Permanence of delayed population model with dispersal loss

Permanence of a dispersal single-species population model where environment is partitioned into several patches is considered. The species not only requires some time to disperse between the patches but also has some possibility to die during its dispersion. The model is described by delay differential equations. The existence of 'super' food-rich patch is proved to be sufficient to ensure partial permanence of the model. It is also shown that partial permanence implies permanence if each food-poor patch is chained to the super food-rich patch. Furthermore, it is proven that partial persistence is ensured if there exist food-rich patches and the dispersion of the species among the patches are small. When the dispersion is large, the partial persistence is realized under relatively small dispersion time.