Persistence analysis of the age-structured population model on several patches
2016 (English)In: Proceedings of the 16th International Conference on Mathematical Methods in Science and Engineering, July 4-8, Rota, Cadiz, Spain, Vol. III / [ed] J. Vigo-Aguiar, Universidad de Cádiz , 2016, Vol. 3, 717-727 p.Chapter in book (Refereed)
We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the system in time-independent case and for periodically changing environment. Under the assumption that every patch can be reached from every other patch, directly or through several intermediary patches, and that net reproductive operator has spectral radius larger than one, we prove that population is persistent on all patches. If the spectral radius is less or equal one, extinction on all patches is imminent.
Place, publisher, year, edition, pages
Universidad de Cádiz , 2016. Vol. 3, 717-727 p.
age-structure, persistence, Kermack-McKendrick equation, Lotcka-Volterra equation
Biological Sciences Mathematics
IdentifiersURN: urn:nbn:se:liu:diva-130231ISBN: 9788460860822OAI: oai:DiVA.org:liu-130231DiVA: diva2:949560
Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016
P. Schwerdtfeger (New Zealand), W. Sprößig (Germany), N. Stollenwerk (Portugal), Pino Caballero (Spain), J. Cioslowski (Poland), J. Medina (Spain), I. P. Hamilton (Canada), J. A. Alvarez-Bermejo (Spain)2016-07-212016-07-212016-08-31Bibliographically approved