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Talk Abstract
On Fitness in Structured Metapopulation Models with an Application to Epidemics

Mats Gyllenberg
Member of the Research Council for Natural Sciences and Technology
Academy of Finland

Department of Mathematics
University of Turku

Fitness is usually defined as the long term exponential growth rate r(E) of a phenotype in a given environment E. In adaptive dynamics this concept of fitness is used for instance to determine a criterion for successful invasion of a rare mutant: Invasion will take place if and only if the fitness of the mutant in the environment set by the resident is positive. If we try to adapt this notion of fitness to metapopulations consisting of local populations in different habitat patches we encounter several difficulties. One is that even if the overall environment defined by the equilibrium metapopulation state is constant, the mutant experiences different conditions in different patches and moreover, these conditions change within a patch as the local resident population grows. It is therefore far from obvious how to define fitness in a metapopulation.

In this talk I shall present a mathematical definition of fitness which applies to a large class of structured metapopulation models. Because infectious diseases can be modelled as metapopulations with the hosts playing the role of patches, the results can be applied to calculating R0 for epidemic models. In addition, the dynamics of infectious diseases in a metapopulation can be treated within this framework.

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  1998-1999 Mathematics in Biology