The theory of the principal eigenvalue is established for the eigenvalue problem associated with a linear time-periodic nonlocal dispersal cooperative system with time delay. Then we apply it to a Nicholson's blowflies population model and obtain a threshold type result on its global dynamics.
This series of four talks is based on Dr. J. Coville's paper [Electronic Journal of Differential Equations, 2007, No. 68, 1-23].
These two talks are based on M. Lewis and B. Li's paper [Bulletin of Mathematical Biology, 74(2012), 2383-2402], and M. Fazly, M. Lewis and H. Wang's paper [SIAM J. Appl. Math., 77(2017), 224-246].
These three talks are based on Heesterbeek and Roberts' paper [Mathematical Biosciences, 206(2007), 3-10] and Shuai, Heesterbeek and van den Driessche's paper [J. Math. Biol., 67(2013), 1067-1082].
In this talk, I will report our recent research on the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means different species may have different spreading speeds. We show that the model system admits a single spreading speed, and it coincides with the minimal wave speed of the spatially periodic traveling waves. A set of sufficient conditions for linear determinacy of the spreading speed is also given.