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%         This software is licensed by Creative Commons BY-NC-SA:         %
%      http://creativecommons.org/licenses/by-nc-sa/3.0/it/legalcode      %
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% File: Jacobian(par)
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% Goal: compute the system Jacobian 
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% Inputs: par: model parameters
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% Outputs: J: the system Jacobian 
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% Remark: symbolic calculus is used
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function J=Jacobian(par)
syms x y z
% Define the equations of the model
f = [par(1)*(1-x/par(2))*x-par(3)*y*x-par(4)*z*x;  
    par(5)*(1-y/par(6))*y-par(7)*y*x-par(8)*y*z; 
    par(9)*(1-z/par(10))*z-par(11)*x*z-par(12)*y*z];
s = [x,y,z];      
J = jacobian(f,s);
end