Modeling Refuge Effect of Submerged Macrophytes in Lake System.

This paper considers a significant problem in biological control of algae issue in ecological environment. A four-dimensional dynamic model is carefully formulated to characterize the interactions among phytoplankton, submerged macrophyte, zooplankton, and general fish class in a lake ecosystem. The predation relationship is modeled by Beddington-DeAngelis functional responses derived from the classical Holling time budget arguments.

Disease dynamics of honeybees with Varroa destructor as parasite and virus vector.

The worldwide decline in honeybee colonies during the past 50 years has often been linked to the spread of the parasitic mite Varroa destructor and its interaction with certain honeybee viruses carried by Varroa mites. In this paper, we propose a honeybee-mite-virus model that incorporates (1) parasitic interactions between honeybees and the Varroa mites; (2) five virus transmission terms between honeybees and mites at different stages of Varroa mites: from honeybees to honeybees, from adult honeybees to the phoretic mites, from brood to the reproductive mites, from the reproductive mites to brood, and from adult honeybees to the phoretic mites; and (3) Allee effects in the honeybee population generated by its internal organization such as division of labor. We provide completed local and global analysis for the full system and its subsystems.