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Models of population dynamics and their applications in genetics. (English) Zbl 1286.92045

Lachowicz, Mirosław (ed.) et al., From genetics to mathematics. Selected papers based on the presentations at the courses and lectures during the school ‘From genetics to mathematics’, Zbązsyń, Poland, October 18–20, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-283-724-0/hbk). Series on Advances in Mathematics for Applied Sciences 79, 103-147 (2009).
Summary: The aim of these lectures is to give a survey of mathematical models and methods of population dynamics. The main subject will be structured models which describe the distribution of population with respect to some parameters such as age, size, maturity or proliferative state of cells. Some models are general, e.g. age-structured model can be applied to human population as well as to a cell population but others will concern specific populations e.g. the population of erythrocytes. We concentrate on models connected with genetics: the Penna model and models describing telomere shortening, distribution of genes in a genome, stochastic gene expression and the cell-cycle.
For the entire collection see [Zbl 1274.92003].

MSC:

92D25 Population dynamics (general)
92B05 General biology and biomathematics
47D06 One-parameter semigroups and linear evolution equations
45K05 Integro-partial differential equations
92D10 Genetics and epigenetics
92D20 Protein sequences, DNA sequences
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