2017/02/20 by Vladimir Kozlov, Kozlov, Vladimir, Sonja Radosavljevic +5
Mathematics · Medicine · #47B65 #47N60 #62P10 #Adaptation and Self-Organizing Systems (nlin.AO) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1702.05979
openalex publication_date 2017/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a system of nonlinear partial 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 and characteristic equations for time-independent and periodical models and prove that permanency is defined by the net reproductive rate for the whole system. If the net reproductive rate is less or equal to one, extinction on all patches is imminent. Otherwise, permanency on all patches is guaranteed. The proof is based on a new approach to analysis of large-time stability.