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\begin{document}

\title{Defining an epidemiological landscape by connecting host movement to
pathogen transmission}



\author[1]{Kezia Manlove}%
\author[2]{Mark Wilber}%
\author[3]{Lauren White}%
\author[4]{Guillaume Bastille-Rousseau}%
\author[5]{Anni Yang}%
\author[6]{Marie Gilbertson}%
\author[7]{Meggan Craft}%
\author[8]{Paul Cross}%
\author[9]{George Wittemyer}%
\author[10]{Kim Pepin}%
\affil[1]{Utah State University}%
\affil[2]{The University of Tennessee Knoxville Institute of Agriculture}%
\affil[3]{National Socio-Environmental Synthesis Center}%
\affil[4]{Southern Illinois University Carbondale}%
\affil[5]{USDA-APHIS National Wildlife Research Center}%
\affil[6]{University of Minnesota Twin Cities}%
\affil[7]{University of Minnesota System}%
\affil[8]{USGS}%
\affil[9]{Colorado State University}%
\affil[10]{United States Department of Agriculture Animal and Plant Health Inspection Service}%


\vspace{-1em}



  
  \date{May 18, 2024}


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\selectlanguage{english}
\begin{abstract}
Environment drives the host movements that shape pathogen transmission
through three mediating processes: host density, host mobility, and
contact. These processes combine with pathogen life-history to give rise
to an ``epidemiological landscape'' that determines spatial patterns of
pathogen transmission. Yet despite its central role in transmission,
strategies for predicting the epidemiological landscape from real-world
data remain limited. Here, we develop the epidemiological landscape as
an interface between movement ecology and spatial epidemiology. We
propose a movement-pathogen pace-of-life heuristic for prioritizing the
landscape's central processes by positing that spatial dynamics for fast
pace-of-life pathogens are best-approximated by the spatial ecology of
host contacts; spatial dynamics for slower pace-of-life pathogens are
best approximated by host densities; and spatial dynamics for pathogens
with environmental reservoirs reflect a convolution of those densities
with the spatial configuration of environmental reservoir sites. We then
identify mechanisms that underpin the epidemiological landscape and
match each mechanism to emerging tools from movement ecology. Finally,
we outline workflows for describing the epidemiological landscape and
using it to predict subsequent patterns of pathogen transmission. Our
framework links transmission to environmental context, providing a
scaffold for mechanistically understanding how environmental context can
generate and shift existing patterns in spatial epidemiology.%
\end{abstract}%



\sloppy


\textbf{Defining an epidemiological landscape by connecting host
movement to pathogen transmission}

\emph{\textbf{Kezia Manlove}, Department of Wildland Resources and
Ecology Center, Utah State University, Logan, UT, 84322, USA.
kezia.manlove@usu.edu}

\emph{\textbf{Mark Wilber}, Department of Forestry, Wildlife, and
Fisheries, University of Tennessee Institute of Agriculture, Knoxville,
TN, USA}

\emph{\textbf{Lauren White}, National Socio-Environmental Synthesis
Center, University of Maryland, Annapolis, MD, USA}

\emph{\textbf{Guillaume Bastille-Rousseau}, Cooperative Wildlife
Research Laboratory, Southern Illinois University, Carbondale, IL,
62901, USA. https://orcid.org/0000-0001-6799-639X}

\emph{\textbf{Anni Yang}, Department of Fish, Wildlife, and Conservation
Biology, Colorado State University, Fort Collins, Colorado, 80523, USA;
National Wildlife Research Center, United States Department of
Agriculture, Animal and Plant Health Inspection Service, Wildlife
Services, National Wildlife Research Center, 4101 Laporte Avenue, Fort
Collins, Colorado, 80521 USA; Department of Geography and Environmental
Sustainability, University of Oklahoma, Norman, OK, 73019, USA}

\emph{\textbf{Marie L. J. Gilbertson}, Department of Veterinary
Population Medicine, University of Minnesota, St. Paul, MN, 55108, USA;
Wisconsin Cooperative Wildlife Research Unit, Department of Forest and
Wildlife Ecology, University of Wisconsin--Madison, Madison, WI, USA;
ORCID 0000-0003-2142-0795}

\emph{\textbf{Meggan E. Craft}, Department of Ecology, Evolution, and
Behavior, University of Minnesota, St. Paul, MN, 55108, USA}

\emph{\textbf{Paul C. Cross}, U.S. Geological Survey, Northern Rocky
Mountain Science Center, Bozeman, MT, 59718, USA}

\emph{\textbf{George Wittemyer}, Department of Fish, Wildlife, and
Conservation Biology, Colorado State University, Fort Collins, Colorado,
80523, USA}

\emph{\textbf{Kim M. Pepin}, National Wildlife Research Center, United
States Department of Agriculture, Animal and Plant Health Inspection
Service, Wildlife Services, National Wildlife Research Center, 4101
Laporte Avenue, Fort Collins, Colorado, 80521 USA}

\emph{This draft manuscript is distributed solely for purposes of
scientific peer review. Its content is deliberative and predecisional,
so it must not be disclosed or released by reviewers. Because the
manuscript has not yet been approved for publication by the U.S.
Geological Survey (USGS), it does not represent any official USGS
finding or policy.}

\emph{Running title}

Modeling the epidemiological landscape

\emph{Keywords}

Transmission hotspot, epidemiological landscape, movement-pathogen
pace-of-life hypothesis, spatial disease dynamics, mining-modeling
approach, multipartite networks, movement mechanisms, host contact, host
mobility

\emph{Article type} : Perspective

\emph{Words in abstract} : 199

\emph{Words in main text} (excluding abstract, acknowledgements,
references, table and figure legends)

7101 (+398 in Box 1) = 7499

\emph{Words in each text box} : Box 1 = 398 words

\emph{Number of references} : 184

\emph{Number of figures, tables, and text boxes}\textbf{:} 6

\emph{Corresponding author}

Kezia R. Manlove, 1595 N 1600 E Logan, UT, 84341, +1 (406) 600-2369,
kezia.manlove@usu.edu

\emph{Statement of authorship} \textbf{}

All authors contributed to manuscript conceptualization. The framework
was developed through a series of discussions among all coauthors. KRM
built all figures and drafted the text. All authors contributed
substantially across multiple rounds of manuscript revision.

\emph{Data accessibility statement}

This paper contains no data.

\par\null

\textbf{Abstract}

Environment drives the host movements that shape pathogen transmission
through three mediating processes: host density, host mobility, and
contact. These processes combine with pathogen life-history to give rise
to an ``epidemiological landscape'' that determines spatial patterns of
pathogen transmission. Yet despite its central role in transmission,
strategies for predicting the epidemiological landscape from real-world
data remain limited. Here, we develop the epidemiological landscape as
an interface between movement ecology and spatial epidemiology. We
propose a movement-pathogen pace-of-life heuristic for prioritizing the
landscape's central processes by positing that spatial dynamics for fast
pace-of-life pathogens are best-approximated by the spatial ecology of
host contacts; spatial dynamics for slower pace-of-life pathogens are
best approximated by host densities; and spatial dynamics for pathogens
with environmental reservoirs reflect a convolution of those densities
with the spatial configuration of environmental reservoir sites. We then
identify mechanisms that underpin the epidemiological landscape and
match each mechanism to emerging tools from movement ecology. Finally,
we outline workflows for describing the epidemiological landscape and
using it to predict subsequent patterns of pathogen transmission. Our
framework links transmission to environmental context, providing a
scaffold for mechanistically understanding how the environment can
generate and shift existing patterns in spatial epidemiology.

\textbf{Introduction}

Environment shapes the spatial, temporal, and behavioral structure of
host movements and pathogen persistence, leading transmission to occur
in some locations but not in others. The particular role the environment
plays depends on the movement ecology of the host and pathogen: wildlife
hosts can shed pathogens as they track resources across the landscape;
livestock pathogens can jump abruptly between habitat patches as hosts
are transported from farm to feedlot; and transmission of human
pathogens often shows spatial signatures associated with work,
caregiving, and social engagement. Environment also structures disease
management efforts targeting specific locations that could give rise to
super-spreading events or transmission hotspots, curtail the spread of
invading epidemic ``waves'', or capitalize on predictable fluctuations
in local transmission patterns.

However, despite these strong implicit connections, our understanding of
the environment-movement-transmission interface remains in its infancy.
Although movement ecology offers an array of tools that could help
integrate environment, host movement, and pathogen deposition, the
tools' outputs are somewhat detached from critical aspects of spatial
transmission and some important components of spatial transmission are
largely overlooked. Moreover, it is unclear how to best integrate the
various processes each tool infers for optimal epidemiological
predictions. Quantifying the environment's role in spatial dynamics of
transmission, appropriately combining constituent processes, and
identifying relevant mechanisms will require a stronger integration of
movement ecology into conventional epidemiological frameworks.

There is a reason why movement and disease ecology developed separately
to this point: they are interested in fundamentally different
relationships. Movement ecology usually explores how individuals
interact with their environments (Nathan et al. 2008), whereas disease
ecology focuses on how individuals interact with one another to allow
for pathogen transmission. Scaling individual-environment interactions
up to predict individual-individual interactions is a long-standing
challenge, and one that potentially distracts from other
transmission-related insights that movement ecology has to offer. That
lacuna is symptomatic of a broader interdisciplinary divide: the spatial
modeling community lacks a systematic way to incorporate mechanistic and
empirical insights from movement ecology into spatial models of
transmission while retaining tractability and transportability beyond
the specific system or landscape at hand. This gap impedes our ability
to identify general principles about how the environment -- both the
local habitat and its broader scale landscape structure --- shapes
spatial patterns of pathogen transmission in real-world environments.

Spatial transmission dynamics depend on three central processes: host
density processes that describe where hosts are located across the
landscape, mobility processes that describe when and how hosts move
among sites, and contact processes that describe the frequency, duration
and form of host-host interactions and how those interactions relate to
rates of pathogen transmission. Together, the host density, mobility,
and contact processes combine with pathogen life-history to form an
epidemiological landscape that interacts with the local volume of
infected hosts to determine epidemiological dynamics through space and
time (Fig. 1). Because it does not incorporate the volume of infected
individuals directly, the epidemiological landscape exists apart from
any specific disease event. Instead, it summarizes the potential for
particular spatial transmission patterns to arise in a given environment
on the basis of local host density, mobility, and contact. Identifying
how density, mobility, and contact relate to the environment, however,
is an open challenge that movement ecology can help to address.

Here, we propose a strategy to strengthen the interface between
environment and transmission by focusing explicitly on the mechanisms
and traits surrounding the epidemiological landscape. First, we use the
epidemiological landscape to formalize the mechanistic relations that
underpin transportable models. We then propose an heuristic that we
refer to as the movement-pathogen pace-of-life hypothesis that suggests
how to prioritize the density, mobility, and contact processes according
to important pathogen life history attributes. Next, we identify a set
of critical mechanisms determining the epidemiological landscape's
structure, and match both the epidemiological landscape's central
processes and our proposed mechanisms to metrics and inferential tools
from movement ecology in sections organized around two research
priorities (Fig. 2). The first priority is to infer specific aspects of
pathogen transmission using existing movement ecology tools; the second
is to determine how social context contributes to patterns of density,
mobility, and contact. Finally, we outline three workflows that blend
mechanisms with movement and transmission data to generate
epidemiological forecasts that are transportable across landscapes and
populations (Fig. 3), and end by identifying existing challenges and
open questions.

\textbf{Using the epidemiological landscape to formalize the mechanistic
relationships that underpin transportable models}

Transportable models --- those that accurately predict spatial
transmission patterns in landscapes and contexts apart from where they
were developed --- are both critically necessary and alarmingly absent
at the spatiotemporal resolution necessary for disease management,
especially in animal systems. Transportable models are especially
important for systems where 1) spillover could occur across a huge
geographic range, making boundary controls infeasible; 2) management
actions shift depending on the specifics of the environmental context at
hand; or 3) research is concentrated around particular pseudo-model
systems but results are expected to extend to a wider suite of
host-pathogen combinations.

Generating transportable predictions of spatial transmission is
complicated because spatial disease dynamics rely on traits at two
levels: traits that emerge from fundamental host-environment and
pathogen pace-of-life mechanisms to shape the epidemiological landscape,
and traits that emerge from the epidemiological landscape to influence
spatial dynamics of transmission (Fig. 1). Which movement and
transmission traits matter most depends on the relationship between host
movements and pathogen life history. Spatial transmission traits like
the occurrence of super-spreading events (Lloyd-Smith et al. 2005) or
the pathogen's rate of spatial spread (Hallatschek et al. 2014) vary
across environments, but explicit connections to underlying
environmental attributes are rarely identified in practice. Risk
assessments built from species-averaged life history or social ecology
traits that make predictions at the scale of species ranges (e.g., Han
et al. 2020) provide valuable insights for pathogens with slower paces
of life whose transmission patterns mirror host presence or densities.
Spatially explicit management of pathogens with faster life histories,
however, requires higher-resolution predictions about exactly where
transmission occurs and how far animals move while infected (Manlove et
al. 2019).

When important spatial transmission traits are known, the
epidemiological landscape can be constructed from those attributes
directly through individual-based models that also account for the
pathogen's life history. Unfortunately, appropriate information for
building these models rarely exists in practice. Even when data are
available, their ability to predict patterns in novel environments is
often constrained through limited spatial replication and uncertainty
about what constitutes an appropriate contrast set of transmission
events that could have occurred but did not. In the absence of direct
data describing spatial transmission, the epidemiological landscape must
be predicted from knowledge about fundamental host-environment and
pathogen-environment interactions, how those interactions vary across
environments, and how the resulting variation governs key features of
spatial transmission (Fig. 1).

Most methods that generate spatially explicit forecasts from underlying
environments and animal movements cover only one facet of the
epidemiological landscape, or extend to only a subset of individuals or
times. While individual-based models can account for multiple processes
and all individuals present, their predictions are laden with the
builder's decisions about which processes to include. Even after
predicting the epidemiological landscape, modelers must decide how to
appropriately capture pathogen life-histories that allow transmission to
occur across temporal lags or over longer distances in space.

Regardless of what approach one takes to model the epidemiological
landscape, accurate out-of-sample prediction always depends on a
clear-eyed consideration of appropriate detail, acknowledgement of
functional responses that could hinder predictions outside the measured
context, and a strong understanding of the system's fundamental
mechanistic drivers. Identifying which processes matter most, and
clarifying what factors help determine transportability across
environmental and social contexts are critical first steps.

Prioritizing processes with the movement-pathogen pace-of-life
hypothesis

Specific processes within the epidemiological landscape can dominate
spatial patterns of transmission in particular situations. Which process
dominates should be predictable on the basis of pathogen life history,
providing a way to prioritize environment-movement-transmission
inquiries and management within particular systems. Pathogens sample
space according to their hosts' movements during infection or through
extra-host movements across environmental media. As a consequence, the
locations that a pathogen encounters are driven by the spatial ecology
of its hosts, and by attributes of its own life-history like infectious
period, mode of transmission, and ability to survive outside the host.
Directly transmitted pathogens with short infectious periods and limited
environmental persistence will disproportionately encounter locations
that hosts visit immediately after contact events. That dependence
should become less severe for pathogens with longer infectious periods
or indirect modes of transmission. As a consequence, whether spatial
transmission patterns are best predicted by host density, mobility, or
contact will depend on the pathogen's life history.

We summarize this expectation through an heuristic that we call
the\emph{movement-pathogen pace-of-life hypothesis} . Under this
heuristic, we expect pathogen intensity and spatial transmission risk to
align with host density patterns when the pathogen's infectious period
is long or modes of transmission are indirect; to align with host
movement or contact patterns when the pathogen's infectious period is
short or modes of transmission are direct; and to align with a
convolution of host densities and environmental reservoirs when the
pathogen's environmental persistence varies across environments. It
follows that environmental drivers of density will be good predictors of
transmission in the first case; environmental drivers of contact will be
best in the second case; and densities should be modeled in interaction
with environmental reservoirs in the final case. Mechanistic inquiries
within a given system can be built forward on the basis of that
prioritization.

Mechanisms connecting hosts, pathogens, and environments

Building transportable models requires understanding how the host,
pathogen, and environment interface with one another, and how these
interfaces combine in the context of the pathogen's pace-of-life.
Articulating particular mechanisms that shape these relationships aids
in their direct examination through a conventional movement ecology
lens, but also suggests a set of measured features -- entities like
number of individuals within some neighborhood of a focal animal, or
values describing environmental covariates surrounding a focal location
-- that could inform mining-modeling approaches (Han et al. 2020;
Wijeyakulasuriya et al. 2020) or be built in as marginal constraints for
multipartite networks to predict the epidemiological landscape (Manlove
et al. 2018; Silk et al. 2018).

Some mechanisms are already well-understood. The propensity of hosts to
form mass aggregations (Lloyd-Smith et al. 2005; Cross et al. 2005) and
stable social bonds (Sah et al. 2017) affects the contact process, as
does the pathogen's mode of transmission and environmental persistence
(Table 1). Synchrony of host life-history events can predictably alter
host densities to produce seasonal pulses in transmission following an
influx of new susceptible hosts (Peel et al. 2014). Density, mobility,
and contact can also vary according to feedbacks between the pathogen
and the host, either through physiological or behavioral shifts
generated by the pathogen via direct or indirect routes (Hughes et al.
2011; Weinstein et al. 2018; Stockmaier et al. 2021; Table 1).

In order to expand beyond these mainstays, we compared treatment of host
density, host mobility, and contact in spatial models of transmission
for human and animal systems. Comparing human and animal approaches let
us simultaneously capitalize on the largely top-down human and livestock
research paradigms (which view host movements as arising primarily
through the host's \emph{a priori} knowledge), and the largely bottom-up
animal movement research paradigm (which view host movements as arising
primarily in response to local environmental context; Meekan et al.
2017; Miller et al. 2019).

In most spatial transmission models for humans and livestock pathogens,
locations where individuals interact (e.g., houses, transit centers,
feedlots) are assumed to be discrete and fixed through time (Keeling et
al. 2001; Riley \& Ferguson 2006; Haw et al. 2020). Site-to-site
mobilities depend on intervening distances and local and surrounding
host densities (Viboud et al. 2006; Simini et al. 2012; Tizzoni et al.
2014). Once site-to-site movements occur, transmission-appropriate
contacts are modeled according to local host density (following a
functional form usually based on \emph{a priori} knowledge about mode of
transmission), and infection rates ultimately depend on the probability
of transmission given appropriate contact.

These assumptions reflect aspects of human movement ecology that may not
hold for free-ranging animals. Most humans are central place foragers
(but see, e.g., Bharti et al. 2009), so assigning individuals to fixed
locations and movement patterns has limited ramifications on model
predictions. This permanent-point-residence assumption is reasonable for
some animal systems (e.g., nesting birds, denning wolves), but for
others, residences are better represented as intensity surfaces, and
even those representations may not be stationary through time. Host
densities and site-to-site mobility rates are typically tied to the
abundance, quality, timing, and spatial distribution of resources, along
with the structure of the intervening landscape (Table 1). What
constitutes a ``resource'', however, varies among hosts (for example, in
humans, a critical resource is other humans; Miller et al. 2019), and
knowledge of host ecology is critical for generating accurate
predictions in animal systems. Humans also spend very little time in
random walks (Table 1; Meekan et al. 2017). Instead, their movements are
dominated by directed moves from a starting point to a pre-ordained
destination. Environmental barriers like mountains and rivers rarely
impede these movements (flight offers a similar ability to some animals;
Table 1).

These human attributes occupy one extreme in host movement
decision-making, while movement patterns derived from resource-driven
random walks occupy the other. Most animal movement systems likely fall
somewhere in-between. Perceiving these attributes as continuua and
comparing the relative positions and movement dynamics of various
species along them might inform \emph{a priori} movement expectations
that could streamline spatial transmission expectations and inform
research, especially for understudied hosts.

\par\null

Linking the environment to spatial ecology of individual hosts and
pathogens

Host-environment and pathogen-environment interactions may produce
reasonable predictions of spatial transmission for pathogens with slower
paces of life and indirect modes of transmission\emph{.} Applied
analyses at the environment-movement-transmission interface have already
proven useful in several of these systems (for example, in models of
anthrax or brucellosis; e.g., Turner et al. 2014; Merkle et al. 2018
respectively), and a few extensions could expand their insights even
further.

Biological underpinnings

The first step toward tailoring the epidemiological landscape to a
particular environment is to identify what ``resources'' are most
relevant to the host's movements and link those resources to patterns of
host density and mobility (Hess 1996; White, Forester, \& Craft 2018).
Resource distributions and accompanying habitat selection functions can
provide the density predictions that we expect to dominate spatial
transmission for pathogens with slower paces of life. However, these
predictions may be insufficient for faster-paced pathogens with short
infectious periods or behaviorally-specific transmission routes, whose
transmission is more dependent on spatial patterns of contact and
mobility. In these cases, a more targeted perspective may be necessary.
There are at least four straight-forward pathways to incorporate
additional complexity through mechanistic attributes of movement:
account for variation in host internal state; account for
environmentally-linked pathogen shedding; account for
environmentally-linked persistence; and account for interactions between
host movements and pathogen prevalence.

Movements arise from the interaction of the environment with the
individual's internal state (Nathan et al. 2008). Individual internal
states vary, however, and overlooking that variation (along dimensions
including sex, age, reproductive status, and infection status) can lead
models to miss systematic patterns of inter-individual variation.
Allowing movement estimates to vary according to basic individual
attributes can help clarify signals and tailor movement predictions to
the particular age, sex, reproductive status, or disease composition of
the population at hand.

Transmission is sometimes tied to particular environmental conditions,
through either host choice (e.g., if hosts preferentially engage in
transmitting behaviors like scent marking, or mating in certain
environments; Clontz et al. 2021), or direct environmental stimulation
(e.g., if environmental irritants directly trigger coughs or other forms
of excretion; Tarlo et al. 2016). When transmission is not distributed
uniformly along the host's movement trajectory, spatial transmission
patterns can be decoupled from aggregate patterns of host density or
mobility. Residency times and return rates also inform expectations
about system epidemiology (for example, the ratio of infectious period
to return-to-residence times determines whether epidemics peak
simultaneously across space; Keeling \& Rohani 2002).

Pathogen attributes also shape environmental persistence of some agents,
leading contamination levels and acquisition rates to vary among
environments even if local pathogen deposition rates are the same (Dorak
et al. 2017). Forces like wind, water, or gravity can also allow for
pathogen mobility outside the host in some cases (for example, cholera
can diffuse along currents, Bertuzzo et al. 2010; and anthrax can
diffuse down hills, Van Ness 1971). If environment-specific pathogen
densities or physical connectivities are known, then they can inform
local pathogen acquisition rates in forward simulation exercises
predicting spatial patterns of transmission.

Host movement ecology sometimes interacts with pathogen prevalence to
abruptly shift spatial patterns of transmission. Indirectly transmitted
pathogens can accumulate in areas where hosts concentrate, leading to
contamination levels that reduce long-term local densities (Boal \&
Mannan 1999), or shift fitness landscapes enough to generate
evolutionary consequences on host spatial phenotypes (Shaw et al. 2018).

Existing integrations with movement ecology

Individual-based models regularly incorporate density and mobility
predictions from habitat- or step selection functions, respectively
(e.g., Fortin et al. 2005; Avgar et al. 2016; Dougherty et al. 2018).
Recent advances accounting for habitat in surrounding locations (Potts
et al. 2014, Table 2) and variation in resource availability (Mysterud
\& Ims 1998; Matthiopoulos et al. 2011; Moreau et al. 2011; Muff et al.
2020) are improving how well these models predict density and mobility
in unsampled landscapes. Path segmentation methods that digest GPS
movement trajectories into blocks of fixes with similar step lengths and
turning angles (Table 2; Edelhoff et al. 2016) can differentiate among
some forms of behavior, compare rates of engagement in those behaviors
across host categories, and connect behavior changes to environmental
and social contexts. Behavioral classifiers are improving with new data
from cameras, animal-borne sensors, and other emerging technologies
(Northrup et al. 2019; Table 2), offering new opportunities to link
transmitting behaviors to specific environments. At the same time,
methods describing residency times and return intervals (Pedersen et al.
2011) are able to connect time spent in random vs. directed search to
particular environmental contexts.

Next steps

Integrating higher-resolution environmental drivers into spatial
transmission predictions requires methods that explicitly account for
spatial or temporal lags between pathogen deposition and acquisition
(Fig. 1). While methods exist to model individual-individual
associations through movement data, the resulting contact patterns are
often specific to a user-specified definition of ``contact''. Methods
that capture asynchronous contacts offer a framework to examine when and
to what extent the definition of contact fundamentally alters expected
spatial transmission dynamics.

A second task is to link the timescales of movement and movement data to
the timescale of pathogen transmission. For example, dispersal and
transmission kernels can describe the rates of spread of plant and
animal invasions as functions of spatial covariates (e.g., Hefley et al
2017). However, kernels could be constructed from daily, seasonal,
annual, or lifetime movements, and it is not obvious which timescale
should be used for predicting spatial transmission.

Third, existing movement data are sometimes ill-suited to capture
critical aspects of the epidemiological landscape, and constructing new
or expanded datasets is sometimes imperative. Spatial transmission of
pathogens with fast life histories will concentrate around locations of
contact. If those locations are either missed because collared animals
rarely encounter one another or biased due to the particular categories
of hosts bearing collars, then spatial transmission forecasts may be
underinformed or inaccurate. For pathogens that can move through
environmental media outside the host, one could model environmental
correlates of pathogen deposition, persistence and acquisition
separately. For pathogens transmitted through specific behaviors, data
on the spatial ecology of relevant modes of transmission, along with
behavior-specific pathogen deposition rates, distances, and persistence
times (Bourouiba 2021), may strengthen spatial predictions.

Fourth, movement predictions need to be able to update dynamically on
the basis of host infection status. Distinct movement patterns among
infected animals are easier to identify when we can reliably estimate
timing of infection from individual pathogen loads or antibody titers.
Antibody kinetic models (Borremans et al. 2016; Pepin et al. 2017;
Prager et al. 2020), new biomonitoring technology that track
temperature, acceleration, and febrile or respiratory responses (Hetem
et al. 2008; Nathan et al. 2012; Adelman et al. 2014; Ahmed et al. 2016,
Harari et al. 2017a; Harari et al. 2017b), and approaches from spatial
phylodynamics (Biek et al. 2007; Kamath et al. 2016) all offer
opportunities here.

Finally, spatial epidemiology may require some entirely new theory and
methods. For instance, a richer framework for understanding the ecology
of long-distance movements would be helpful, given the outsized role
those movements play in the speed and structure of pathogen invasion
(Hallatschek \& Fisher 2014; Wijeyakulasuriya et al. 2019).

Linking host social ecology to patterns of mobility and contact

Host contacts determine the spatial transmission patterns of directly
transmitted pathogens, especially those with fast life-histories; and
host contacts are driven by social, as well as spatial, factors. Social
forces introduce a new layer of heterogeneity into the epidemiological
landscape, especially if contacts are not randomly distributed across an
animal's movements. Direct contact patterns for most species are likely
much more overdispersed than one would expect if individuals moved
independently and at random due to conspecific attraction. The influence
of social attraction on the epidemiological landscape is not limited to
contact, and social dynamics may also inform patterns of density and
mobility.

Epidemiological interest in social drivers of movement aligns well with
a growing emphasis on social factors in movement ecology as a whole (van
Beest et al. 2014). However, understanding where contacts occur and how
each occurrence interfaces with the physical environment remains
underexplored.

Biological underpinnings

At the population level, the environment can interact with host social
ecology to fundamentally alter host density and mobility processes,
often at annual scales. For example, environmentally-linked birth pulses
can lead to seasonally-elevated densities, and compact breeding seasons
can have important bearing on mobilities, especially among males seeking
mates. Seasonal shifts in density and mobility can induce heterogeneity
in persistence and spreading dynamics of pathogens with faster
life-histories, but their effects will be more limited when pathogen
life histories are slow. Other aspects of socially driven movement like
dispersal may also shift with population-level host densities, though
these shifts may also be tied to overall environmental resource
availability.

Within populations, social factors often push local densities away from
expectations based on individual-environment interactions to generate
spatial clustering. Spatially clustered hosts can produce temporal
pulses in pathogen incidence, especially for pathogens with faster
paces-of-life (Supplementary Text 1), and attributes like group size,
stability, and social configuration are particularly important in
shaping early epidemic progression in those systems (e.g., Cross et al.
2005; Sah et al. 2017; Bansal, Grenfell, \& Meyers 2007; respectively).
Group size and environmental context are often interdependent. Different
habitats may be optimal for groups of different sizes, leading to
different habitat selection by larger groups than by smaller ones. If
habitat selection varies with group size, then transmission events
should concentrate at locations favored by larger groups, especially if
transmission rates vary according to host density.

Group cohesion may also respond to environmental context, with important
consequences on transmission in fast-paced pathogens. Hosts that live in
stable social groups can exhibit contact processes that do not track
with conventional density-dependent expectations, imposing a form of
behaviorally mediated frequency dependence with knock-on effects for
pathogen transmission (e.g., Cross et al. 2013; Manlove et al. 2014).
Environmental correlates of group stability remain relatively
underexplored (with the exceptions of environmentally driven
soundscapes, lines-of-sight, and shared small space use, e.g., McComb et
al. 2000; Strandburg-Peshkin et al. 2013; Pinter-Wolman et al. 2017
respectively). A better general understanding of how the environment
relates to group cohesion and fission-fusion rates would be useful.

At an individual level, the social environment contains its own risks
and resources which compete with environmental factors to shape host
movement decisions. How socially driven movement affects transmission
likely varies across systems, and potential mediating mechanisms could
range from resource availability (Castillo-Contreras et al. 2018;
Podg\selectlanguage{ngerman}órski et al. 2013), to resource dispersion (Brandell et al. 2021),
or seasonal shifts in social aggregation and sexual segregation
(Wasserberg et al. 2009; Oraby et al. 2014). Human disease management
activities can also disrupt the social environment, sometimes generating
unintended consequences (Sokolow et al. 2019) through actions like
culling (Donnelly et al. 2003) or translocation (Aiello et al. 2014).

Healthy animals may respond behaviorally to infected hosts (Croft et al.
2011) if they are cognizant of and responsive to disease presence, and
some pathogens actively manipulate host behaviors to aid in their
transmission (Koella, Sørensen, \& Anderson 1998; Vyas et al. 2007;
Rosatte et al. 2006). Analogs to ``social distancing'' exist in a
variety of non-human animal systems, accompanied by nuances including
responses that vary in proportion to one's own susceptibility and social
distancing exceptions for sick relatives (Stockmaier et al. 2021;
Townsend et al. 2020). Pathogens with severe mortality burdens can also
alter local host densities, shifting the epidemiological landscape
through alterations to any and all density-dependent aspects of movement
and transmission.

Existing integrations with movement ecology

Two arms of ecology -- movement and behavior -- are tackling questions
about how social dynamics interface with patterns of host density,
mobility, and contact. Movement ecologists are extending their
individual-environment framework to account for the presence of other
individuals both \emph{in vivo} (Jesmer et al. 2018) and \emph{in
silico} (Couzin et al. 2005; Couzin et al. 2011). Methods are emerging
that allow spatial and social covariates to interact in common models of
location and mobility (for example, in analyses of density-dependent
habitat selection and its consequences, e.g., Webber \& Vander Wal
20181). At the same time, behavioral ecologists have built out their
methods (which focus on individual-individual interactions and are thus
often most applicable for models of contact) to account for spatial
confounding. This is one motivation, for example, of pre-data
permutation techniques, especially those that rely on group-incidence
matrices (e.g., Farine 20135; Farine 2017). The behavioral emphasis,
however, is often on causal inference about system organizing factors,
not necessarily prediction to novel settings. Methods adjust for, but
often do not explicitly draw inference to, environmental context.

As of now, scaling up from individuals to populations in both the
movement and behavioral domains requires extrapolation across many
upsampled animals. Spatial epidemiologists may benefit from workflows
that focus more directly on group-level data that capture aspects of
fission-fusion dynamics, and describe group compositional changes
through time (e.g., Aureli et al. 2008; Palla et al. 2005; Figure 3).

Next steps

One urgent task for identifying social drivers of movement is to develop
methods that can scale up from a subset of collared individuals to infer
social and spatial dynamics across an entire population. If instruments
are not deployed in proportion to local host densities, then areas with
a higher ratio of collars to animals may be flagged as potential
transmission hubs due to sampling alone. There are statistical methods
for drawing inference from partially-observed contact data (e.g., Cross
et al. 2013; Yang et al. 2021), but higher collar densities may also be
necessary in some settings (Gilbertson, White, \& Craft 2021). Scaling
up from individuals to populations often requires information about
inter-individual attraction, along with auxiliary data on population
densities or group sizes. Collaring studies are often designed to
capture individual-environment, as opposed to individual-individual,
interactions, but different design emphases may be necessary for
questions about transmission (Plowright et al. 2019). Statistical
guidance on how to best structure sampling designs to capture
individual-environment vs. individual-individual interactions would be
helpful.

A second task is to infer how social factors drive movement of
instrumented animals. While it is feasible to include social covariates
(both those describing the state of the focal individual and those
describing the social environment) in standard state-switching or
resource selection models, gathering appropriate social covariate data
can be labor-intensive (Webber \& Vander Wal 2018; Albery et al. 2021).
Co-occurring data on kinship, dominance, and affiliative histories that
inform the stability of social bonds are rare, and concerted efforts to
capture both locational and social covariates would strengthen our basis
for understanding the social-spatial interface.

Bipartite networks can directly connect spatial and social interactions
(Fortuna et al. 2009; Manlove et al. 2018), and a third task is to
explore whether graph-based approaches could help infer spatial patterns
of transmission. Bipartite structures form the basis of the
spatially-embedded social networks that are widely used human
epidemiological modeling (e.g., Balcan et al. 2009; Box 1). These models
connect individuals to one another through shared space use. Individual
association networks and spatial networks can both be built as
projections of the bipartite structure to uncover locations with high
levels of social connectivity.

Continuous-space mechanistic models (flocking dynamics models and their
progeny) that allow spatial and social factors to interact directly also
show potential (e.g., Dong et al. 2019; Buscarino et al. 2014; Levis et
al. 2019). In real-world animal systems, researchers have used ideas
from flocking dynamics to capture spatial and social mechanisms in
individual-based models (IBMs; e.g., White, Forester, and Craft 2018;
Pepin, Golnar, \& Podgórski 2021). Currently, these models are
constrained by limited information on attributes like interindividual
distances that are crucial for appropriate parameterization. Generating
the requisite input parameters poses statistical challenges that are
only beginning to be addressed (Richardson \& Gorochowski 2015; Hooten
et al. 2018; Wilber et al. in review), forming a final important task
for integrating social factors into spatial transmission modeling.

Modern workflows

Predicting the epidemiological landscape and emergent spatial
transmission is a methodologically diverse objective, with approaches
ranging from mechanistic tactics based on fundamental attributes of the
system to more descriptive phenomenological approaches. New methods for
Eulerian data (which capture aspects of space and time but are agnostic
to individual identity) can infer transmission kernels as functions of
the environment (Hefley et al. 2017), potentially expanding the utility
of PDEs, semi-spatial, and metapopulation transmission models through
methods like landscape homogenization (Box 1; Garlick et al. 2011).
Eulerian approaches require data reflecting patterns that change over
both space and time. This makes them especially useful for studying and
predicting novel pathogen spread (especially for pathogens with slower
paces-of-life or important environmental reservoirs), but less-useful
for managing endemic transmission or designing mitigation strategies for
pathogens whose spatial ecologies hinge on patterns of host contact.
Here, we focus instead on workflows for Lagrangian data (which track
location, time, and identity of focal animals, for example through GPS
collars or other animal-borne sensors) that can inform the
metapopulation and individual-based modeling approaches (Box 1)
better-equipped to investigate the spatial dynamics of endemic pathogens
and pathogens with faster paces-of-life.

Conventionally, researchers used Lagrangian data to identify drivers of
spatial transmission by 1) correlating aspects of transmission with
aspects of the environment; 2) building forward from those relationships
to separately investigate key processes underlying spatial epidemiology;
and finally 3) re-integrating process-specific inferences to generate
predictions. Each of these steps has historically been ad hoc, and there
is relatively little systematic guidance about which covariates to
explore, which processes to prioritize, or how to properly integrate
predictions across multiple processes. Errors can arise at each of these
phases, but modern workflows offer new opportunities for reducing their
impacts (Fig. 3).

All workflows begin with a preliminary correlative inquiry relating
pathogen prevalence to environmental attributes (ideally, using existing
datasets that track changes in hypothetically relevant environmental
covariates). A brainstorming phase usually follows, during which
researchers should consider the interplay of movement and pathogen
pace-of-life, along with plausible mechanistic drivers and how they
relate to the epidemiological landscape (Table 1). After this point, the
workflows diverge.

In the mechanistic workflow, researchers then separately model density,
mobility, and contact as functions of the physical environment, using
distinct datasets and methods for each process (Table 2). Ideally,
density should be characterized first and predicted over the spatial
domain so that population fragmentation metrics derived from the density
surface can be included as covariates in models of mobility. Contact,
along with its relationship with both group size and engagement in
transmitting behaviors, often requires distinct data derived from
proximity loggers or direct observations. The epidemiological landscape
can be constructed by predicting densities and subsequent mobilities on
the basis of environmental covariates, and assigning site-specific
transmission rates as functions of local environments and host
densities. Predictions should be validated through pathogen data
whenever possible, though mobility and density models can be validated
using movement data alone where transmission data do not exist. The
strength of the mechanistic workflow lies in its ability to draw causal
inference between emergent movements and underlying drivers, which
should improve resulting model transportability (but see Open
Challenges: Extending outside the measured context below). Its
fundamental weakness is that it is not sharply attuned to the social
ecology of the host, so it may work best in systems where hosts move
independently of one another and do not exhibit tight group formation or
fidelity.

The multipartite network workflow places social and spatial connections
on common footing from the start. This approach requires defining
spatiotemporal cut-offs within which individuals are categorized as
``associating'' on the basis of a time lag defined by the pathogen's
ability to persist in the environment. Individuals are then mapped to
locations where associations occur, and then clustered to delineate
spatial nodes. The individuals and spatial nodes are configured into a
bipartite network (that potentially also tracks timing; Manlove et al.
2018), which can be projected down to generate unipartite individual and
spatial networks. Uncertainty in network connection strengths can be
reduced through application of existing (or cheaply available) spatial
data on group sizes or habitat preferences that inform marginal degree
distributions of both the spatial and the social graphs (Manlove et al.
2018; Cross et al. 2019). Location-specific transmission potentials
could then be linked to environmental covariates and used to predict
hotspots in novel settings. Whether forecasted hotspots actually harbor
more host aggregations can be validated using local movement data, and
whether those aggregations lead to transmission can be validated through
pathogen data when those data exist. The strength of the multipartite
network workflow is its balancing of spatial and social forces. Its
fundamental weaknesses are its dependence on a collaring intensity
high-enough to capture some contact events. Guidance regarding how to
best discretize space and account for spatial autocorrelation is still
emerging.

The final workflow builds from mining-modeling approaches for disease
dynamics (Han et al. 2020). Data mining can be applied to a specific
process within the epidemiological landscape, or to animal movement
trajectories as a whole (Table 2; Fig. 3); we focus on the latter here.
First, potential mechanistic drivers need to be translated into
quantifiable ``features'' that can be measured along individual movement
trajectories. These features (perhaps coupled with pathogen-associated
features like prevalence) are used to train machine learning algorithms
that are validated against a subset of withheld trajectories, and then
used to forecast movements for all individuals. Density, mobility, and
contact do not need to be treated separately here because each can be
derived from the forecasted movement trajectories. Features can reflect
both spatial and social processes (Table 2), and feature importance can
help inform future research to isolate and test specific mechanisms.
Movement forecasts can be adjusted for time lags derived from pathogen
pace-of-life (e.g., Wilber et al. in review) to predict transmission.
The strengths of the mining-modeling workflow are its ability to weight
social and spatial factors in tandem, and its ability to scale up across
individuals or landscapes. Its weaknesses lie in its dependence on
appropriately identified features, its limited insights regarding causal
mechanisms, and its abbreviated track record of application in movement
ecology and spatial epidemiology.

Accurate prediction does not ensure effective intervention if the
system's mechanistic drivers remain unknown. Mechanistically defining
the epidemiological landscape can add insights that purely
phenomenological multipartite network or mining-modeling approaches
cannot. Ideally, the phenomenological workflows could be used in
iteration with mechanistic approaches. For example, one could use ctmm
and outputs from a method for capturing temporally lagged transmission
to predict contacts, and then use mining approaches to link those
inferred contacts to environmental context.

Open challenges

Connecting the epidemiological landscape's central processes

Pathogen transmission depends on many processes, and methods to
integrate these processes and appropriately propagating error remain in
short supply. This issue applies to both the mechanistic and the
network-based workflows, and can encumber some aspects of the
mining-modeling approaches as well. Appropriately integrating processes
should be a major focus for spatial epidemiological theory in the
immediate future.

Identifying an appropriate level of detail

Which biological details to include depends on the resolution of
available data and the effort's specific objectives. Mechanisms should
be included if they are central to the overarching question or alter
relevant predictions. Decisions about which biological details to
include should precede decisions about model construction, since some
approaches cannot capture certain mechanisms (Box 1). The relative
timescales of host movements, environmental fluxes, and pathogen
pace-of-life are also informative. Processes that change slowly relative
to system epidemiology could be treated as constant; but processes that
change quickly enough to affect disease incidence may need to be dynamic
(Supplementary Text 1; Funk et al. 2015).

The temporal resolution of movement data is often under the researcher's
control, though it trades off against device longevity through battery
and memory capacity (Kays et al. 2015). Background knowledge about the
timescales of relevant movements and behaviors can inform the timescale
at which locations are recorded (Benhamou 2014; McClintock et al. 2014).
Since rare, longer-distance moves are critical drivers of pathogen
invasion speed, optimal disease invasion collaring might rely on slower
fix rates and longer lifetimes as well as sampling across sex and age
categories. On the other hand, extracting direct contacts from
continuous time movement models will require much higher-resolution
data, typically with fix rates in excess of one point per hour.

The spatial resolution of movement data is often determined by the
particular technology involved, but researchers often control the
spatial extent over which devices are deployed and thus the range of
environmental covariates and density of collars within particular areas.
Estimating environmental effects will be most efficient when the
predictors vary substantially within the study's spatial domain, but if
direct contacts need to be observed, then collar densities should remain
high in some areas. Ideally, one should know the ratio of collars
deployed to host density across the study. Habitat attributes that are
consistent across the study area can be excluded from local predictions,
but should be considered if the model is used to predict dynamics in
novel contexts.

Finally, strengthening modeling infrastructure to allow for reliable
inference often takes substantial effort (for example, through improved
models of critical environmental covariates, increased performance of
disease diagnostic tests, or refinements to statistical methodologies).
Although this burden may diminish as methods improve, shortcutting
variable development can be costly, and investment in variable
development will nearly always be necessary to some degree.

Extending outside the measured context

While non-linear functional responses between environmental covariates
and the epidemiological landscape's central processes do not preclude
extrapolation, their presence should be considered when predicting in
unsampled environments. Non-linearities are the rule, not the exception,
in animal movement, and are expected from first principles alone (Avgar,
Betini, \& Fryxell 2020). Meta-analyses of how habitat-selection,
step-selection, or other attributes of movement vary across environments
would help to generate baseline expectations about how availability
affects density and movement, especially for hosts of common interest.

Disease feedbacks can also exhibit non-linear functional responses. A
low-density population recovering from disease may exhibit fundamentally
different rates of long-distance movement than nearby populations where
densities are high; and age-specific mortality burdens can influence
social structure, especially if mortalities concentrate among older and
more knowledgeable individuals. The relationship between time since
pathogen deposition and instantaneous rate of transmission may also be
nonlinear (Almberg et al. 2011; Richardson \& Gorochowski 2015). This
continuum remains underexplored (Breban 2013), leaving epidemiologists
with no clear guidance about how to weight the force of infection
arising from different modes of transmission over time.

Finally, predictions can fail in environments containing habitat types
or social contexts that never arose in the training environment. Host
populations with seasonal birth pulses may exhibit different habitat
selection patterns than populations where birth pulses are diffuse, and
habitats that are seasonally abandoned at some latitudes may be occupied
year-round at others. In these cases, researchers may do well to take a
more mechanistic approach to transportable modeling that draws from
first principles of host biology.

\textbf{Conclusion}The interface between movement and disease ecology
offers exciting opportunities to improve spatial models of pathogen
transmission and motivate work on understudied mechanisms shaping animal
movement. Rapid advances and emerging workflows in both movement and
disease ecology provide this interface a strong foundation and numerous
opportunities for synergistic development to the advantage of both
fields. However, shifts in emphasis are still needed to better define
the epidemiological landscape and ultimately improve epidemiological
forecasts and management. The epidemiological landscape, consisting of
host density, mobility, and contact components, provides a conceptual
bridge connecting spatial mechanisms to spatial dynamics of pathogen
transmission and subsequent management. Focused inquiry around the
upstream mechanisms and downstream phenomena surrounding the
epidemiological landscape may reveal novel opportunities for targeted
data collection, application of existing tools from movement ecology,
and development of new methods and theory. We hope that this synthesis
sparks additional discourse that can advance perspectives in spatial
epidemiology and strengthen the bridge between movement and disease
ecology.

Acknowledgements

\selectlanguage{english}\selectlanguage{english}Any use of trade, firm, or product names is for descriptive purposes
only and does not imply endorsement by the U.S. Government.

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Figure legends

\textbf{Figure 1. Conceptual integration of environment, movement, and
pathogen transmission.} (1a) and (1b) Mechanistic drivers link
environmental context to host movements and pathogen life histories,
producing sets of traits that could be inferred via conventional methods
or defined~\emph{a priori} ~to serve as features for machine learning.
(2) Pathogen and host movement traits define an epidemiological
landscape, consisting of host density, mobility, and contact patterns.
These in turn generate patterns in spatial epidemiology, captured
through both spatially explicit dynamic models and spatial transmission
traits. When data on spatial transmission traits exist, they can act as
a basis for assessing the importance of the density, mobility, and
contact processes (red arrows from (3) to (2)). If density, mobility,
and contact (2) are directly measured, they can feed forward into models
of transmission; otherwise they can be inferred or predicted using the
mechanisms and features identified in stages (1a) and (1b).

\textbf{Figure 2. A strategy to improve integration of movement and
disease.} Movement insights for disease ecology can be grouped into two
priority areas --- linking environment to spatial ecology of hosts and
pathogens, and linking host social ecology to patterns of mobility and
contact (A). Modern inferential tools in movement ecology offer
opportunities to relate high-resolution descriptions of an animal's
movements to drivers in both priority areas (C). However, in each case,
the integration of movement insights with epidemiological models hinges
on newly emergent or as-yet-undeveloped methods that connect movement
inference to critical aspects of the epidemiological landscape (B).
Overcoming the gaps will allow for direct prediction of the
epidemiological landscape from base principles of movement, improving
the transportability of predictions in spatial disease dynamics.

\textbf{Figure 3. Hypothetical workflows using the epidemiological
landscape.} Each workflow uses animal movement trajectories to forecast
movements from environmental covariates, adjusts movement forecasts
according to time lags imposed by pathogen life-history, and integrates
with disease models (Box 1) to predict spatiotemporal transmission
dynamics. Auxiliary data can enter the workflows (examples indicated by
steps flagged with dark green arrows), but may limit model
transportability. Many of the methods already exist (checkmarks), though
it is not always clear how they should be connected. Other methods have
been proposed and prototyped, but are as-yet untested on real-word data
(blue triangles). A third group remains strictly hypothetical (red
stars). ''RSF'' = resource selection function; ''SSF'' = step selection
function; ''CTMM'' = continuous time movement model; ''UD'' =
utilization distribution; ''CTMC'' = continuous time Markov chain.
``MoveSTIR'' accounts for temporal lags between pathogen deposition and
acquisition (Wilber et al. in review). Method details are in Table 2.

Boxes

\textbf{Box 1: Spatial models of pathogen transmission}

\emph{Partial Differential Equations} (PDEs) describe the size of the
infected class over continuous space and time. Their\emph{host density}
models are continuous, and often homogeneous (but see Garlick et al.
2011, Hefley et al. 2017). The\emph{mobility} model\textsuperscript{1}
is a spatial diffusion rate and a corresponding functional form.
\emph{Outputs} include existence, structure, and speed of traveling
epidemic waves and spatially explicit times to epidemic peak.
\emph{Assumptions:}animals move according to the kernel, which is often
isotropic and independent of environment; transmission occurs locally.

\emph{Semi-spatial and static network models} allow pairwise
interactions within local neighborhoods. The \emph{host density}model is
implicit, but relies on discrete units with corresponding disease
states. The \emph{mobility} model is defined through pairwise coupling
coefficients between the ``locations'', along with a specified
``neighborhood'' with which each location interacts.\emph{Outputs} are
usually derived from a master equation or simulation.
\emph{Assumptions:} known network structure and disease status; \emph{a
priori} definition of ``neighborhood'' (depending on analytical
approach).

\emph{Metapopulation models} track disease dynamics at physical
locations coupled with one another across space. The \emph{host density}
and \emph{mobility} models mirror those of semi-spatial models, though
locations are now spatially explicit, and mobility can include explicit
functions of geographic distance. \emph{Outputs}include spatial
spreading rate, spatial synchrony among subunits, and individual- and
patch-level reproductive numbers.\emph{Assumptions:} \emph{a priori}
knowledge of system connectivity.

\emph{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. The\emph{host density} model
can be continuous or discrete. The\emph{mobility} model typically allows
an individual's state and environment to interact through a set of
movement rules.\emph{Outputs} range from a simple wave front of disease
spread to each individual's spatiotemporally explicit contribution to
reproductive numbers. \emph{Assumptions:} depend on model specifics.

\emph{Spatially embedded social networks} describe disease dynamics
across multipartite networks whose nodes correspond explicitly to
locations in space. \emph{Inputs} are bipartite networks linking
individuals to locations of different types (households, peer groups,
etc.), The \emph{host density} model is a set of spatial centroids
associated with each group, and \emph{mobility} models can be distance-,
gravity-, or radiation-based. \emph{Outputs}include estimates of
R\textsubscript{0}, total epidemic size, and spatial and temporal
patterns of transmission.\emph{Assumptions:} constant connectivities;
central-place space use patterns.

\textsuperscript{1}The \emph{contact process} is often subsumed into a
constant transmission rate or absorbed into the\emph{mobility model} .

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