A stochastic mathematical model of the within-herd transmission dynamics of Porcine Reproductive and Respiratory Syndrome Virus (PRRSV): fade-out and persistence.

A stochastic, mathematical model of a farrow-finish pig herd was developed and used to investigate the within-herd transmission dynamics of PRRSV, and to examine patterns of on-farm persistence and fade-out. The model was structured to represent the management of a typical European pig herd. Three parameters determining the natural history of infection were derived from the literature. Transmission parameters were chosen using PRRSV antibody data from a cross-sectional study of 103 pig herds (Evans et al., 2008). The seroprevalence by age was generated from the model at 21-day intervals and was compared to the cross-sectional field data using log-likelihood, accounting for the accuracy of the ELISA test used. The model was run for various isolation practices of purchased gilts, contact structure, herd size and the frequency of re-introduction of infectious gilts. The time-dependent log-likelihood patterns varied between herds in a similar way to patterns observed from serological values from the 103 farms. Essentially they indicated two patterns of seroprevalence: herds in which PRRSV was stably persistent, and herds in which PRRSV was unstable, either recently introduced or recently faded-out. With a herd size of 327 sows with identical management, fade-out of virus occurred within 4 weeks in 21.9% of simulations. Without isolation of gilts from sows, fade-out within 250 days decreased from 81.6% to 14.3% and for herd sizes of 75, 150, 300 and 600, the probability of persistence of virus for >1200 days was 4%, 13.4%, 20.4% and 18.2%, respectively. Introduction of virus at a rate of approximately 0.37 times per year resulted in virus persisting for >1200 days in 32.4% of simulations, compared with 17.6% for no re-introduction. Fade-out of virus was most likely to occur within breeding females before virus reached young stock. Persistence was more likely once PRRSV was present in piglets which in turn infected rearing-pigs. The probability of persistence was higher with increased herd size, increased contact between different age groups and increased re-introduction of infectious gilts. The ability of the model to capture the variability in cross-sectional, age-related serological patterns suggests that the processes of re-introduction, persistence and fade-out of PRRSV play critical roles in PRRSV epidemiology. The potential importance to pig production and transmission of virus between herds is discussed.