Box 1: Spatial models of pathogen transmission
Partial Differential Equations (PDEs) describe the size
of the infected class over continuous space and time. Theirhost density models are continuous, and often homogeneous
(but see Garlick et al. 2011, Hefley et al. 2017). Themobility model1 is a spatial diffusion
rate and a corresponding functional form. Outputs include
existence, structure, and speed of traveling epidemic waves and
spatially explicit times to epidemic peak. Assumptions:animals move according to the kernel, which is often isotropic and
independent of environment; transmission occurs locally.
Semi-spatial and static network models allow pairwise
interactions within local neighborhoods. The host densitymodel is implicit, but relies on discrete units with corresponding
disease states. The mobility model is defined through
pairwise coupling coefficients between the “locations”, along with a
specified “neighborhood” with which each location interacts.Outputs are usually derived from a master equation or
simulation. Assumptions: known network structure and
disease status; a priori definition of “neighborhood”
(depending on analytical approach).
Metapopulation models track disease dynamics at physical
locations coupled with one another across space. The host
density and mobility models mirror those of semi-spatial
models, though locations are now spatially explicit, and mobility can
include explicit functions of geographic distance. Outputsinclude spatial spreading rate, spatial synchrony among subunits, and
individual- and patch-level reproductive numbers.Assumptions: a priori knowledge of system
connectivity.
IBMs allow movement and transmission to emerge
organically from predefined rules applied to a set of actors. Inputs are
individual-level attributes and parameters that govern them. Thehost density model can be continuous or discrete. Themobility model typically allows an individual’s state and
environment to interact through a set of movement rules.Outputs range from a simple wave front of disease spread
to each individual’s spatiotemporally explicit contribution to
reproductive numbers. Assumptions: depend on model
specifics.
Spatially embedded social networks describe disease
dynamics across multipartite networks whose nodes correspond explicitly
to locations in space. Inputs are bipartite networks
linking individuals to locations of different types (households, peer
groups, etc.), The host density model is a set of spatial
centroids associated with each group, and mobility models
can be distance-, gravity-, or radiation-based. Outputsinclude estimates of R0, total epidemic size, and
spatial and temporal patterns of transmission.Assumptions: constant connectivities; central-place space
use patterns.
1The contact process is often subsumed
into a constant transmission rate or absorbed into themobility model .