Predicting the Ability of Preclinical Diagnosis To Improve Control of Farm-to-Farm Foot-and-Mouth Disease Transmission in Cattle

ABSTRACT Foot-and-mouth disease (FMD) can cause large disruptive epidemics in livestock. Current eradication measures rely on the rapid clinical detection and removal of infected herds. Here, we evaluated the potential for preclinical diagnosis during reactive surveillance to reduce the risk of between-farm transmission. We used data from transmission experiments in cattle where both samples from individual animals, such as blood, probang samples, and saliva and nasal swabs, and herd-level samples, such as air samples, were taken daily during the course of infection. The sensitivity of each of these sample types for the detection of infected cattle during different phases of the early infection period was quantified. The results were incorporated into a mathematical model for FMD, in a cattle herd, to evaluate the impact of the early detection and culling of an infected herd on the infectious output. The latter was expressed as the between-herd reproduction ratio, Rh, where an effective surveillance approach would lead to a reduction in the Rh value to <1. Applying weekly surveillance, clinical inspection alone was found to be ineffective at blocking transmission. This was in contrast to the impact of weekly random sampling (i.e., using saliva swabs) of at least 10 animals per farm or daily air sampling (housed cattle), both of which were shown to reduce the Rh to <1. In conclusion, preclinical detection during outbreaks has the potential to allow earlier culling of infected herds and thereby reduce transmission and aid the control of epidemics.


S1.1 Data
To estimate parameters for foot-and-mouth disease virus (FMDV) in cattle we used data from a series of one-to-one transmission experiments (1). In these experiments uninfected recipient cattle were challenged by exposure (for approximately eight hours) to FMDV-infected donor animals at two, four, six and eight days post infection of the donor.
For each challenge the outcome was recorded, that is whether or not transmission occurred.

S1.2 Bayesian framework
Data from the challenge experiments were used to define an indicator variable (δ ij ) such that δ ij =0 if transmission did not occur following the ith challenge by infected animal j (where the challenge started and stopped at (0) ij  and (1) ij  days post infection, respectively) and δ ij =1 if it did. The probability of transmission following the ith challenge by infected animal j (i.e. δ ij =1) is given by, Here β j (τ) is the infectiousness of animal j at τ days post infection, which is given by, where β 0 is the transmission parameter and E j and I j are the latent and infectious periods for the animal. The latent and incubation periods were assumed to follow a bivariate log normal distribution, that is, are the mean and covariance matrix (on the log scale), respectively. The infectious period was assumed to follow a log normal distribution, g(I), with parameters μ I and σ I .
The likelihood for the challenge data (comprising the challenge outcomes, δ ij , and the times at which clinical signs were first observed for each animal, C j ) can be written as, where  is a vector of model parameters and E={E j } and I={I j } are the latent and infectious periods for each animal, respectively. Because the latent and infectious periods are not directly observed, they were included in the analysis as parameters to be estimated.
The priors for the latent, infectious and incubation period parameters were assumed to follow normal (the μs) or gamma (the σs) distributions such that the expected values for the priors yielded log normal distributions with the same mean and variance as the distributions for the latent, infectious and incubation periods in cattle presented in a meta-analysis of these parameters for FMDV serotype O (2) (see their table III). Specifically, parameters for each prior were: µ E (mean 1.13 and shape parameter 5); σ E (mean 0.54 and shape parameter 3); µ I (mean 1.37 and shape parameter 5); σ I (mean 0.49 and shape parameter 3); µ C (mean 1.65 and shape parameter 5); and σ C (mean 0.47 and shape parameter 3). A Uniform(-1,1) prior was used for the correlation parameter, while an informative exponential prior (with mean 5) was used for the transmission rate (3). All priors were assumed to be independent of one another.
Samples from the joint posterior distribution were generated using an adaptive Metropolis algorithm (4), modified so that the scaling factor was tuned during burn-in to ensure an acceptance rate of between 20% and 40% for more efficient sampling of the target distribution (5). Two chains of 600,000 iterations were run, with the first 100,000 iterations discarded to allow for burn-in of the chain. The chains were then thinned (taking every one hundredth sample) to reduce autocorrelation amongst the samples. Convergence was assessed visually and by examining the Gelman-Rubin statistic using the coda package (6) in R (7).

S1.3 Results
Summary statistics for the marginal posterior densities are presented in Table S1. FIG S1 Effect of sample size on detection and reduction of the herd reproduction ratio (R h ), when sampling is done once a week. Panel 1 shows the results for the baseline scenario and panel 2 shows the scenario with a shorter latent period and longer infectious period (Table 1).
"None" means that no surveillance is carried out and infected farm is not detected (no samples taken). "Clinical" means that farmer will notice and report clinical signs on average  Table 1). The transmission rate and incubation period were kept the same for both scenarios. The shaded area under the red line (daily prevalence of infectious cattle) represent the overall herd infectiousness over time. The area under this curve is proportional to the between herd reproduction ratio ℎ .