Implements the XH component using a Susceptible-Infectious-Prophylaxis (SIP) compartmental model of malaria infection dynamics. Individuals in \(P\) are protected from infection but not from becoming infectious; they re-enter susceptibility when prophylaxis wanes.
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 (\(\xi(t)\))
sigmarate of mass screen-and-treat (\(\sigma(t)\))
etarate of prophylaxis waning
Btime-dependent birth rate function \(B(t, H)\)
Dlinear operator (matrix) for mortality, migration, aging, and transfers
$$ \begin{array}{rl} dH/dt &= B(t,H) + D \cdot H \\ dI/dt &= (1-\rho)hS - (r + \xi + \sigma)I + D \cdot I \\ dP/dt &= \rho hS + \xi(S+I) + \sigma I - \eta P + D \cdot P \\ \end{array}$$ where \(h\) is the force of infection and \(S = H - I - P\).