Evaluating growth measures in an immigration process subject to binomial and geometric catastrophes - Jesus R. Artalejo; A. Economou; M.J. Lopez-Herrero (Mathematical Biosciences and Engineering)
Populations are often subject to the effect ofcatastrophic events that cause mass removal. In particular, metapopulationmodels, epidemics, and migratory flows provide practical examples ofpopulations subject to disasters (e.g., habitat destruction, environmentalcatastrophes). Many stochastic models have been developed to explain thebehavior of these populations. Most of the reported results concern themeasures of the risk of extinction and the distribution of the populationsize in the case of total catastrophes where all individuals in thepopulation are removed simultaneously. In this paper, we investigate thebasic immigration process subject to binomial and geometric catastrophes;that is, the population size is reduced according to a binomial or ageometric law. We carry out an extensive analysis including first extinctiontime, 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 someemphasis is put to show that some of them deserve extra attention.