Spreading speeds and traveling waves in competitive recursion systems.

This paper is concerned with the spreading speeds and traveling wave solutions of discrete time recursion systems, which describe the spatial propagation mode of two competitive invaders. We first establish the existence of traveling wave solutions when the wave speed is larger than a given threshold. Furthermore, we prove that the threshold is the spreading speed of one species while the spreading speed of the other species is distinctly slower compared to the case when the interspecific competition disappears. Our results also show that the interspecific competition does affect the spread of both species so that the eventual population densities at the coexistence domain are lower than the case when the competition vanishes.

Dynamics of an epidemic model with advection and free boundaries.

This paper deals with the propagation dynamics of an epidemic model, which is modeled by a partially degenerate reaction-diffusion-advection system with free boundaries and sigmoidal function. We focus on the effect of small advection on the propagation dynamics of the epidemic disease. At first, the global existence and uniqueness of solution are obtained. And then, the spreading-vanishing dichotomy and the criteria for spreading and vanishing are given. Our results imply that the small advection make the disease spread more difficult.

Invasion entire solutions in a time periodic Lotka-Volterra competition system with diffusion.

This paper is concerned with invasion entire solutions of a monostable time periodic Lotka-Volterra competition-diffusion system. We first give the asymptotic behaviors of time periodic traveling wave solutions at infinity by a dynamical approach coupled with the two-sided Laplace transform. According to these asymptotic behaviors, we then obtain some key estimates which are crucial for the construction of an appropriate pair of sub-super solutions. Finally, using the sub-super solutions method and comparison principle, we establish the existence of invasion entire solutions which behave as two periodic traveling fronts with different speeds propagating from both sides of x-axis. In other words, we formulate a new invasion way of the superior species to the inferior one in a time periodic environment.

[Fabrication of larynx-shape tissue engineered cartilage by means of filling together with wrapping with pedicle myofascial flap].

OBJECTIVE: To explore the method of fabricating larynx-shape tissue engineered cartilage by means of filling together with wrapping with pedicle myofascial flap. METHODS: Serial steps of solution casting, extrusion molding and particulate leaching were used to make larynx-shape [poly (3-hydroxybutyrate-co-3-hydroxyhexanoate), PHBHH] biomaterial models. The chondrocytes were seeded onto PHBHH models to form cell-PHBHH composites for culture in vitro for one week and then to fill and wrap larynx-shape composites with pedicle myofascial flap. After that to implant larynx-shape composites in situ on the back of adult New Zealand white rabbits (experimental groups n = 9). Control groups (n = 3) were the same measure as experimental groups but without chondrocytes on PHBHH models. Finally, morphological observation, HE & special staining and immunohistochemical test were conducted to evaluate the cartilage regeneration and its shape at 6, 8 and 12 weeks following implantation. RESULTS: The PHBHH models appeared to be hollow half-trumpet with edges and corners of larynx-shape and its porosity > 90%. Pedicle myofascial flap using fascia as lining presented rich blood supply and had enough to fill and wrap larynx-shape composites. Tissue engineered larynx-shape cartilage specimens could be harvested at different period. It was demonstrated that the cartilaginous tissue formed in 6 weeks after implantation through histological and immunohistochemical examination and further maturity in 12 weeks and 18 weeks. But no cartilaginous tissue showed without chondrocytes on PHBHH as control groups to implant at the same time. CONCLUSION: It seems that pedicled myofascial flap showed sufficient blood supply and that the filling together with wrapping method with pedicled myofascial flap is appropriate for fabricating larynx-shape tissue engineered cartilage.