Ergodic stationary distribution and practical application of a hybrid stochastic cholera transmission model with waning vaccine-induced immunity under nonlinear regime switching

Considering the effect of stochasticity including white noise and colored noise, this paper aims to study a hybrid stochastic cholera epidemic model with waning vaccine-induced immunity and nonlinear telegraph perturbations. First, we derive a critical value ${?}_0^C$ related to the basic reproduction number ${?}_0$ of the deterministic model. The key aim of this paper is to generalize the θ-stochastic criterion method proposed by the recent work (Han et al. in Chaos Solit Fract 140:110238, 2020) to eliminate nonlinear telegraph perturbations. Next, via constructing several θ-stochastic Lyapunov functions and using the generalized method, we further prove that the stochastic model have a unique ergodic stationary distribution under ${?}_0^C>1$. Results show that the prevention and control of cholera epidemic depend on low transmission rate and small telegraph perturbations. Finally, the corresponding numerical simulations are performed to illustrate our analytical results and a practical application on the Somalia cholera outbreak is shown at the end of this paper.     

Kinetics Study of the Thermal Decomposition of Post-consumer Poly(Ethylene Terephthalate) in an Argon Atmosphere

The thermal decomposition of post-consumer samples of a carbonated water bottle made of poly(ethylene terephthalate), PC-PET, was examined by linear temperature programing under an argon atmosphere to determine its mass loss kinetics. A simple kinetic model, called the first order pseudo single-component model, was used. The total weight-loss of each sample assumed to be in two periods, with each period corresponding to a one step decomposition of the PC-PET to volatiles. Three methods for determining the kinetic parameters by thermal gravimetric analysis were examined: differential analysis at a constant heating rate (differential), temperatures of a given conversion at a number of heating rates (isoconversional), and the maximum rate at multiple heating rates (peak temperature). The latter two multiple heating rates methods results were comparable to each other but they were not in agreement with the results from the differential method. The results of the differential method were insensitive to the heating rate and consistent with kinetics data reported in the literature for PET.     

Thermal decomposition of model compound of algal biomass

This contribution investigates thermal decomposition of leucine, as a representative model compound for amino acids in algal biomass. We map out potential energy surface for a wide array of unimolecular and self-condensation reactions operating in the decomposition of leucine. Decarboxylation and dehydration of leucine ensues by eliminating CO₂ and –OH, respectively, from the –COOH group attached to the α-carbon. The molecular channel for deamination involves cleavage of NH₂ from α-carbon of leucine. The activation energies for direct elimination of CO₂, NH₃, and H₂O from a leucine molecule lie within 20.7 kJ/mol of each other. Activation energies for these decomposition pathways reside below the bond dissociation enthalpy of H–C(α) of 323.1 kJ/mol. The decarboxylation, deamination, and dehydration pathways, via radical-prompted pathways, systematically require lower energy barriers, in reference to closed-shell reaction corridors. Detailed computations at the CBS-QB3 level provide the Arrhenius rate parameters for the unimolecular and bimolecular reactions, and standard enthalpies of formation, standard entropies, and heat capacities for all the products and intermediates. A kinetic analysis of gas-phase reactions, within the context of a plug-flow reactor model, accounts qualitatively for the formation of major products observed experimentally in the thermal degradation of the condensed-phase leucine. Among notable N-containing species, the model predicts the prevailing of NH₃ over HCN and HNCO, in addition to corresponding appreciable concentrations of amines, imines, and nitriles. Our detailed kinetic investigation illustrates a negligible contribution of the self-condensation reactions of leucine in the gas phase.