Spatial characterizations of bacterial dynamics for food safety: Modeling for shared water processing environments
Bacterial dynamics occurring in shared water environments during food processing are typically modeled assuming a homogeneous mixing profile. However, given the tank configurations, and water recirculation and reuse specifications used in many facilities, uniform mixing is not always applicable. Towards this goal, we here developed a novel reaction-diffusion-advection model that captures temporal and spatial variations in the water tanks under dynamic conditions. We utilize the dynamics involved in poultry chilling as an example, as this process features a comprehensive interplay of bacteria, water chemistry and water flow dynamics, as well as determining bacteria levels on carcasses moving into final phases of the food production chain, thus directly influencing public health risk. Well-posedness, existence and uniqueness of positive steady-state solutions with global stability are proved, as well as an estimation of the time scale of convergence to the steady-state solution provided. Simulations are used to verify the analytical results incorporating parameters informed by experimental data from generic, non-pathogenic E. coli, and predictively estimate the time to equilibrium. We show that during a typical 8 h processing shift, the model reaches steady state within 2 h, applying this result to validate model simulations against commercial data. The calibrated model predicts a distribution of E. coli levels on post-chill carcasses with mean and standard deviation of 3.35 {+/-} 0.56 Log10 CFU/carcass, which closely compares to the experimentally observed distribution of 3.55 {+/-} 0.64 Log10 CFU/carcass in an industrial setting. Our results reinforce the key role of space in quantifying essential mechanisms that govern water chemistry and E. coli dynamics during poultry chilling. Our model is an important tool to improve decision making for pathogen control during poultry chilling, as well as a blueprint from which models for processing other commodities like fresh produce and pork can be established.