Stochastic Modeling of Imperfect Salmonella Vaccines in an Adult Dairy Herd

Zhao Lu, Yrjö T. Gröhn, Rebecca L. Smith, Jeffrey S. Karns, Ernest Hovingh, Ynte H. Schukken

Research output: Contribution to journalArticlepeer-review


Salmonella is a major cause of bacterial foodborne disease. Human salmonellosis results in significant public health concerns and a considerable economic burden. Dairy cattle are recognized as a key source of several Salmonella serovars that are a threat to human health. To lower the risk of Salmonella infection, reduction of Salmonella prevalence in dairy cattle is important. Vaccination as a control measure has been applied for reduction of preharvest Salmonella prevalence on dairy farms. Salmonella vaccines are usually imperfect (i.e., vaccines may provide a partial protection for susceptible animals, reduce the infectiousness and shedding level, shorten the infectious period of infected animals, and/or curb the number of clinical cases), and evaluation of the potential impacts of imperfect Salmonella vaccines at the farm level is valuable to design effective intervention strategies. The objective of this study was to investigate the impact of imperfect Salmonella vaccines on the stochastic transmission dynamics in an adult dairy herd. To this end, we developed a semi-stochastic and individual-based continuous time Markov chain (CTMC) vaccination model with both direct and indirect transmission, and applied the CTMC vaccination model to Salmonella Cerro transmission in an adult dairy herd. Our results show that vaccines shortening the infectious period are most effective in reducing prevalence, and vaccines decreasing host susceptibility are most effective in reducing the outbreak size. Vaccines with multiple moderate efficacies may have the same effectiveness as vaccines with a single high efficacy in reducing prevalence, time to extinction, and outbreak size. Although the environment component has negligible contributions to the prevalence, time to extinction, and outbreak size for Salmonella Cerro in the herd, the relative importance of environment component was not assessed. This study indicates that an effective vaccination program against Salmonella Cerro spread in the herd can be designed with (1) vaccines with a single high efficacy in reducing either the infectious period or susceptibility of the host, or (2) if such single high efficacy vaccines are not available, vaccines with multiple moderate efficacies may be considered instead. These findings are also of general value for designing vaccination program for Salmonella serotypes in livestock.

Original languageEnglish (US)
Pages (from-to)541-565
Number of pages25
JournalBulletin of Mathematical Biology
Issue number3
StatePublished - Mar 2014
Externally publishedYes


  • Dairy cattle
  • Imperfect vaccines
  • Infectious disease
  • Mathematical modeling
  • Salmonella

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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