%
%          SIR_rhs
%
  function dy = SIR_rhs(t,y,params);

  global N 

  beta = params(1);
  gamma = params(2);
  mu = params(3);

  S = y(1);
  I = y(2);
  S_mu = y(3);
  I_mu = y(4);
  S_beta = y(5);
  I_beta = y(6);
  S_gamma = y(7);
  I_gamma = y(8);
  Svec = [S_mu; I_mu; S_beta; I_beta; S_gamma; I_gamma];
  J = [(-mu-beta*I) -beta*S; beta*I (beta*S-(gamma+mu))];
  Der = blkdiag(J,J,J); 
  Grad = [(N-S); -I; -I*S; I*S; 0; -I];
  Sen = Der*Svec + Grad;

%
% Construct the right-hand side
%
  dy = [mu*(N-S) - beta*I*S;
        beta*I*S - (gamma+mu)*I;
        Sen];