Dynamics in Space: The herd immunity threshold and the critical community size are key
dynamical concepts in understanding the local persistence of infectious
disease. The former defines the
deterministic conditions necessary for an infection to spread and the latter is
describes the phenomenological observation that the rate at which local incidence
drops to 0 (“fade-out”), due to failure of infected individuals to successfully
transmit, decreases as communities increase in size. Despite conditions that
preclude persistent transmission (i.e. R0<1) or increase the likelihood of
local stochastic fade-out, infection may persist at the regional scale through
metapopulation dynamics. A metapopulation, as originally defined Hanski 2008,
is a collection of sub-populations, or patches, that each have a non-zero
probability of extinction, but are maintained through a process of continual
re-establishment due to migration from extant to extinct patches. In the context of infectious disease, the
patches of a metapopulation are consistent with small outbreaks in local
communities that are likely fade-out locally, either deterministically because
R0<1 or stochastically because the communities are small Grenfell 1997. Consistent with the theory of
metapopulations, infection may be maintained regionally if there is sufficient
migration between patches that each patch is likely to seed infection in
another patch prior to local fade-out. Thus,
this dynamic phenomenon creates regional stability (i.e. persistence) despite
local instability (i.e. frequent and predictable fade-out).