Small-scale pig farmers’ behavior, silent release of African swine fever virus and consequences for disease spread

The expanding distribution of African swine fever (ASF) is threatening the pig industry worldwide. Most outbreaks occur in backyard and small-scale herds, where poor farmers often attempt to limit the disease’s economic consequences by the emergency sale of their pigs. The risk of African swine fever virus (ASFV) release via this emergency sale was investigated. Simulation modeling was used to study ASFV transmission in backyard and small-scale farms as well as the emergency sale of pigs, and the potential impact of improving farmers and traders’ clinical diagnosis ability–its timeliness and/or accuracy–was assessed. The risk of ASFV release was shown to be high, and improving farmers’ clinical diagnosis ability does not appear sufficient to effectively reduce this risk. Estimates obtained also showed that the distribution of herd size within the backyard and small-scale sectors influences the relative contribution of these farms to the risk of release of infected pigs. These findings can inform surveillance and control programs.


Model description
ASFV transmission. A stochastic, individual-based, discrete-time state-transition model was developed to simulate the spread of ASFV through a small-scale pig herd (main document, Fig. 4). All pigs are initially susceptible (S) and are assumed to have equal risk of infection once a first pig is infected with ASFV. An infected pig is first infected but not yet infectious (Exposed, E), and subsequently becomes infectious but not showing clinical signs (Latent, L) and then infectious with clinical signs (C) until it either recovers or dies (DR). The time step used in the model was 1 day.
All animals were considered equally susceptible and there was no immunity to ASFV at the time an infected animal was introduced into the herd. Also, all animals were fully infectious during the infectious period (both latent and clinical states) and developed clinical signs. After developing the disease, pigs could either die or recover and become resistant to reinfection by ASFV during the whole duration of the outbreak. Pigs of a same herd were assumed to mix randomly, and the same transition risks were assumed to apply to all animals in the herd.
The continuous-time analogue of our model of transmission dynamics of ASF within a given pig herd can therefore be expressed by the following equations: where β is the transmission coefficient, f 1 , is the risk of an animal becoming infectious without signs between time t and t+1, f 2 is the risk of an infected animal becoming infectious with signs between time t and t+1 and d is the risk of an animal dying or recovering between time t and t+1.
Because the model operates in discrete time and involves populations of various sizes, the probability that a susceptible pig becomes infected at a given time step was approximated by a Binomial distribution, such as: In this study, we assumed transmission being density-dependent, so that p, the probability of an effective contact between any two pigs in each time step, is given by: where N denotes the herd size. This is to reflect the fact that when the herd size increases, the farm density also increases and so does the probability of contacts between pigs 1 .
The effective contact rate, k, was defined as where D is the duration of the disease and R 0 is the basic reproduction number. R 0 corresponds to the number of secondary infections caused by a single infected individual introduced into a totally susceptible population 2 .
Herd sizes (N) of 5 and 10 pigs were used to represent backyard and traditional small-scale farms, and 30 pigs were used for small-scale semi-commercial farms.
Due to the paucity of information on the transmissibility of ASF, 3 scenarios of R 0 were considered in this study, selected on the basis of estimates for other highly contagious animal diseases. Firstly, the minimum and maximum plausible values for R0 were set using estimates for classical swine fever (CSF), because of its epidemiological similarities with ASF for pig-to-pig transmission. The values of 1.5 and 15 were derived from two studies 3,4 . Secondly, the value of 3 was selected as the most likely R 0 for ASF. This is because a number of studies for CSF, avian influenza or foot-and-mouth disease, other highly transmissible diseases, yielded R 0 around 3 3,5-9 For each infected animal, the transition times from each infectious stage to the next depends on the incubation period, latent period, and duration of disease for ASFV. As pigs are considered to become infectious 1 to 2 days before they become clinically diseased, a Uniform(1,2) distribution was used to represent the time from latency to onset of clinical signs. For both incubation period and duration of disease, Weibull distributions were used because they allow to model time until occurrence of an event when the probability of occurrence changes with time 10 and its distribution is right-skewed. Both incubation period and disease duration were formulated using a constant element (to set the minimum duration of state) and a stochastic one (Weibull(shape, scale)) for determining the duration of the state according to values reported in the literature (see main text, Table 1).
Farmer's behavior and emergency sale of pigs. Factors related to the farmer's reaction in case of ASF outbreak were included in the model. Firstly, the time to detection and sale, T, represents the time taken by farmers to detect clinical signs in affected pigs and cull or sell animals. It is modeled as the time between the day a first animal starts showing clinical signs and the day the farmer proceeds with the emergency sale of his swine herd. Times T of 5 to 35 days represented potential variation in the time taken by farmers to detect clinical signs in affected pigs and proceed with the emergency sale of pigs 11,12 . Secondly, the ability of farmers and/or traders to correctly identify animals with clinical ASF was represented by the sensitivity and specificity of his clinical diagnosis. The sensitivity of the farmer or trader's clinical diagnosis, Se, is the probability that farmers/traders will notice clinical signs in pigs that have declared the disease (i.e. pigs in the infectious clinical stage, C) and send them to slaughter. The specificity of the clinical diagnosis, Sp, is the probability that pigs without ASF clinical disease will be correctly identified as non-ASF clinical cases,. Some pigs may be wrongly identified as clinical cases of ASF (false clinical), either because they show clinical signs due to other diseases or because their (non-sickly) behavior was perceived as a sign of the diseasethe judgment of the farmer or trader being influence by the local context and presence of at least one clinical case on the farm. Animals correctly recognized as non-ASF clinical cases (negative clinical), either susceptible or infected, and clinical pigs in which signs have not been noticed by the farmer or trader (undetected clinical) are sold to traders or on markets (emergency sale) (main document, Fig. 4). Among these animals, the infected and infectious ones will contribute to the further spread of the disease. Se and Sp values of 0.5, 0.75 and 0.9 were used to represent low to high accuracy of the farmer or trader's clinical diagnosis ability. With Se and Sp = 0.5, animals have a 50% chance of being correctly diagnosed as clinical or non-clinical, while for values of 0.9 they have a 90% chance of being correctly diagnosed. Due to the non-specific nature of ASF clinical signs, especially in the early stages of the disease, values closer to 1 were not used.
At time T, each animal of the herd has a Binomial probability of being sent to the abattoir. In the case of clinically infected animals (C), the success probability of the Binomial distribution is equal to Se. For non-clinical animals (S, E and L), this success probability is equal to: 1 -Sp. Animals that are not sent to the abattoir are sold to traders or at markets. Each simulation stops right after the emergency sale is performed. As described in the main text, different scenarios were implemented to assess the effect of the three factors on the effectiveness of the control strategy.

Model outputs
Due to the stochastic nature of the model, simulation was replicated for each scenario and parameters combination until a stable average behavior was reached (n = 1500). All analyses and implementation of the model were conducted in R version 2.14.1 13 .
The risk of release of ASFV from backyard and small-scale farms via the emergency sale of pigs was characterized by the probability that at least one infected animal remained at the end of the simulation and was sold to intermediaries (P(E+L+C)>0). This probability was also called the probability of release of at least one infected animal, or the probability of silent release, and was calculated across the 1,500 simulations run for each scenario.
The proportion of animals in a herd that was infected and released, p inf , was calculated at the end of each simulation for the different scenarios considered: