The Basic Approach to Age-Structured Population Dynamics
Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modeling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behavior of solutions, and numerical approximation.
With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics.
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The Basic Approach to Age-Structured Population Dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods. Springer Professional. Back to the search result list. Table of Contents Frontmatter Chapter 1. Why Age Structure? An Introduction Abstract.
Mathematical Model of Three Age-Structured Transmission Dynamics of Chikungunya Virus
When modeling population dynamics, the first step is to identify some significant variables that allow the division of the population into homogeneous subgroups in order to describe its dynamics through the interaction of these groups, ruled by mechanisms that depend on those variables. Thus, the dominant chord of this chapter will still be exponential growth resulting from the interplay of fertility and mortality, i.
However, exponential growth will now be modulated, flattened, smashed and bent, due to the underlying age structure. However, even though on the one hand numbers come from measurements, as we have seen in the first chapter, on the other hand our mathematical description in Chap. The model we treated in Chap.
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Obviously, this is not realistic given the many changes that the real world undergoes, ultimately nullifying any predictions from the stable population theory. In fact, a complex combination of factors, independent of the population size, may determine time-specific variations of both mortality and fertility so that we may observe, for example, demographic trends, periodic oscillations or sudden changes in the vital parameters.
In the previous chapters we presented a linear model that can be considered the age-structured version of the so-called Malthus model. Thus, the criticisms of the latter also apply to the former: exponential growth is no more realistic for age-structured models than it is for unstructured ones, unless we just want to follow the growth of the population for a limited time during which the restrictive assumptions that we have made are satisfied. Here we prove an existence and non-existence result for travelling wave solutions.
- Mathematical theory of age-structured population dynamics - Mimmo Iannelli - Google Libros!
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ISBN 13: 9788842702504
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