X Component Derivatives for the SIS Model

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