How to implement extended kalman filter in the absence of matrices B, D, and vector u of the state space?

Hi all,

I have a non-linear continuous EDOS model, which form a dynamic system of an epidemiological disease, in which I want to estimate some parameters of this model with the extended kalman filter. I discretized and linearized the template as suggested by the article https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7483235 and trying to implement how it implemented it. Note that I increased the state vector by placing the parameter to be estimated and put the values of the other variables of the vector. I do not know how to implement, so what may seem trivial to me is still a seven-headed creature. In my model the matrix B and the vector u are null. The implementation I want to reproduce is from equation (17) to (24). Can someone help me ? Immensely grateful!

The code developed so far follows the attachment to better verify what has already been done!