  We take up a recently proposed compartmental SEIQR model with delays, ignore
loss of immunity in the context of a fast pandemic, extend the model to a
network structured on infectivity, and consider the continuum limit of the same
with a simple separable interaction model for the infectivities $\beta$.
Numerical simulations show that the evolving dynamics of the network is
effectively captured by a single scalar function of time, regardless of the
distribution of $\beta$ in the population. The continuum limit of the network
model allows a simple derivation of the simpler model, which is a single scalar
delay differential equation (DDE), wherein the variation in $\beta$ appears
through an integral closely related to the moment generating function of
$u=\sqrt{\beta}$. If the first few moments of $u$ exist, the governing DDE can
be expanded in a series that shows a direct correspondence with the original
compartmental DDE with a single $\beta$. Even otherwise, the new scalar DDE can
be solved using either numerical integration over $u$ at each time step, or
with the analytical integral if available in some useful form. Our work
provides a new academic example of complete dimensional collapse, ties up an
underlying continuum model for a pandemic with a simpler-seeming compartmental
model, and will hopefully lead to new analysis of continuum models for
epidemics.
