The fundamentals and theoretical concepts of modeling age structured populations.
LE3 .A278 2011
Master of Science
Mathematics and Statistics
Mathematics & Statistics
There are populations of single species that exhibit uctuations and oscillations in their growth such that it is necessary to use structured dynamic models in order to accurately capture such behaviours. Speci cally, we examine age-structured mod- els. In this thesis, two time-continuous, age-structured models are considered of the partial di erential equation and delay di erential equation types as well as a time-continuous, age discrete model in the form of a system of ordinary di erential equations. For each type of age-structured model, common concepts used in demog- raphy are discussed such as Lotka`s r, stable age distribution and reproductive value. These are asymptotic quantities that are formally de ned for linear models. In this work, the relevance of these demographic quantities are further extended to nonlinear models where analogous quantities such as the population`s xed point and the zero growth reproductive value are shown to play important roles in the discussion of the dynamics of nonlinear models.
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