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.     

Generalized gradient approximation adjusted to transition metals properties: Key roles of exchange and local spin density

Perdew-Burke-Ernzerhof (PBE) and PBE adapted for solids (PBEsol) are exchange-correlation (xc) functionals widely used in density functional theory simulations. Their differences are the exchange, μ, and correlation, β, coefficients, causing PBEsol to lose the Local Spin Density (LSD) response. Here, the μ/β two-dimensional (2D) accuracy landscape is analyzed between PBE and PBEsol xc functional limits for 27 transition metal (TM) bulks, as well as for 81 TM surfaces. Several properties are analyzed, including the shortest interatomic distances, cohesive energies, and bulk moduli for TM bulks, and surface relaxation degree, surface energies, and work functions for TM surfaces. The exploration, comparing the accuracy degree with respect experimental values, reveals that the found xc minimum, called VV, being a PBE variant, represents an improvement of 5% in mean absolute percentage error terms, whereas this improvement reaches ~11% for VVsol, a xc resulting from the restoration of LSD response in PBEsol, and so regarded as its variant.     

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The novel heteronuclear complexes [{cis-PtCl (NH₃)(μ-pyrazine)ZnCl (terpy)}](ClO₄)₂ (Pt-L1-Zn) and [{cis-PtCl (NH₃)(μ-4,4′-bipyridyl)ZnCl (terpy)}](ClO₄)₂ (Pt-L2-Zn) (where terpy = 2,2′:6′,2′′-terpyridine, L1 = pyrazine, L2 = 4,4′-bipyridyl) were synthesized and characterized. The pK_a values were determined, and based on them it was established that the π-acceptor ability of the pyrazine bridging ligand is more affective on lower pK_a values. The kinetic measurements of the substitution reactions with biologically relevant ligands, such as guanosine-5′-monophosphate (5′-GMP), inosine-5′-monophosphate (5′-IMP) and glutathione (GSH), were studied at pH 7.4. The reactions were followed under pseudo-first-order conditions by UV–Vis spectrophotometry. The order of reactivity of the investigated biomolecules for the first reaction is 5′-GMP > 5′-IMP > GSH, while for the second is 5′-IMP > GSH. Pt-L1-Zn complex is more reactive than Pt-L2-Zn. The cytotoxic activity of heteronuclear Pt-L1-Zn and Pt-L2-Zn complexes was determined on human colorectal cancer cell line (HCT-116) and human breast cancer cell line (MDA-MB-231). Both complexes significantly reduced cell viability on tested cell lines and exerted significant cytotoxic effects, with better effect on HCT-116 cells than cisplatin, especially after 72 hr (IC₅₀ < 0.52 μM). The Pt-L2-Zn complex showed higher activity against human breast cancer cells (MDA-MB-231) than cisplatin after 72 hr. The higher reactivity toward DNA constituent and significant cytotoxic activity may be attributed to the different geometry, Lewis acidity of different metal centers, as well as, to choice of bridging ligands.     

An improved generalized predictive control algorithm based on the difference equation CARIMA model for the SISO system with known strong interference

ABSTRACT

The single input single output (SISO) system with known strong interference is widely used in various occasions. Due to its strong interference, the control accuracy is hard to guarantee. To solve this problem, an improved generalized predictive control (IGPC) algorithm is developed. The IGPC firstly builds the difference equation CARIMA (Controlled Auto-Regressive Integrated Moving-Average) model of the SISO system and then treats the system as a two input single output (TISO) system and calculates its predictive vector, then transforms it into a SISO system and uses the TISO system predictive vector to calculate the SISO system control increment. A new parameter called phase coefficient is added to inhibit the control lag. Simulations are performed to make the comparison among the traditional GPC, PID control, velocity synchronization control (VSC), fuzzy adaptive PID control (FAPID), model-based robust PID control (BPID) and the IGPC. Results show that IGPC has best performance compared to the others. Finally, experiments are developed which proved that the IGPC algorithm has a higher accuracy in the SISO system with known strong interference than that of VSC.