ dIdt; dNdt];
  end % prob4f
  
  %-----------------------------------------------------------------------

end  % prob4

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