Abstract
We study a mathematical model of immune response by T cells where the regulatory T cells (Treg) inhibit interleukin 2 (IL-2) secretion. We model the suppression of the autoimmune line of T cells after a different line of T cells responded to a pathogen infection. In this paper, we show that if the population of the pathogen responding line of T cells becomes large enough, the competition for IL-2 and the increase in the death rates may lead to a depletion in the concentration of autoimmune T cells. Provided this lasts for a sufficiently long time, the concentration of autoimmune T cells can be brought down to values inside the basin of attraction of the controlled state, and autoimmunity can be suppressed.

Abstract

Abstract
Sensory tests are quality assurance tools commonly used to measure and/or detect the presence of abnormal characteristics perceived through the senses in lots of raw material and final products in many manufacturing and food industries. In this paper two acceptance sampling plans for sensory evaluation are designed, and an illustration of the performance of such plans applied to a real data set is presented.

Abstract

Abstract

Abstract
Experimental incapacity to track microbe-microbe interactions in structures like biofilms, and the complexity inherent to the mathematical modelling of those interactions, raises the need for feasible, alternative modelling approaches. This work proposes an agent-based representation of the diffusion of N-acyl homoserine lactones (AHL) in a multicellular environment formed by Pseudomonas aeruginosa and Candida albicans. Depending on the spatial location, C. albicans cells were variably exposed to AHLs, an observation that might help explain why phenotypic switching of individual cells in biofilms occurred at different time points. The simulation and algebraic results were similar for simpler scenarios, although some statistical differences could be observed (p<0.05). The model was also successfully applied to a more complex scenario representing a small multicellular environment containing C. albicans and P. aeruginosa cells encased in a 3-D matrix. Further development of this model may help create a predictive tool to depict biofilm heterogeneity at the single-cell level.