Transmission parameters estimated for Salmonella typhimurium in swine using susceptible-infectious-resistant models and a Bayesian approach

Background: Transmission models can aid understanding of disease dynamics and are useful in testing the efficiency of control measures. The aim of this study was to formulate an appropriate stochastic Susceptible-Infectious-Resistant/ Carrier (SIR) model for Salmonella Typhimurium in pigs and thus estimate the transmission parameters between states. Results: The transmission parameters were estimated using data from a longitudinal study of three Danish farrow-to-finish pig herds known to be infected. A Bayesian model framework was proposed, which comprised Binomial components for the transition from susceptible to infectious and from infectious to carrier; and a Poisson component for carrier to infectious. Cohort random effects were incorporated into these models to allow for unobserved cohort-specific variables as well as unobserved sources of transmission, thus enabling a more realistic estimation of the transmission parameters. In the case of the transition from susceptible to infectious, the cohort random effects were also time varying. The number of infectious pigs not detected by the parallel testing was treated as unknown, and the probability of non-detection was estimated using information about the sensitivity and specificity of the bacteriological and serological tests. The estimate of the transmission rate from susceptible to infectious was 0.33 [0.06, 1.52], from infectious to carrier was 0.18 [0.14, 0.23] and from carrier to infectious was 0.01 [0.0001, 0.04]. The estimate for the basic reproduction ration (R0) was 1.91 [0.78, 5.24]. The probability of non-detection was estimated to be 0.18 [0.12, 0.25]. Conclusions: The proposed framework for stochastic SIR models was successfully implemented to estimate transmission rate parameters for Salmonella Typhimurium in swine field data. R0 was 1.91, implying that there was dissemination of the infection within pigs of the same cohort. There was significant temporal-cohort variability, especially at the susceptible to infectious stage. The model adequately fitted the data, allowing for both observed and unobserved sources of uncertainty (cohort effects, diagnostic test sensitivity), so leading to more reliable estimates of transmission parameters.