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 \(\cal H\).
The parameter \(\xi\) can be modified by setting mass_treat
to a
non-zero function of time.
# S3 method for class 'SIP'
dXdt(t, y, pars, i)
a numeric vector
The parameters are defined in make_Xpar_SIP