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A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the problem a...
A model which consists of a predator and two prey species is presented. The prey compete for the same limited resource (food). The predator preys on both prey species but with different severity. We show that the coexistence of all three species is possible in a mean-field approach, whereas from Monte Carlo simulation it follows that the stochastic fluctuations drive one of the prey populations into extinction.
This paper is devoted to the study of a predator-prey model in a patchy environment.
The model represents the interactions between phytoplankton and zooplankton in the water column.
Two patches are considered with respect to light availability: one patch is associated to the
surface layer, the second patch describes the bottom layer. We show that this spatial heterogeneity
may destabilize the predator-prey system, even in oligotrophic system where the nutrient is low
enough to avoid ”paradox-enrichment”...
In this paper, we study the question of existence and uniqueness of entropy solutions for a system of nonlinear partial differential equations with general anisotropic diffusivity and transport effects, supplemented with no-flux boundary conditions, modeling the spread of an epidemic disease through a heterogeneous habitat.
We give a survey of results on global stability for deterministic compartmental epidemiological
models. Using Lyapunov techniques we revisit a classical result, and give a simple proof.
By the same methods we also give a new result on differential susceptibility and infectivity models
with mass action and an arbitrary number of compartments. These models encompass the so-called
differential infectivity and staged progression models. In the two cases we prove that if the basic
reproduction ratio...
We present a unified mathematical approach to epidemiological models with parametric
heterogeneity, i.e., to the models that describe individuals in the population as having
specific parameter (trait) values that vary from one individuals to another. This is a
natural framework to model, e.g., heterogeneity in susceptibility or infectivity of
individuals. We review, along with the necessary theory, the results obtained using the
discussed approach....
Si considera l'equazione stocastica che modellizza la dinamica di popolazioni di due specie di tipo preda-predatore sotto perturbazioni stocastiche. Si dimostrano in primo luogo l'esistenza e l'unicità della soluzione dell'equazione; per questo è essenziale introdurre una funzione ausiliaria con cui si costruiscono soluzioni approssimate. Si dimostra inoltre che, se non sono presenti perturbazioni stocastiche dovute alla stocasticità demografica, ma solo perturbazioni stocastiche rappresentanti...
We discuss stochastic dynamics of finite populations of individuals playing symmetric games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players and the noise level. In the case of two-player games with two symmetric Nash equilibria, when the number of players increases, the population undergoes multiple transitions between its equilibria.
A theorem on estimates of solutions of impulsive parabolic equations by means of solutions of impulsive ordinary differential equations is proved. An application to the population dynamics is given.
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