Vladimir Kozlov: Permanency of age-structured population models on several temporally variable patches

We consider a mathematical model consisting of nonlinear differential equations that describes an age-structured population inhabiting several temporally varying patches. We prove existence and uniqueness of solution and analyze its large-time behavior in cases when the environment is constant and when it changes periodically. A pivotal assumption is that individuals can disperse and that each patch can be reached from every other patch, directly or through several intermediary patches.

We introduce the net reproductive operator, net reproductive rate and characteristic equations for time-independent and periodical models and show how these objects are connected with the large time behavior of the model. We prove that permanency is defined by the net reproductive rate only. If the net reproductive rate is less or equal to one, extinction on all patches is imminent. Otherwise, permanence on all patches is guaranteed. Some examples will be presented.

This is a joint work with S.Radosavljevic, V.Tkachev and U.Wennergren (Linköping University)