% Function to calculate the Hessian of R0 to the entries of fertility % matrix F. % % Input: % U = the transition matrix (n by n matrix) % F = the fertility matrix (n by n matrix) % % Function outputs result of Equation (63) (n^2 by n^2 matrix). % function H = HR0_F(U, F) A = U + F; [n, n] = size(A); In = eye(n); F = A-U; N = inv(In - U); R = F*N; HR0R = Hlambda_A(R); % H[R0,vecR], using Eq (24) B = kron(N,In) * HR0R * kron(N',In); % Eq (62) H = 1/2*(B + B'); end