ext-model
Compartments
g — vaccination lag
period.
e — vaccine
effectiveness.
v — vaccination rate.
r — infection rate.
Equations
$$ \begin{aligned} \frac{dS^u}{dt} &= -vS^u-rS^u\\ \frac{dS^g}{dt} &= +vS^u-rS^g-g^{-1}S^g\\ \frac{dS^v}{dt} &= +g^{-1}S^g-r(1-e)S^v\\ \frac{dI^u}{dt} &= +rS^u-d^{-1}I^u\\ \frac{dI^v}{dt} &= +rS^g+r(1-e)S^v-d^{-1}I^v\\ \frac{dR^u}{dt} &= +d^{-1}I^u-vR^u\\ \frac{dR^v}{dt} &= +d^{-1}I^v+vR^u\\ \end{aligned} $$