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This paper investigates a nonlocal dispersal epidemic model under the multiple nonlocal distributed delays and nonlinear incidence effects. First, the minimal wave speed c ∗ and the basic reproduction number R 0 are defined, which determine the existence of traveling wave solutions. Second, with the help of the upper and lower solutions, Schauder's fixed point theorem, and limiting techniques, the traveling waves satisfying some asymptotic boundary conditions are discussed. Specifically, when ℛ 0 > 1 , for every speed c > c ∗ there exists a traveling wave solution satisfying the boundary conditions, and there is no such traveling wave solution for any 0 < c < c ∗ when ℛ 0 > 1 or c > 0 when ℛ 0 < 1. Finally, we analyze the effects of nonlocal time delay on the minimum wave speed. [ABSTRACT FROM AUTHOR]

Considering the importance of time delay phenomenon in disease transmission and the interdependence of time delay and spatial location, a reaction-diffusion SIR epidemic model with nonlocal time delay (or time-space time delay) is proposed and the travelling wave solutions are discussed. Specifically, we define the basic reproduction number $ \mathcal {R}_0 $ R0 and the critical wave speed $ c^* $ c∗. For every wave speed $ c\geq c^* $ c≥c∗, the existence of travelling wave solutions is studied by using the upper–lower solutions, the fixed-point theorem and some limit techniques when $ \mathcal {R}_0 \gt 1 $ R0>1. The nonexistence of travelling waves when $ \mathcal {R}_0 \gt 1 $ R0>1 for any $ 0 \lt c \lt c^* $ 0c>0 is also proved. Finally, the influence of time-delay on disease propagation, especially the critical wave speed, is discussed through analysis and simulations. [ABSTRACT FROM AUTHOR]

Methoxy poly(ethylene glycol)-block-poly(L-lactide) (MPEG-b-PLLA) has a wide range of applications in pharmaceuticals and biology, and its structure and morphology have been thoroughly studied. In the experiment, we synthesized MPEG-b-PLLA with different block lengths using the principle of ring-opening polymerization by controlling the amount of lactic acid added. The thermodynamic properties of copolymers and the crystallization properties of blends were studied separately. The crystallization kinetics of PDLA/MPEG-b-PLA and PLLA/MPEG-b-PLA composite films were studied using differential scanning calorimetry (DSC). The results indicate that the crystallization kinetics of composite films are closely related to the amount of block addition. The crystallinity of the sample first increases and then decreases with an increase in MPEG-b-PLLA content. These results were also confirmed in polarized optical microscope (POM) and wide-angle X-ray diffraction (WAXD) tests. When 3% MPEG-b-PLLA was added to the PDLA matrix, the blend exhibited the strongest crystallization performance. [ABSTRACT FROM AUTHOR]