The SEIRV module for the XH component

Source: R/host-xde-SEIRV.R

Implements the XH component using a Susceptible-Exposed-Infectious-Recovered-Vaccinated (SEIRV) compartmental model of human infection dynamics, extending SEIR with a vaccinated compartment.

State Variables

H

total human (or host) population density

E

density of exposed (infected but not yet infectious) humans

I

density of infectious humans

R

density of recovered humans

V

density of vaccinated humans

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

Parameters

b

transmission probability from mosquito to human

c

transmission probability from human to mosquito

tau

rate of progression from exposed to infectious

r

clearance rate for infections

alpha

proportion of births that are vaccinated

varepsilon

proportion of recovered individuals that gain vaccine-like protection

gamma

rate of loss of immunity in \(R\)

B

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

D

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

Dynamics

$$ \begin{array}{rl} dH/dt &= B(t,H) + D \cdot H \\ dE/dt &= hS - \tau E + D \cdot E \\ dI/dt &= \tau E - rI + D \cdot I \\ dR/dt &= (1-\varepsilon)rI - \gamma R + D \cdot R \\ dV/dt &= \alpha B(t,H) + \varepsilon rI + D \cdot V \\ \end{array}$$ where \(h\) is the force of infection.