14  Chapter 14 — Spatial and Network Spread

Applied Epidemiology in Aquaculture — Part V: Detection & Response

Where this sits — Respond and Anticipate. SRS “lives in neighbourhoods, not just farms.” Controlling a propagated disease means acting at the scale it spreads — across space and through the movement and water-connectivity networks that link sites. This advanced chapter equips both the Respond (where is it going?) and Anticipate (which sites are structurally high-risk?) phases.

14.1 Overview

Chapters 4–13 treated each farm as an island. It isn’t. Disease clusters in space and travels along networks — fish movements, shared water, neighbouring cages — and ignoring that structure under-controls the disease. This chapter maps disease, tests for spatial clustering (Moran’s I, with a nod to scan statistics), and analyses the movement network to find the sites that broker spread. These are exactly the methods behind the author’s SRS work, which showed that about 70% of SRS stays within its own neighbourhood and that removing the most connected farms is among the most effective control strategies.

We use farms_spatial.csv (40 farms with coordinates and SRS mortality) and movements.csv (a site-to-site movement network).

14.2 14.1 Preparation

pacman::p_load(rio, here, tidyverse, igraph)   # sf, spdep for production spatial work
farms <- import(here("data", "farms_spatial.csv"))
mov   <- import(here("data", "movements.csv"))

14.3 14.2 Mapping and spatial clustering

The first step is always a map — plot farms, size or colour by SRS mortality, and look:

ggplot(farms, aes(x, y, size = srs_rate, colour = srs_rate)) +
  geom_point() + scale_colour_viridis_c() +
  labs(size = "SRS %", colour = "SRS %")

Eyeballing is not enough; we test whether high-mortality farms sit near other high-mortality farms. Moran’s I measures spatial autocorrelation, from −1 (perfect dispersion) through 0 (random) to +1 (strong clustering):

# inverse-distance, row-standardised weights; Moran's I in base R
# (spdep::moran.test wraps this with a significance test)
# -> Moran's I = 0.27  (expected under randomness = -0.03)

Moran’s I = 0.27, well above the ~0 expected by chance — SRS mortality is spatially clustered, not scattered. For finer resolution, scan statistics (the smerc/SaTScan family) locate where the clusters are: applied to five years of Caligus monitoring across 784 Chilean farms, this approach found 26 distinct infestation clusters (Lepe-López et al., 2021), and the author’s spatial models put Moran’s I for SRS mortality and antimicrobial use at 0.51–0.57 (Montt et al., in press). Endemic–epidemic (hhh4) models further show that ~70% of SRS is persistence within the same neighbourhood, with cross-neighbourhood spread almost entirely between farms under 5 km apart.

14.4 14.3 Movement and connectivity networks

Disease also travels along networks — live-fish movements, well-boat routes, shared management. Represent sites as nodes and movements as edges, then measure each site’s role:

g <- graph_from_data_frame(mov, directed = TRUE)
degree(g)       |> sort(decreasing = TRUE) |> head()   # most-connected sites
betweenness(g)  |> sort(decreasing = TRUE) |> head()   # brokers of spread
components(g)$no                                        # 1 connected component

The network has 40 sites, 113 movements, mean degree 5.7, and forms a single connected component — so an introduction anywhere can, in principle, reach everywhere. Three hub sites (S12, S05, S01) carry far more connections than the rest, and the top betweenness sites (S01, S12, S08) are the brokers — the sites whose removal most fragments the network. This is not abstract: fish movements drove the spread of ISA virus across Chilean salmon farming in 2007–2009 (Mardones et al., 2011, 2013), and hydrodynamic connectivity means farms downstream of an infected site can reach ~100% prevalence within weeks (Bravo et al., 2020).

The payoff is targeted control. Rather than treating all sites equally, simulations of Aysén found that removing about 30% of the most connected farms per neighbourhood — the hubs identified exactly as above — was among the most effective regional strategies (Lam et al., 2025). Network position is risk.

14.5 14.4 Interpretation on the farm

Spatial and network analysis reframes control from the cage to the landscape. For Anticipate, a site’s coordinates and network position predict its structural risk before any fish gets sick — siting and area design (primordial prevention) are spatial decisions. For Respond, the map and the network tell you where an outbreak will go next and which sites to prioritise for fallowing, movement restriction or heightened surveillance. The recurring finding across the author’s work — SRS is a neighbourhood problem — means the most powerful interventions are coordinated across farms, not perfected within one.

14.6 14.5 Exercises

Try it yourself (14.1). Map the farms by SRS rate and compute Moran’s I. Does the value support clustering? What would an I near 0 have meant for your control strategy?

14.2 Build the movement network and list the five highest-degree sites. Explain why a site’s degree matters for its biosecurity priority.

14.3 Compute betweenness and compare the top sites to the top-degree sites. Why might a site with modest degree but high betweenness be especially dangerous?

14.4 The network is a single connected component. What does that imply for the feasibility of eradicating SRS by farm-level action alone, and what does it argue for instead?

14.7 Summary & what’s next

  • Disease is rarely random in space: Moran’s I (0.27 here) tests clustering; scan statistics locate clusters.
  • Movement/connectivity networks reveal hubs (high degree) and brokers (high betweenness) — the sites that drive and could fragment spread.
  • A single connected component means farm-level action alone cannot contain a propagated disease — area-based, coordinated control is required.
  • Spatial/network position is both an Anticipate risk and a Respond target.

In Chapter 15 — PICO, Systematic Review and Meta-analysis we move to Safeguard: framing answerable questions and synthesising all the evidence — the method behind this book’s own case-study papers.

14.8 References & further reading

  • Lepe-López M, …, Álvarez J, Mardones FO. Caligus infection: spatial distribution and scan-statistic clusters. Front Vet Sci. 2021;8:595024.
  • Mardones FO, et al. Fish movements and the spread of ISA virus in Chile, 2007–2009. 2011; and within-farm ISA spread, 2013.
  • Bravo F, et al. Hydrodynamic connectivity and SRS spread. Aquac Environ Interact. 2020;12:263–279.
  • Lam CT, et al. Simulated regional SRS control, including removal of highly connected farms. Prev Vet Med. 2025;243:106595.
  • Montt R, Mardones FO, Reyes P, Rojas H. Spatial clustering of SRS mortality and antimicrobial use. Aquaculture, in press.
  • Stevenson M. Investigation of Spatial Patterns of Animal Disease. 2020. — spatial methods in R.

Files for this chapter: data/farms_spatial.csv, data/movements.csv, and scripts/make_spatial_network.R (new).