title: Stability and persistence in ODE models for populations with many stages.
abstract: A model of ordinary differential equations is formulated for populations which are structured by many stages. The model is motivated by ticks which are vectors of infectious diseases, but is general enough to apply to many other species. Our analysis identifies a basic reproduction number that acts as a threshold between population extinction and persistence. We establish conditions for the existence and uniqueness of nonzero equilibria and show that their local stability cannot be expected in general. Boundedness of solutions remains an open problem though we give some sufficient conditions.
authors.affiliation: Department of Mathematics and Philosophy, Columbus State University, Columbus, Georgia 31907, United States. fan_guihong@columbusstate.edu.
authors.forename: Guihong
authors.initials: G
authors.lastname: Fan
authors.forename: Yijun
authors.initials: Y
authors.lastname: Lou
authors.forename: Horst R
authors.initials: HR
authors.lastname: Thieme
authors.forename: Jianhong
authors.initials: J
authors.lastname: Wu
mesh_terms: D000818:Animals; D003198:Computer Simulation; D053476:Extinction, Biological; D005716:Game Theory; D008018:Life Cycle Stages / Q000502:physiology*; D008954:Models, Biological; D011158:Population Growth; D011235:Predatory Behavior / Q000502:physiology*; D012098:Reproduction / Q000502:physiology*; D013987:Ticks / Q000502:physiology*