KPP transition fronts in a one-dimensional two-patch habitat.

This paper is concerned with the existence of transition fronts for a one-dimensional two patch model with KPP reaction terms. Density and flux conditions are imposed at the interface between the two patches. We first construct a pair of suitable super- and sub solutions by making full use of information of the leading edges of two KPP fronts and gluing them through the interface conditions.

Reduction in Obesity-Related Hepatic Fibrosis by SR1664.

Peroxisome-proliferator-activated receptor gamma (PPARγ) is a transcription factor with adipogenic, insulin-sensitizing, and antifibrotic properties. Strong PPARγ activators, such as the thiazolidinediones, can induce unwanted effects such as edema, weight gain, and bone loss, and therefore selective modulators of PPARγ are in development. We previously reported that one selective PPARγ modulator, SR1664, reduced toxin-induced hepatic fibrosis and the activation of hepatic stellate cells (HSCs), the main collagen-producing liver cell in fibrosis.

Adaptation in a heterogeneous environment II: to be three or not to be.

We propose a model to describe the adaptation of a phenotypically structured population in a H-patch environment connected by migration, with each patch associated with a different phenotypic optimum, and we perform a rigorous mathematical analysis of this model. We show that the large-time behaviour of the solution (persistence or extinction) depends on the sign of a principal eigenvalue, [Formula: see text], and we study the dependency of [Formula: see text] with respect to H. This analysis sheds new light on the effect of increasing the number of patches on the persistence of a population, which has implications in agroecology and for understanding zoonoses; in such cases we consider a pathogenic population and the patches correspond to different host species.