Compute the derivatives for SIP compartmental model: $$ \begin{array}{rrrrcc} dS/dt =& - (h +\xi) S &+ r I & + \eta P & + d{\cal H}(S) &+ B(t, H) \\ dI/dt =& (1-\rho) h S & - (r+\xi) I &&+ d{\cal H}(I) \\ dP/dt =& (\rho h +\xi)S & +\xi I & - \eta P &+ d{\cal H}(P) \end{array} $$ where \(H = S+I+P\); \(B(t, H)\) is the time-dependent birth rate; and the \(d{\cal H}\) operator computes derivatives for the demographic model \(\cal H\).
# S3 method for class 'SIP'
dXdt(t, y, pars, i)a numeric vector
The parameters are defined in create_Xpar_SIP