No abstract

In Europe, the Eastern grey squirrel is an allochthonous species causing severe impacts on the native red squirrel. The invasive species establishes complex relationships with the native one, out-competing it through resource and disease-mediated competition. However, recent research shed light on the potential role of a predator, the pine marten, in reversing the outcome of the competition between squirrels. Here, we investigate this hypothesis developing a one predator-two prey ecoepidemic model, including disease (squirrel poxvirus) transmission. We assess the equilibria of the dynamical system and investigate their sensitivity to ecosystem parameters changes through numerical simulations.Our analysis reveals that the system is more likely to evolve toward points where the red squirrels thrive than toward a disease-and-red-squirrels-free point. Although the disease is likely to remain endemic in the system, the introduction of the pine marten destabilizes previous equilibria, favouring the native squirrel and facilitating wildlife managers in their efforts to protect it. Nevertheless, the complete eradication of grey squirrels could be achieved only for specified values of the predation rates and pine marten carrying capacity. The active management of grey squirrel populations remains therefore necessary to try to eradicate the invader from the system.

We address the issue of point value reconstructions from cell averages in the context of third-order finite volume schemes, focusing in particular on the cells close to the boundaries of the domain. In fact, most techniques in the literature rely on the creation of ghost cells outside the boundary and on some form of extrapolation from the inside that, taking into account the boundary conditions, fills the ghost cells with appropriate values, so that a standard reconstruction can be applied also in the boundary cells. In Naumann et al. (Appl. Math. Comput. 325: 252–270. 10.1016/j.amc.2017.12.041, 2018), motivated by the difficulty of choosing appropriate boundary conditions at the internal nodes of a network, a different technique was explored that avoids the use of ghost cells, but instead employs for the boundary cells a different stencil, biased towards the interior of the domain. In this paper, extending that approach, which does not make use of ghost cells, we propose a more accurate reconstruction for the one-dimensional case and a two-dimensional one for Cartesian grids. In several numerical tests, we compare the novel reconstruction with the standard approach using ghost cells.

We address the issue of point value reconstructions from cell averages in the context of third order finite volume schemes, focusing in particular on the cells close to the boundaries of the domain. In fact, most techniques known in the literature rely on the creation of ghost cells outside the boundary and on some form of extrapolation from the inside that, taking into account the boundary conditions, fills the ghost cells with appropriate values, so that a standard reconstruction can be applied also in boundary cells. In (Naumann, Kolb, Semplice, 2018), motivated by the difficulty of choosing appropriate boundary conditions at the internal nodes of a network, a different technique was explored that avoids the use of ghost cells, but instead employs for the boundary cells a different stencil, biased towards the interior of the domain.In this paper, extending that approach, which does not make use of ghost cells, we propose a more accurate reconstruction for the onedimensional case and a two-dimensional one for Cartesian grids. In several numerical tests we compare the novel reconstruction with the standard approach using ghost cells.