Estimation of bacterial growth parameters in a vegetable food with Markov chain Monte Carlo method

The prediction of the growth of microorganisms in foods has become a major concern among researchers in order to improve the standard and quality of certain types of food. Microbial growth models are therefore required to predict bacterial growth in accordance with the defined circumstances and input parameters. Unfortunately, these input parameters are frequently unknown or guessed, therefore they constitute sources of uncertainties for the results obtained with a forward simulation of the model. In the present work, an approximate one-dimensional model has been applied for the growth of Escherichia coli O157:H7 in lettuce in order to predict model input parameters. The solution to the forward model was obtained by solving simultaneous partial differential diffusion equations that accounts for heat and biomass transfer. The source term in the biomass transfer equation was represented as a function of temperature and an inverse approach was applied to estimate the unknown constants involved in the source term, along with the effective diffusivity of biomass based on the simulated measurements. The inverse problem solution was accomplished using Markov Chain Monte Carlo method (MCMC) with Metropolis-Hastings sampling strategy. A good agreement was found between the estimated parameters and the exact values used to generate the simulated measurements.