1,721,006 research outputs found
MODELING A REHAB–RECOVERY–RELAPSE CYCLE WITH COMMUNITY DEPENDENCE VIA ODES
No full textIn this paper, we introduce a rehab-recovery-relapse cycle model to study the interaction between healthy individuals, individuals that might develop substance use disorders (SUD), which for simplicity here we will call susceptible individuals, individuals with SUD, and individuals recovered in a rehab community. We measure the community's health through a system defined by four non-linear ordinary differential equations in which we include a rehab community. After computing the SUD-free and coexistence equilibrium points, we find the feasibility and stability conditions of an equivalent and reduced system obtained by nondimensionalizing the equations of the original model. We have numerically investigated the importance of the parameter values on the model's outcome via a one- and two-strain parameter analysis. From the numerical results, we observe that an efficient rehab community can be characterized by (i) a high recovery rate (the individuals stay in that community as little time as possible) and (ii) permanent rehabilitation being preferred at the expense of a low recovery rate
Two mathematical models for dissolved oxygen in a lake--CMMSE-16
No full textIn this paper two mathematical models for handling water pollution are introduced. In the first one we assume that algae and fungi are in competition for resources that come from wastewater, while in the second one we introduce explicitly the equation of nutrients. Both algae and fungi need dissolved oxygen (DO) for their biological process of growth. But there is a difference, indeed algae produce it too and in a higher quantity than the one they use. For the first model it is shown that if the coexistence equilibrium exists, it is stable without additional conditions. If the competition rate between algae and fungi is not high for a chosen set of parameters the stability of the coexistence equilibrium is reached even without an external constant input of DO in the system. For the second model we have found the matching equilibrium points with the ones of the first model, furthermore other two equilibria are found
The Beddington-De Angelis and the HTII product response functions: Application to polluted ecosystems biodegradation
No full textIn this paper we consider an aquatic ecosystem consisting of bacteria, organic pollutants and dissolved oxygen. By formulating two suitable mathematical models for their interactions, we investigate the sustainability in time of this ecosystem
Stopping waves: geometric analysis of coupled bursters in an asymmetric excitation field
No full textBursting is a type of electrical activity seen in many neurons and endocrine cells where episodes of action potential firing are interspersed by silent phases. Here, we investigate partial synchrony and wave propagation in a population of square-wave bursters. In particular, by using a prototypical polynomial bursting model and slow/fast bifurcation analysis, we study why electrically coupled model bursters typically synchronize very easily, as reflected in the tendency for simulated excitation waves to propagate far into the region of silent cells when an excitation gradient is imposed. Such simulation is inspired by, but does not reproduce, experimentally observed Ca2+ waves in pancreatic islets exposed to a glucose gradient. Our analyses indicate a possible modification of the model so that the excitation waves stop at the border between active and silent cells. We verify this property by simulations using such a modified model for a chain, and for a cubic cluster, of coupled cells. Furthermore, we show how our one- and two-parameter bifurcation analyses allow us to predict where the simulated waves stop, for both the original model and the modified version
A theoretical model of plant species competition: The case of invasive Carpobrotus sp. pl. and native Mediterranean coastal species
No full textPrey herding and predators’ feeding satiation induce multiple stability
No full textIn this paper we study a predator–prey model assuming that the prey population gather together in herd and considering feeding satiation for the predator population as well. After analyzing the equilibrium points of the model, their stability and the existence of bifurcations we show the existence of multistability for three different equilibrium points via numerical simulations. This last analysis is performed using the bSTAB software and its extensions. It allows to compute the basin of stability values and to plot bifurcation diagram surfaces with respect to the model parameters
Shape effects on herd behavior in ecological interacting population models
No full textIn this paper, we introduce several dynamical systems modeling two-populations interactions. The main idea is to assume that the individuals of one of the populations gather together in herds, thus possess a social behavior, while individuals of the second population show a more individualistic attitude. We model the fact that the interaction between the two populations occurs mainly through the perimeter of the herd in a 2D space or through the total surface area for populations that live in a 3D space. This idea has already been explored earlier, but here we even accommodate the model for herds that assume fractal shapes. We account for all types of the populations intermingling: symbiosis, competition and predator-prey interactions. In the cases of obligated mutualism for the individualistic population and of competition, the stable solution attained by the populations is independent of the shape of the herd. (C) 2017 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved
Wastewater bioremediation using white rot fungi: Validation of a dynamical system with real data obtained in laboratory
No full textNowadays, wastewater treatment has become an important issue in view of the ever increasing worldwide paucity of abundant and clean water supplies. In this work, we propose a mathematical model describing the process of decolorization of textile industry wastewater and validate it using data from a laboratory experiment. To this aim, a selected white rot fungus, capable of degrading a wide range of recalcitrant compounds, is used against Remazol Brilliant Blue Reactive dye. The real data obtained in laboratory are use to fit the parameters of our model. The qualitative analysis is performed to study the behavior of the wastewater and of the fungus as functions of time. In the present study the, carbon (glucose) has an important role in the system since it can sustain the fungal metabolism and growth. Furthermore a more general mathematical model is studied, considering an open system where there is a constant input and output of pollutant and nutrients respectively
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