### Abstract

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.

Original language | English |
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Article number | 101 |

Journal | BMC Veterinary Research |

Volume | 10 |

Issue number | 101 |

DOIs | |

Publication status | First published - 2014 |

### Keywords

- Bayesian approach
- Salmonella typhimurium
- Transmission parameters

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## Cite this

Correia-Gomes, C., Economou, T., Bailey, T., Brazdil, P., Alban, L., & Niza-Ribeiro, J. (2014). Transmission parameters estimated for

*Salmonella typhimurium*in swine using susceptible-infectious-resistant models and a Bayesian approach.*BMC Veterinary Research*,*10*(101), [101]. https://doi.org/10.1186/1746-6148-10-101