Implements the XH component using a Susceptible-Infectious-Recovered-Susceptible (SIRS) compartmental model of human infection dynamics, extending SIR with waning immunity so that recovered individuals return to the susceptible class.
Htotal human (or host) population density
Idensity of infectious humans
Rdensity of recovered (temporarily immune) humans
Note: susceptible density \(S = H - I - R\).
btransmission probability from mosquito to human
ctransmission probability from human to mosquito
rclearance rate for infections
gammarate of waning immunity (loss of \(R\))
Btime-dependent birth rate function \(B(t, H)\)
Dlinear operator (matrix) for mortality, migration, aging, and transfers
$$ \begin{array}{rl} dH/dt &= B(t,H) + D \cdot H \\ dI/dt &= hS - rI + D \cdot I \\ dR/dt &= rI - \gamma R + D \cdot R \\ \end{array}$$ where \(h\) is the force of infection and \(S = H - I - R\).