Stochastic models of foot and mouth disease in feral pigs in the Australian semi-arid rangelands.
Abstract
Foot and mouth disease (FMD) is one of the world's most important livestock diseases and pigs Sus scrofa are highly susceptible. In countries with significant feral pig populations, such as Australia, the possibility that FMD may become established in these populations is a cause of considerable concern. Current models of FMD in feral pigs in Australia are based on deterministic population and behavioural parameters. However, the population dynamics of feral pigs in the semi-arid regions of Australia vary stochastically, in concert with the biomass of rainfall-driven pasture. This study explored how stochastic variation in the population dynamics of feral pigs in semi-arid rangelands affected the probability of persistence of an FMD epizootic, and its impact on the density of feral pigs. A stochastic model of feral pig population dynamics, with death rate linked to vegetation and rainfall, was linked to a deterministic model of FMD in feral pigs. Unlike the fully deterministic model, the stochastic model predicted inevitable extinction of the disease. When the transmission coefficient for FMD (β) was set at the mean value of 9 km2 pig-1 day-1, the mean persistence time of the epizootic (in 1000 simulations) was 3338 days, with a maximum persistence time of 8439 days. On average the FMD epizootic reduced the population density of feral pigs, compared with the density of uninfected pig populations, by between 54 and 43% for transmission coefficients (β) equal to the estimated likely mean and minimum values (9.0 km2 pig-1 day-1 and 2.5 km2 pig-1 day-1), respectively. This compares with a suppression of 27% in density for the equivalent deterministic model. Further stochasticity was introduced to the linked population and disease model by making the transmission coefficient β stochastic with values based on radio-telemetry of a population of feral pigs in the semi-arid rangelands over an 18-month period. The addition of a stochastically varying β lowered the mean persistence time of the simulated epizootic to 1037 days in 1000 simulations and reduced the maximum persistence time to 3907 days. Pig density was reduced by 45% compared with uninfected populations. Synthesis and applications. These simulations suggest that any control programme to suppress a FMD outbreak in feral pigs in the semi-arid rangelands of Australia should take account of prevailing environmental conditions when aiming to reduce feral pig populations beneath a threshold density (NT) below which the disease cannot persist. As the NT is higher than for the equivalent deterministic model, the disease may be easier to control than such models suggest.