Populations are often subject to the effect of
catastrophic events that cause mass removal. In particular, metapopulation
models, epidemics, and migratory flows provide practical examples of
populations subject to disasters (e.g., habitat destruction, environmental
catastrophes). Many stochastic models have been developed to explain the
behavior of these populations. Most of the reported results concern the
measures of the risk of extinction and the distribution of the population
size in the case of total catastrophes where all individuals in the
population are removed simultaneously. In this paper, we investigate the
basic immigration process subject to binomial and geometric catastrophes;
that is, the population size is reduced according to a binomial or a
geometric law. We carry out an extensive analysis including first extinction
time, number of individuals removed, survival time of a tagged individual,
and maximum population size reached between two consecutive extinctions.
Many explicit expressions are derived for these system descriptors, and some
emphasis is put to show that some of them deserve extra attention.
Citation: Jesus R. Artalejo, A. Economou, M.J. Lopez-Herrero. Evaluating growth measures in an immigration process subject to binomial and geometric catastrophes[J]. Mathematical Biosciences and Engineering, 2007, 4(4): 573-594. doi: 10.3934/mbe.2007.4.573
Abstract
Populations are often subject to the effect of
catastrophic events that cause mass removal. In particular, metapopulation
models, epidemics, and migratory flows provide practical examples of
populations subject to disasters (e.g., habitat destruction, environmental
catastrophes). Many stochastic models have been developed to explain the
behavior of these populations. Most of the reported results concern the
measures of the risk of extinction and the distribution of the population
size in the case of total catastrophes where all individuals in the
population are removed simultaneously. In this paper, we investigate the
basic immigration process subject to binomial and geometric catastrophes;
that is, the population size is reduced according to a binomial or a
geometric law. We carry out an extensive analysis including first extinction
time, number of individuals removed, survival time of a tagged individual,
and maximum population size reached between two consecutive extinctions.
Many explicit expressions are derived for these system descriptors, and some
emphasis is put to show that some of them deserve extra attention.
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