1,721,474 research outputs found
The Influence of Diseases on Lotka-Volterra Systems
No full textVenturino, Ezio. (1992). The Influence of Diseases on Lotka-Volterra Systems. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/1802
Fare gruppo cambia tutto. Capire l’evoluzione degli ecosistemi con la matematica
No full textUn secolo fa, i primi modelli matematici per popolazioni interagenti che descrivevano le popolazioni di animali consideravano solo le interazioni tra individui isolati. Ma in natura molte specie vivono in gruppo, perché ciò aumenta la loro capacità di difesa e sopravvivenza. Noi studiamo modelli che tengono conto del comportamento collettivo di alcune specie animali, in modo da poter prevedere meglio come si comportano prede, predatori, competitori e specie mutualiste e nell'ottica di comprendere e preservare meglio gli ecosistemi reali
A kinetic theory approach to modeling prey–predator ecosystems with expertise levels: analysis, simulations and stability considerations
No full textHow do predator interference, prey herding and their possible retaliation affect prey-predator coexistence?
Full text linkIn this paper, focusing on individualistic generalist predators and prey living in herds which coexist in a common area, we propose a generalization of a previous model, namely, a two-population system that accounts for the prey response to predator attacks. In particular, we suggest a new prey-predator interaction term with a denominator of the Beddington-DeAngelis form and a function in the numerator that behaves as N for small values of N, and as N^alpha for large values of N, where N denotes the number of prey. We can take the savanna biome as a reference example, concentrating on large herbivores inhabiting it and some predators that feed on them. Only two conditionally stable equilibrium points have emerged from the model analysis: the predator-only equilibrium and the coexistence one. Transcritical bifurcations from the former to the latter type of equilibrium, as well as saddle-node bifurcations of the coexistence equilibrium have been identified numerically by using MATLAB. In addition, the model was found to exhibit bistability. Bistability is studied by using the MATLAB toolbox bSTAB, paying particular attention to the basin stability values. Comparison of coexistence equilibria with other prey-predator models in the literature essentially shows that, in this case, prey thrive in greater numbers and predators in smaller numbers. The population changes due to parameter variations were found to be significantly less pronounced
Mitigating negative effects of EBHSV-infected eastern cottontail invasion in Italy using Z-type control on a four-population system
No full textThe introduction in Italy of eastern cottontails (Sylvilagus floridanus) for hunting purposes has influenced the local predator-prey dynamics of the red foxes (Vulpes vulpes) and native European hares (Lepus europaeus). Although no direct competition seems to occur between the two lagomorphs, the cottontail invasion damages the indigenous hare population. Indeed, the invasive lagomorphs cause hyperpredation of red foxes on native hares and are also carriers of viruses and parasites. This paper focuses on the situation in which EBHSV-infected eastern cottontails are introduced in a region of virus-free European hares. To avoid the extinction of native lagomorphs and to contain the invasive ones, we look at two possible biological control actions using the Z-type control method on a four-population reference system. In particular, we consider an indirect control of the invasive prey acting on predators and a combination of this indirect control with direct control on native prey. The corresponding Z-controlled models are investigated analytically and numerically. In both cases, the Z-type control significantly reduces the number of equilibria and the convergence of the cottontail population to the desired state is ensured. The hare survival, instead, is guaranteed only in the second case. Overall, mathematically speaking, the second Z-type control action seems the best solution. However, in the cases in which the indirect control on cottontails allows the native prey survival, this control may be preferable since it involves only one control function and seems more practicable. In any case, in the choice of control action, ecosystem managers need to consider each specific situation, taking into account various elements from a biological and practical point of view
A Note on an Epidemic Model with Cautionary Response in the Presence of Asymptomatic Individuals
Full text linkWe analyse a simple disease transmission model accounting for demographic features and an illness appearing in two forms, asymptomatic and symptomatic. Its main feature is the epidemic-induced fear of the population, for which contacts are reduced, responding to increasing symptomatic numbers. We find that in the presence of asymptomatic individuals, if the progression rate to symptomatic is high, protection measures may prevent the whole population becoming infected. The results also elucidate the importance of assessing transmission rates as quickly as possible
A PROBABILISTIC PHENOTYPE DYNAMICAL MODEL FOR SYMPATRIC SPECIATION: SOME PROPERTIES AND NUMERICAL RESULTS
No full textSympatric speciation is an important phenomenon in Evolution: A population being able to express two different phenotypes gives rise to a new species without a physical separation from the original population. In this paper, we describe a model that describes the sympatric speciation process using a population dynamics approach. Our aim is to point out some dynamical features that could be observed in a population where a sympatric speciation process is going on. Some interesting stochastic effects are discussed by means of numerical simulations
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
Diseased Social Predators
No full textSocial predators benefit from cooperation in the form of increased hunting success, but may be at higher risk of disease infection due to living in groups. Here, we use mathematical modeling to investigate the impact of disease transmission on the population dynamics benefits provided by group hunting. We consider a predator–prey model with foraging facilitation that can induce strong Allee effects in the predators. We extend this model by an infectious disease spreading horizontally and vertically in the predator population. The model is a system of three nonlinear differential equations. We analyze the equilibrium points and their stability as well as one- and two-parameter bifurcations. Our results show that weakly cooperating predators go unconditionally extinct for highly transmissible diseases. By contrast, if cooperation is strong enough, the social behavior mediates conditional predator persistence. The system is bistable, such that small predator populations are driven extinct by the disease or a lack of prey, and large predator populations survive because of their cooperation even though they would be doomed to extinction in the absence of group hunting. We identify a critical cooperation level that is needed to avoid the possibility of unconditional predator extinction. We also investigate how transmissibility and cooperation affect the stability of predator–prey dynamics. The introduction of parasites may be fatal for small populations of social predators that decline for other reasons. For invasive predators that cooperate strongly, biocontrol by releasing parasites alone may not be sufficient
Prey 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
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