Open Access Research article

Invasion and transmission of Salmonella Kentucky in an adult dairy herd using approximate Bayesian computation

Zhao Lu1*, Rebecca M Mitchell1, Rebecca L Smith1, Jeffrey S Karns2, Jo Ann S van Kessel2, David R Wolfgang3, Ynte H Schukken1 and Yrjo T Grohn1

Author Affiliations

1 Section of Epidemiology, Department of Population Medicine and Diagnostic Sciences, College of Veterinary Medicine, Cornell University, Ithaca, NY 14853, USA

2 Environmental Microbial and Food Safety Laboratory, Agriculture Research Service, USDA, Beltsville, MD 20705, USA

3 Department of Veterinary and Biomedical Sciences, Pennsylvania State University, University Park, PA 16802, USA

For all author emails, please log on.

BMC Veterinary Research 2013, 9:245  doi:10.1186/1746-6148-9-245

Published: 5 December 2013



An outbreak of Salmonella Kentucky followed by a high level of sustained endemic prevalence was recently observed in a US adult dairy herd enrolled in a longitudinal study involving intensive fecal sampling. To understand the invasion ability and transmission dynamics of Salmonella Kentucky in dairy cattle, accurate estimation of the key epidemiological parameters from longitudinal field data is necessary. The approximate Bayesian computation technique was applied for estimating the transmission rate (β), the recovery rate (γ) and shape (n) parameters of the gamma distribution for the infectious (shedding) period, and the basic reproduction ratio (R0), given a susceptible-infectious-recovered-susceptible (SIRS) compartment model with a gamma distribution for the infectious period.


The results report that the mean transmission rate (β) is 0.417 month-1 (median: 0.417, 95% credible interval [0.406, 0.429]), the average infectious period (γ-1) is 7.95 months (median: 7.95, 95% credible interval [7.70, 8.22]), the mean shape parameter (n) of the gamma distribution for the infectious period is 242 (median: 182, 95% credible interval [16, 482]), and the mean basic reproduction ratio (R0) is 2.91 (median: 2.91, 95% credible interval [2.83, 3.00]).


This study shows that Salmonella Kentucky in this herd was of mild infectiousness and had a long infectious period, which together provide an explanation for the observed prevalence pattern after invasion. The transmission rate and the recovery rate parameters are inferred with better accuracy than the shape parameter, therefore these two parameters are more sensitive to the model and the observed data. The estimated shape parameter (n) has large variability with a minimal value greater than one, indicating that the infectious period of Salmonella Kentucky in dairy cattle does not follow the conventionally assumed exponential distribution.

Epidemiological modeling; Approximate Bayesian computation; Transmission dynamics; Salmonella; Dairy cattle