Implements the XH component using a delay Susceptible-Exposed-Infectious-Susceptible (SEISd) model of human infection dynamics. This is a delay differential equation (or delay difference equation) version of the SEIS model, in which the exposed period is modelled as a fixed delay \(\nu\) rather than an exponential rate.

State Variables

H

total human (or host) population density

E

density of exposed (infected but not yet infectious) humans

I

density of infectious humans

Note: susceptible density \(S = H - E - I\).

Parameters

b

transmission probability from mosquito to human

c

transmission probability from human to mosquito

nu

intrinsic incubation period (fixed delay, in days)

r

clearance rate for infections

B

time-dependent birth rate function \(B(t, H)\)

D

linear operator (matrix) for mortality, migration, aging, and transfers

Dynamics

$$ \begin{array}{rl} dH/dt &= B(t,H) + D \cdot H \\ dE/dt &= hS - \dot{E}(t-\nu) + D \cdot E \\ dI/dt &= \dot{E}(t-\nu) - rI + D \cdot I \\ \end{array}$$ where \(h\) is the force of infection, \(S = H - E - I\), and \(\dot{E}(t-\nu)\) is the rate cases were exposed \(\nu\) days ago (computed via deSolve::lagderiv).