Dynamic analysis of deterministic and stochastic SEIR models incorporating the Ornstein-Uhlenbeck process.

In this paper, we introduce a Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model and analyze it in both deterministic and stochastic contexts, incorporating the Ornstein-Uhlenbeck process. The model incorporates a nonlinear incidence rate and a saturated treatment response. We establish the basic properties of solutions and conduct a comprehensive stability analysis of the system's equilibria to assess its epidemiological relevance.

Modeling time scale of integration in equilibrium passive sampling.

Passive samplers (PSs) deployed in the field for several months provide a time-averaged measurement of the freely dissolved concentration of pollutants, which is important for assessing ecological exposure and estimating pollutant loads. A comprehensive theoretical modeling assessment of the sampling time scale of integration (TSI) of an equilibrium PS is required to correctly interpret the results. We address this knowledge gap by modeling exchange kinetics of polychlorinated biphenyl congeners in low-density polyethylene (PE) PS based on diffusive transport and first-order kinetics.

Designing Highly Potent Side-Chain Lactam-Bridged Cyclic Competence-Stimulating Peptide-Based Quorum-Sensing Modulators in .

, a Gram-positive bacterium found in the oral microbiome, shows promise as an oral probiotic for preventing dental caries. It exhibits a reverse correlation with , a key caries-causing pathogen, likely due to its production of hydrogen peroxide, a process mediated by quorum sensing (QS). In this work, we set out to develop novel lactam-based cyclic analogues of the competence stimulating peptide (CSP) signal utilized by for QS activation.