Hi everyone,
I am currently having a set of differential equations, namely
dB = - mu*S,
dS = mu*S - beta*S*I + gamma*I - nu_s*S,
dI = beta*S*I - gamma*I - alpha*I - nu_i*I,
dP = nu_s*S + nu_i*I, and
dD = alpha*I,
as well as a dataset, containing observations of the states of B, S, I, P, and D.
I am trying to estimate the parameter [mu, beta, gamma, alpha, nu_s, nu_i], using the econometrics toolbox approach to estimate state space models with unknown parameters.
The state transition matrix A, with unknown parameter denoted as NaN is
A = [0 NaN 0 0 0;...
0 NaN NaN 0 0;...
0 NaN NaN 0 0;...
0 NaN NaN 0 0;...
0 0 NaN 0 0]
In accordance with the documentation, I formulated the parameter mapping function:
function [A,B,C,D,Mean0,Cov0,StateType] = timeInvariantParamMap(params)
A = [0 -params(1) 0 0 0;...
0 params(1)-params(3) params(4)-params(2) 0 0;...
0 0 params(2)-params(4)-params(5)-params(6) 0 0;...
0 params(3) params(6) 0 0; 0 0 params(5) 0 0];
B = [params(7) 0 0 0 0;...
0 params(8) 0 0 0;...
0 0 params(9) 0 0;...
0 0 0 params(10) 0;...
0 0 0 0 params(11)];
C = eye(5);
D = zeros(5,1);
Mean0 = [30161, 3, 0, 0, 0];
Cov0 = [];
StateType = [0, 0, 0, 0, 0];
end
But I don't know, how to incorporate the term beta*S*I, so a state variable in the transition matrix. The current approach just ignores that fact
Since the econometrics toolbox is a quite new tool, I was not able to find any related Q&As.
I would really appreciate any hint on my problem, as well as additional information.
Best regards,
David
