Synthesis and Application of Specific N2H4 Fluorescent Probes with AIE Effect Based on Pyrazole Structure.

Two fluorescent probes, Y1-2 were synthesized from 2-acetonaphthone, 4-acetylbiphenyl, and phenyl hydrazine by Vilsmeier-Haack reaction and Knoevenagel condensation. Their recognition efficacies for N2H4 were tested by UV-visible absorption spectroscopy and fluorescence emission spectroscopy. The recognition mechanism were studies by density-functional theory calculations, and the effect of pH on N2H4 recognition was also studied. The results showed that the probe Y1-2 has high selectivity and a low detection limit for N2H4, and the recognition of N2H4 can be accomplished at physiological pH. The probes have had obvious aggregation-induced luminescence effect, large Stokes shift, high sensitivity, and can be successfully applied to live cell imaging.

Global stability for a class of HIV virus-to-cell dynamical model with Beddington-DeAngelis functional response and distributed time delay.

A HIV virus-to-cell dynamical model with distributed delay and Beddington-DeAngelis functional response is proposed in this paper. Using the characteristic equations and analytical means, the principle reproduction number R0 on the local stability of infection-free and chronic-infection equilibria is established. Furthermore, by constructing suitable Lyapunov functionals and using LaSalle invariance principle, we show that if R0 ≤ 1 the infection-free equilibrium is globally asymptotically stable, while if R0 > 1 the chronic-infection equilibrium is globally asymptotically stable. Numerical simulations are presented to illustrate the theoretical results. Comparing the effects between discrete and distributed delays on the stability of HIV virus-to-cell dynamical models, we can see that they could be same and different even opposite.

Complex dynamic behavior in a viral model with state feedback control strategies.

With the consideration of mechanism of prevention and control for the spread of viral diseases, in this paper, we propose two novel virus dynamics models where state feedback control strategies are introduced. The first model incorporates the density of infected cells (or free virus) as control threshold value; we analytically show the existence and orbit stability of positive periodic solution. Theoretical results imply that the density of infected cells (or free virus) can be controlled within an adequate level. The other model determines the control strategies by monitoring the density of uninfected cells when it reaches a risk threshold value. We analytically prove the existence and orbit stability of semi-trivial periodic solution, which show that the viral disease dies out. Numerical simulations are carried out to illustrate the main results.

A state dependent pulse control strategy for a SIRS epidemic system.

With the consideration of mechanism of prevention and control for the spread of infectious diseases, we propose, in this paper, a state dependent pulse vaccination and medication control strategy for a SIRS type epidemic dynamic system. The sufficient conditions on the existence and orbital stability of positive order-1 or order-2 periodic solution are presented. Numerical simulations are carried out to illustrate the main results and compare numerically the state dependent vaccination strategy and the fixed time pulse vaccination strategy.