Implements the XH component using a delay Susceptible-Infectious-Prophylaxis (SIPd) model of malaria infection dynamics. This is the delay differential equation version of the SIP model, in which the duration of prophylaxis \(\eta\) is modelled as a fixed delay.
Htotal human (or host) population density
Idensity of infectious humans
Pdensity of humans under chemoprophylaxis
Note: susceptible density \(S = H - I - P\).
btransmission probability from mosquito to human
ctransmission probability from human to mosquito
rclearance rate for infections
rhofraction of new infections immediately treated / entering \(P\)
xirate of mass drug administration (\(\xi\))
etaprophylaxis duration (fixed delay, in days)
Btime-dependent birth rate function \(B(t, H)\)
Dlinear operator (matrix) for mortality, migration, aging, and transfers
$$ \begin{array}{rl} dH/dt &= B(t,H) + D \cdot H \\ dI/dt &= (1-\rho)hS - (r + \xi)I + D \cdot I \\ dP/dt &= (\rho h + \xi)S + \xi I - \dot{\mathcal{H}}(P) + D \cdot P \\ \end{array}$$ where \(\dot{\mathcal{H}}(P)\) is the delayed outflow from \(P\), computed via deSolve::lagderiv.