Compute Derivatives for the SIS X-Model

Compute the derivatives for SIS compartmental model. Here, the model includes human demographic changes, and it is computed in an equivalent form: $$\begin{array}{rl}dH/dt=& B(t,H)+D\cdot H\\ dI/dt=& h(H-I)-rI-\xi (t)+D\cdot I\end{array}$$ where $S=H-I$ ; $\xi (t)$ is a function to simulate mass treatment; $B(t,H)$ is the time-dependent birth rate; and $D$ is a linear operator, a matrix describing demographic changes, including mortality, migration, and aging;