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Knipl Diana (University College London): Large number of steady states in spatially explicit models

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Thursday, 31. March 2016, 10:00 - 12:00
Abstract. In this talk, we investigate steady states and their stability in two general compartmental patch-models. The first model is applicable to describe the spread of an infectious disease when individuals travel between several different cities. When the locations are isolated the system may admit several steady states, including equilibria with mixed disease free and endemic components. However, many of the fixed points might disappear when mobility of individuals between the patches is incorporated; the usual situation is that only fully endemic steady states and the disease free equilibrium persist with mobility. We provide a mathematical procedure and precisely describe in terms of the local reproduction numbers and the movement network whether a
steady state of the disconnected system continues or ceases to exist for low-volume mobility. Another model for the spatial dispersal of animal populations will also be presented, where we assume that local density dependence  varies between the habitats. It will be illustrated how mobility is capable of rescuing local populations from extinction.
Location : Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged

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