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Definition of "population dynamics" |
a variety of models used to describe evolution, growth, kinetics, and dynamics of diverse populations. Population dynamics models may be stochastic or deterministic, discrete or continuous, differential or integral, and cover a number of mathematical tools from ordinary differential and difference equations, through partial differential, integro differential, functional and integral equations to particle systems, cellular automata, neural networks and genetic algorithms. The type of the model depends on the type of population, the objective of modeling, available data, knowledge of phenomena, etc. The most often modeled and analyzed populations include human and animal populations for demographic and epidemiologic purposes, cell populations including cancer, blood, bone marrow, eukaryotic cells, virus, bacteria, fungi, genomes, and biomolecules. Control problems in population dynamics may be formulated in terms of optimal treatment protocols (for example cell-cycle-specific control), vaccination, harvesting strategies, modulation of growth and so on. The simplest models are found by clustering distributed in reality systems into lumped compartments. It leads to compartmental models of population dynamics. Linear models could be obtain under hypotheses of Malthusian (exponential) growth of the population. If, however, such a model is used to describe the evolution of the population under control (for example treatment by drugs, vaccination, harvesting), the model is no longer linear, and the simplest class of control models that could be used is given by bilinear control systems. Since real populations never grow unboundedly, more realistic models are given by nonlinear models with saturation effects. The simplest nonlinear differential models represent logistic, Pearl–Verlhurst, Michaelis–Menton, and Gompertz dynamics. |
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