Persistent distribution functions for the dispersion of structured populations |
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Institution: | 2. “Elias” University Emergency Hospital, Bucharest, Romania;3. University Emergency Hospital, Bucharest, Romania |
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Abstract: | This paper primarily expounds upon the problem of persistent age-state distribution functions for the dispersion of structured populations. A general model is introduced, based on the following assumptions: 1) the state of an individual of age a is characterized by a set of random variables X1, X2,…, XQ (weight, size, etc.) obeying a phenomenological master equation; 2) the birth function λ depends on the age a' of parents and on the state variables X1,…, XQ of the newborns; 3) the mortality function is composed of two additive terms—the first contribution depends only on age while the second contribution depends on the total population density; 4) the population diffuses to avoid crowding. These hypotheses define a nonlinear population model for which time- and space-persistent age-state distribution functions eventually may occur even if the total population density is time- and space-dependent. A biological interpretation of the main results is given in terms of the distribution function of the state vector at birth. In the last part of the paper a generalized model is presented, assuming that the behavior of an individual is described by a system of age-dependent master equations 29]. |
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