1,720,987 research outputs found
Biodegradation of organic pollutants in a water body
No full textIn this paper we introduce a non-linear model for the biodegradation of organic pollutants in a water body. We assume that the pollutants are removed using fungi, that need nutrients and dissolved oxygen to thrive. We show that after an initial phase the process can be rendered entirely self-sustained, even without the constant supply of fungi, thereby becoming economically very much appealing
Eco-epidemiological interactions with predator interference and infection
No full textPredator interference is a form of competition between predator individuals over access to their prey. There is broad empirical evidence for interference to exist in different strengths in various types of ecological communities. At the same time, parasites are increasingly recognized to alter food web structure and dynamics. In order to investigate the eco-epidemiological interplay between interference and infection, we develop and analyze mathematical models of a predator-prey system, where the predators are subject to both interference and infectious disease. In the absence of infection, equilibrium predator density is known to show a non-monotonic response to interference by first increasing and then decreasing with increasing interference levels. We show that predator infection can change this pattern into a monotonically decreasing predator response to interference, provided the transmissibility is large enough and the pathogenicity is moderate such that the impact of disease on host population density prevails over interference effects. This holds for both types of disease transmission studied here, density-dependent and frequency-dependent. For density-dependent transmission, we find that intermediate values of interference can facilitate disease persistence, whereas the disease would disappear for small or large interference levels. By contrast, for frequency-dependent transmission, disease emergence is independent of interference levels. These dynamic interactions may be important for the understanding of potential biocontrol measures and of spread patterns of zoonotic diseases
Interactions obtained from basic mechanistic principles: Prey herds and predators
No full textWe investigate four predator–prey Rosenzweig–MacArthur models in which the prey exhibit herd behaviour and only the individuals on the edge of the herd are subjected to the predators’ attacks. The key concept is the herding index, i.e., the parameter defining the characteristic shape of the herd. We derive the population equations from the individual state transitions using the mechanistic approach and time scale separation method. We consider one predator and one prey species, linear and hyperbolic responses and the occurrence of predators’ intraspecific competition. For all models, we study the equilibria and their stability and we give the bifurcation analysis. We use standard numerical methods and the software Xppaut to obtain the one-parameter and two-parameter bifurcation diagrams
Approximation of basins of attraction for bistable dynamical system for olive disease control
No full textIn this paper the bistability of a mathematical model for the control of an olive tree disease is studied. The basin of stability values were computed for three different pairs of bistable equilibrium points by using the software bSTAB. Moreover an extension of the software functionalities is made, first by approximating the shape of the attractors in three dimensions and second by extending the sensitivity study with respect to some important parameters of the numerical scheme, e.g. hyperparameters, to the two dimensional case. Analogously, the bifurcation diagram of the basin of stability values with respect to one parameter of the model was extended to the two dimensional case where two parameters of the model can vary simultaneously. Finally an approximation of the surfaces of the sensitivity analysis and bifurcation diagrams were made
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
A mathematical modeling approach to assess biological control of an orange tree disease
No full textThe model presented and investigated here describes the interaction between the orange tree and two different microorganisms, the pathogen fungus Guignardia citricarpa and the antagonist Trichoderma harzianum T1A. The pathogen-free point and coexistence are the only possible system's equilibria. The pathogen-free point bifurcates from coexistence when the antagonist strength is sufficiently high, but does not appear to be much dependent on the amount of beneficial fungus employed. This result represents a relevant guideline for the applied ecologist and for the farmers. Sensitivity analysis in suitable parameter spaces is performed numerically
INFLUENCE of ASYMPTOMATIC PEOPLE on MALARIA TRANSMISSION: A MATHEMATICAL MODEL for A LOW-TRANSMISSION AREA CASE
No full textMalaria remains a primary parasitic disease in the tropical world, generating high morbidity and mortality in human populations. Recently, community surveys showed a high proportion of asymptomatic cases, which are characterized by a low parasitemia and a lack of malaria symptoms. Until now, the asymptomatic population is not treated for malaria and thus remains infective for a long time. In this paper, we introduce a four-dimensional mathematical model to study the influence of asymptomatic people on malaria transmission in low-transmission areas, specifically using data from Brazil. The equilibrium points of the system are calculated, and their stability is analyzed. Via numerical simulations, more in-depth analyzes of the space of some crucial parameters on the asymptomatic population are done, such as the per capita recovery rates of symptomatic and asymptomatic people, the ratio of the density of mosquitoes to that of humans, the mortality rate of mosquitoes and the probability of undergoing asymptomatic infection upon an infectious mosquito bite. Our results indicate that the disease-free equilibrium is inside the stability region if asymptomatic people are treated and/or the ratio of the density of mosquitoes to that of humans is decreased and/or the mortality rate of mosquitoes is increased
How political choices shaped Covid connectivity: The Italian case study
No full textThe importance of implementing new methodologies to study the ever-increasing amount of Covid-19 data is apparent. The aftermath analysis of these data could inform us on how specific political decisions influenced the dynamics of the pandemic outbreak. In this paper we use the Italian outbreak as a case study, to study six different Covid indicators collected in twenty Italian regions. We define a new object, the Covidome, to investigate the network of functional Covid interactions between regions. We analyzed the Italian Covidome over the course of 2020, and found that Covid connectivity between regions follows a sharp North-South community gradient. Furthermore, we explored the Covidome dynamics and individuated differences in regional Covid connectivity between the first and second waves of the pandemic. These differences can be associated to the two different lockdown strategies adopted for the first and the second wave from the Italian government. Finally, we explored to what extent Covid connectivity was associated with the Italian geographical network, and found that Central regions were more tied to the structural constraints than Northern or Southern regions in the spread of the virus. We hope that this approach will be useful in gaining new insights on how political choices shaped Covid dynamics across nations
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
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