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Vitamin D has been proven to be a strong stimulator of mechanisms associated with the elimination of pathogens. Because of its recognized effectiveness against viral infections, during SARS-CoV-2 infection, the effects of Vitamin D supplementation have been the object of debate. This study aims to contribute to this debate by the means of a qualitative phenomenological mathematical model in which the role of Vitamin D and its interactions with the innate immune system are explicitly considered. We show that Vitamin D influx and degradation can be considered as possible control parameters for the disease evaluation and recovery. By varying Vitamin D influx, three dynamical scenarios have been found with different modalities of recovery from the disease. Inside each scenario, Vitamin D degradation has been related to different degrees of severity in disease development. Interestingly, the emergence of hysteretic phenomenologies when Vitamin D influx is too low can be related to the onset of Long-COVID syndrome, confirming clinical evidence from recent studies on the topic. [ABSTRACT FROM AUTHOR]

A new fractional q-order variation of the RothC model for the dynamics of soil organic carbon is introduced. A computational method based on the discretization of the analytic solution along with the finite-difference technique are suggested and the stability results for the latter are given. The accuracy of the scheme, in terms of the temporal step size h, is confirmed through numerical testing of a constructed analytic solution. The effectiveness of the proposed discrete method is compared with that of the classical discrete RothC model. Results from real-world experiments show that, by adjusting the fractional order q and the multiplier term ζ (t , q) , a better match between simulated and actual data can be achieved compared to the traditional integer-order model. [ABSTRACT FROM AUTHOR]

We propose novel positive numerical integrators for approximating predator-prey models. The schemes are based on suitable symplectic procedures applied to the dynamical system written in terms of the log transformation of the original variables. Even if this approach is not new when dealing with Hamiltonian systems, it is of particular interest in population dynamics since the positivity of the approximation is ensured without any restriction on the temporal step size. When applied to separable M-systems, the resulting schemes are proved to be explicit, positive, Poisson maps. The approach is generalized to predator-prey dynamics which do not exhibit an M-system structure and successively to reaction-diffusion equations describing spatially extended dynamics. A classical polynomial Krylov approximation for the diffusive term joint with the proposed schemes for the reaction, allows us to propose numerical schemes which are explicit when applied to well established ecological models for predator-prey dynamics. Numerical simulations show that the considered approach provides results which outperform the numerical approximations found in recent literature. [ABSTRACT FROM AUTHOR]

Protected areas are experiencing increased levels of human pressure. To enable appropriate conservation action, it is critical to map and monitor changes in the type and extent of land cover/use and habitat classes, which can be related to human pressures over time. Satellite Earth observation (EO) data and techniques offer the opportunity to detect such changes. Yet association with field information and expert interpretation by ecologists is required to interpret, qualify and link these changes to human pressure. There is thus an urgent need to harmonize the technical background of experts in the field of EO data analysis with the terminology of ecologists, protected area management authorities and policy makers in order to provide meaningful, context-specific value-added EO products. This paper builds on the DPSIR framework, providing a terminology to relate the concepts of state, pressures, and drivers with the application of EO analysis. The type of pressure can be inferred through the detection of changes in state (i.e. changes in land cover and/or habitat type and/or condition). Four broad categories of changes in state are identified, i.e. land cover/habitat conversion, land cover/habitat modification, habitat fragmentation and changes in landscape connectivity, and changes in plant community structure. These categories of change in state can be mapped through EO analyses, with the goal of using expert judgement to relate changes in state to causal direct anthropogenic pressures. Drawing on expert knowledge, a set of protected areas located in diverse socio-ecological contexts and subject to a variety of pressures are analysed to (a) link the four categories of changes in state of land cover/habitats to the drivers (anthropogenic pressure), as relevant to specific target land cover and habitat classes; (b) identify (for pressure mapping) the most appropriate spatial and temporal EO data sources as well as interpretations from ecologists and field data useful in connection with EO data analysis. We provide detailed examples for two protected areas, demonstrating the use of EO data for detection of land cover/habitat change, coupled with expert interpretation to relate such change to specific anthropogenic pressures. We conclude with a discussion of the limitations and feasibility of using EO data and techniques to identify anthropogenic pressures, suggesting additional research efforts required in this direction. [ABSTRACT FROM AUTHOR]

Abstract: We consider explicit symplectic partitioned Runge–Kutta (ESPRK) methods for the numerical integration of non-autonomous dynamical systems. It is known that, in general, the accuracy of a numerical method can diminish considerably whenever an explicit time dependence enters the differential equations and the order reduction can depend on the way the time is treated. In the present paper, we demonstrate that explicit symplectic partitioned Runge–Kutta–Nyström (ESPRKN) methods specifically designed for second order differential equations , undergo an order reduction when , independently of the way the time is approximated. Furthermore, by means of symmetric quadrature formulae of appropriate order, we propose a different but still equivalent formulation of the original non-autonomous problem that treats the time as two added coordinates of an enlarged differential system. In so doing, the order reduction is avoided as confirmed by the presented numerical tests. [Copyright &y& Elsevier]

Abstract: Most physical phenomena are described by time-dependent Hamiltonian systems with qualitative features that should be preserved by numerical integrators used for approximating their dynamics. The initial energy of the system together with the energy added or subtracted by the outside forces, represent a conserved quantity of the motion. For a class of time-dependent Hamiltonian systems this invariant can be defined by means of an auxiliary function whose dynamics has to be integrated simultaneously with the system’s equations. We propose splitting procedures featured by a SB 3 A property that allows to construct composition methods with a reduced number of determining order equations and to provide the same high accuracy for both the dynamics and the preservation of the invariant quantity. [Copyright &y& Elsevier]

Soil Organic Carbon (SOC) is one of the key indicators of land degradation. SOC positively affects soil functions with regard to habitats, biological diversity and soil fertility; therefore, a reduction in the SOC stock of soil results in degradation, and it may also have potential negative effects on soil-derived ecosystem services. Dynamical models, such as the Rothamsted Carbon (RothC) model, may predict the long-term behaviour of soil carbon content and may suggest optimal land use patterns suitable for the achievement of land degradation neutrality as measured in terms of the SOC indicator. In this paper, we compared continuous and discrete versions of the RothC model, especially to achieve long-term solutions. The original discrete formulation of the RothC model was then compared with a novel non-standard integrator that represents an alternative to the exponential Rosenbrock–Euler approach in the literature. [ABSTRACT FROM AUTHOR]

A major neglected weakness of many ecological models is the numerical method used to solve the governing systems of differential equations. Indeed, the discrete dynamics described by numerical integrators can provide spurious solution of the corresponding continuous model. The approach represented by the geometric numerical integration, by preserving qualitative properties of the solution, leads to improved numerical behaviour expecially in the long-time integration. Positivity of the phase space, Poisson structure of the flows, conservation of invariants that characterize the continuous ecological models are some of the qualitative characteristics well reproduced by geometric numerical integrators. In this paper we review the benefits induced by the use of geometric numerical integrators for some ecological differential models. [ABSTRACT FROM AUTHOR]

Improving strategies for the control and eradication of invasive species is an important aspect of nature conservation, an aspect where mathematical modeling and optimization play an important role. In this paper, we introduce a reaction‐diffusion partial differential equation to model the spatiotemporal dynamics of an invasive species, and we use optimal control theory to solve for optimal management, while implementing a budget constraint. We perform an analytical study of the model properties, including the well‐posedness of the problem. We apply this to two hypothetical but realistic problems involving plant and animal invasive species. This allows us to determine the optimal space and time allocation of the efforts, as well as the final length of the removal program so as to reach the local extinction of the species. [ABSTRACT FROM AUTHOR]

We evaluate a mathematical model of the predator–prey population dynamics in a fragmented habitat where both migration processes between habitat patches and prey control policies are taken into account. The considered system is examined by applying the aggregation method and different dynamical scenarios are generated. The resulting implications are then discussed, their primary aim being the conservation of the wolf population in the Alta Murgia National Park, a protected area situated in the Apulian Foreland and also part of the Natura 2000 network. The Italian wolf is an endangered species and the challenge for the regional authorities is how to formulate conservation policies which enable the maintenance of the said wolf population while at the same time curbing that of the local wild boars and its negative impact on agriculture. We show that our model provides constructive suggestions in how to combine wild boar abatement programs awhile maintaining suitable ecological corridors which ensure wolf migration, thus preserving wolves from extinction. [ABSTRACT FROM AUTHOR]