Compute the derivatives for SIP compartmental model: $$ \begin{array}{rl} dH/dt =& B(t,H) + D \cdot H \\ dI/dt =& (1-\rho) h S - (r+\xi+\sigma ) I + D \cdot I \\ dP/dt =& \rho h S + \xi (S+I) + \sigma I - \eta P + D \cdot P \end{array} $$ where \(S = H-I-P\); \(B(t, H)\) is the time-dependent birth rate; and \(D\) the demographic matrix.
The model sets up ports for mass treatment:
the parameter xi_t is computed as \(\xi'(t) = \xi + \mbox{mda}(t)\)
the parameter sigma_t is computed as \(\sigma'(t) = \sigma + \mbox{msat}(t)\)
The functions mda and msat are set to zero. To configure mass treatment, see ramp.control
# S3 method for class 'SIP'
dXHdt(t, y, xds_obj, i)a numeric vector
The parameters are defined in make_XH_obj_SIP