Wetlands are essential for global biogeochemical cycles and ecosystem services, with the dynamics of soil organic carbon (SOC) serving as the critical regulatory mechanism for these processes. However, accurately modeling carbon dynamics in wetlands presents challenges due to their complexity. Traditional approaches often fail to capture spatial variations, long-range transport, and periodical flooding dynamics, leading to uncertainties in carbon flux predictions. To tackle these challenges, we introduce a novel extension of the fractional RothC model, integrating temporal fractional-order derivatives into spatial dimensions. This enhancement allows for the creation of a more adaptive tool for analyzing SOC dynamics. Our differential model incorporates Richardson–Richard's equation for moisture fluxes, a diffusion–advection–reaction equation for fractional-order dynamics of SOC compounds, and a temperature transport equation. We examine the influence of diffusive movement and sediment moisture content on model solutions, as well as the impact of including advection terms. Finally, we validated the model on a restored wetland scenario at the Ebro Delta site, aiming to evaluate the effectiveness of flooding strategies in enhancing carbon sequestration and ecosystem resilience.

Models of soil organic carbon (SOC) frequently overlook the effects of spatial dimensions and microbiological activities. In this paper, we focus on two reaction-diffusion chemotaxis models for SOC dynamics, both supporting chemotaxis-driven instability and exhibiting a variety of spatial patterns as stripes, spots and hexagons when the microbial chemotactic sensitivity is above a critical threshold. We use symplectic techniques to numerically approximate chemotaxis-driven spatial patterns and explore the effectiveness of the piecewise Dynamic Mode Decomposition (pDMD) to reconstruct them. Moreover, we analyse the predictive performance of the pDMD for moderate time horizons. Our findings show that pDMD is effective at precisely recreating and predicting chemotaxis-driven spatial patterns, therefore broadening the range of application of the method to classes of solutions different than Turing patterns. By validating its efficacy across a wider range of models, this research lays the groundwork for applying pDMD to experimental spatiotemporal data, advancing predictions crucial for soil microbial ecology and agricultural sustainability.

We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the reactivity of the non-spatial and spatial dynamics, stability analyses, and numerical continuation to uncover detailed aspects of this system’s pattern-forming potential. In addition to patterning in Turing unstable parameter regimes, reactivity of the spatial system can itself lead to a range of parameters where a spatially uniform state is asymptotically stable, but exhibits transient growth that can induce pattern formation. We show that this occurs in the bistable region of a subcritical Turing bifurcation. Intriguingly, such bistable regions appear in two spatial dimensions, but not in a one-dimensional domain, suggesting important interplays between geometry, transient growth, and the emergence of multistable patterns. We discuss the implications of our analysis for the bacterial soil organic carbon system, as well as for reaction-transport modeling more generally.

Bursting behaviors, driven by environmental variability, can substantially influence ecosystem services and functions and have the potential to cause abrupt population breakouts in host-parasitoid systems. We explore the impact of environment on the host-parasitoid interaction by investigating separately the effect of grazing-dependent habitat variation on the host density and the effect of environmental fluctuations on the average host population growth rate. We hence focus on the discrete host-parasitoid Beddington-Free-Lawton model and show that a more comprehensive mathematical study of the dynamics behind the onset of on-off intermittency in host-parasitoid systems may be achieved by considering a deterministic, chaotic system that represents the dynamics of the environment. To this aim, some of the key model parameters are allowed to vary in time according to an evolution law that can exhibit chaotic behavior. Fixed points and stability properties of the resulting 3D nonlinear discrete dynamical system are investigated and on-off intermittency is found to emerge strictly above the blowout bifurcation threshold. We show, however, that, in some cases, this phenomenon can also emerge in the sub-threshold. We hence introduce the novel concept of long-term reactivity and show that it can be considered as a necessary condition for the onset of on-off intermittency. Investigations in the time-dependent regimes and kurtosis maps are provided to support the above results. Our study also suggests how important it is to carefully monitor environmental variability caused by random fluctuations in natural factors or by anthropogenic disturbances in order to minimize its effects on throphic interactions and protect the potential function of parasitoids as biological control agents.

Ecological systems are subject to environmental variability and fluctuations: understanding the role of such stochastic perturbations in inducing on–off intermittency is the central motivation for this study. This research extends the exploration of parameters leading to the emergence of on–off intermittency within a discrete Beddington-Free-Lawton host-parasitoid model. We introduce random perturbation factors that impact both the grazing intensity and the growth rate of the host population. An intriguing aspect of this study is the numerical evidence of the reactivity of the free-parasitoid fixed point as a route to on–off intermittency. This finding is significant because it sheds light on how stable ecological equilibria can transition into intermittency before progressing toward chaotic behaviour. Moreover, our study explores the host-parasitoid coupling within the Beddington-Free-Lawton model when it is applied to a complex network, a significant framework for modelling ecological interactions. The paper reveals that such network-based interactions induce parasitoid bursts that are not observed in a single population scenario.

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.

We tackle the problem of coupling a spatiotemporal model for simulating the spread and control of an invasive alien species with data coming from image processing and expert knowledge. In this study, we implement a spatially explicit optimal control model based on a reaction-diffusion equation which includes an Holling II type functional response term for modeling the density control rate. The model takes into account the budget constraint related to the control program and searches for the optimal effort allocation for the minimization of the invasive alien species density. Remote sensing and expert knowledge have been assimilated in the model to estimate the initial species distribution and its habitat suitability, empirically extracted by a land cover map of the study area. The approach has been applied to the plant species Ailanthus altissima (Mill.) Swingle within the Alta Murgia National Park. This area is one of the Natura 2000 sites under the study of the ongoing National Biodiversity Future Center (NBFC) funded by the Italian National Recovery and Resilience Plan (NRRP), and pilot site of the finished H2020 project ECOPOTENTIAL, which aimed at the integration of modeling tools and Earth Observations for a sustainable management of protected areas. Both the initial density map and the land cover map have been generated by using very high resolution satellite images and validated by means of ground truth data provided by the EU Life Alta Murgia project (LIFE12 BIO/IT/000213), a project aimed at the eradication of Ailanthus altissima in the Alta Murgia National Park

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 ?(t,q), a better match between simulated and actual data can be achieved compared to the traditional integer-order model.

To evaluate changes in the Soil Organic Carbon (SOC) index, one of the key indicators of land degradation neutrality, soil carbon modeling is of primary importance. In litera-ture, the analysis has been focused on the stability characterization of soil carbon steady states and in the calculation of the resilience of the stable equilibria. Neither stability nor resilience, however, provide any information about transient dynamics, and models with highly resilient equilibria can exhibit dramatic transient responses to perturbations. To trace how environmental changes affect the transient dynamics of SOC indicator, we use the concept of generalized reactivity (g-reactivity) to models belonging to two main classes: the first-order, linear and semilinear carbon transfer models and fully nonlinear microbe-explicit models. A novel formulation of a general two-dimensional model allows to deal with different functional forms and to perform a systematic analysis of both stabil-ity of soil carbon equilibria and SOC-reactivity. Using temperatures and Net Primary Pro-duction (NPP) data of Alta Murgia National Park, the RothC, MOMOS and the fully implicit dynamical planar system are compared in predicting the impact of increased temperatures in the years 2005-2019 on the asymptotic stability of carbon steady states and in increas-ing the SOC-reactivity.(c) 2023 Elsevier Inc. All rights reserved.

The SOC change index, defined as the normalized difference between the actual Soil Organic Carbon and the value assumed at an initial reference year, is here tailored to the RothC carbon model dynamics. It assumes as a baseline the value of the SOC equilibrium under constant environmental conditions. A sensitivity analysis is performed to evaluate the response of the model to changes in temperature, Net Primary Production (NPP), and land use soil class (forest, grassland, arable). A non-standard monthly time-stepping procedure has been proposed to approximate the SOC change index in the Alta Murgia National Park, a protected area in the Italian Apulia region, selected as a test site. The SOC change index exhibits negative trends for all the land use considered without fertilizers. The negative trend in the arable class can be inverted by a suitable organic fertilization program here proposed.

We analyze a second-order accurate implicit-symplectic (IMSP) scheme for reaction-diffusion systems modeling spatiotemporal dynamics of predator-prey populations. We prove stability and errors estimates of the semi-discrete-in-time approximations, under positivity assumptions. The numerical simulations confirm the theoretically derived rates of convergence and show an improved accuracy in the second-order IMSP in comparison with the first-order IMSP, at same computational cost.

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. 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.

In this paper, we use the Z-control approach to get further insight on the role of awareness in the management of epidemics that, just like Covid-19, display a high rate of overexposure because of the large number of asymptomatic people. We focus on a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori. Exploiting the potential of awareness to produce social distancing and self-isolation among susceptibles, we use it as an indirect control on the class of infective individuals and apply the Z-control approach to detect what trend must awareness display over time in order to eradicate the disease. To this aim, we generalize the Z-control procedure to appropriately treat an uncontrolled model with more than two governing equations. Analytical and numerical investigations on the resulting Z-controlled system show its capability in controlling some representative dynamics within both the backward and the forward scenarios. The awareness variable is qualitatively compared to Google Trends data on Covid-19 that are discussed in the perspective of the Z-control approach, inferring qualitative indications in view of the disease control. The cases of Italy and New Zealand in the first phase of the pandemic are analyzed in detail. The theoretical framework of the Z-control approach can hence offer the chance to reflect on the use of Google Trends as a possible indicator of good management of the epidemic.

Trends of soil organic carbon (SOC) are significant indicators for land and soil degradation. Decrease in SOC compromises the efforts to achieve by 2030, a land degradation neutral world, as required by Target 15.3 of the Seventeen Sustainable Development Goals (SDGs) adopted by United Nations in September 2015. Differential models, as the Rothamsted Carbon model (RothC) [1], can be useful tools to predict SOC changes, taking into account the interactions among climate, soil and land use management. In this talk, we illustrate some results on the application of a novel nonstandard discretization [2] of the continuous RothC model [3] for assessing the SOC indicator in Alta Murgia National Park, a protected area in Apulia region in the south of Italy. A procedure for determining the initial plant input necessary to run the model is described. Moreover, in order to detect the factors that determine the size and direction of SOC changes, a local sensitivity analysis based on the so-called direct method is performed. This work received fundings from the REFIN project N.0C46E06B (Regione Puglia, Italy) and from the European Union's Horizon 2020 research and innovation programme under grant agreement No 871128 (H2020-eLTER-PLUS project).

We apply the Z-control approach to a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori. Exploiting the potential of awareness to produce social distancing and self-isolation among susceptibles, we use it as an indirect control on the class of infective individuals and apply the Z-control approach to detect what trend awareness must display over time in order to eradicate the disease. To this aim, we generalize the Z-control procedure to appropriately treat an uncontrolled model with more than two governing equations. Analytical and numerical investigations on the resulting Z-controlled system show its capability in controlling some representative dynamics within both the backward and the forward scenarios. The awareness variable is qualitatively compared to Google Trends data on Covid-19 and qualitative indications are inferred in view of the disease control.

A novel model is here introduced for theSOC change indexdefinedas the normalized difference between the actual Soil Organic Carbon and thevalue assumed at an initial reference year. It is tailored on the RothC carbonmodel dynamics and assumes as baseline the value of the SOC equilibriumunder constant environmental conditions. A sensitivity analysis is performedto evaluate the response of the model to changes of temperature, Net PrimaryProduction (NPP), and land use soil class (forest, grassland, arable). A non-standard monthly time-stepping procedure has been proposed to approximatethe SOC change index in the Alta Murgia National Park, a protected areain the Italian Apulia region, selected as test site. In the case of arable class,the SOC change index exhibits a negative trend which can be inverted by asuitable organic fertilization program here proposed.

The diffusive behaviour of simple random-walk proposals of many Markov Chain Monte Carlo (MCMC) algorithms results in slow exploration of the state space making inefficient the convergence to a target distribution. Hamiltonian/Hybrid Monte Carlo (HMC), by introducing fictious momentum variables, adopts Hamiltonian dynamics, rather than a probability distribution, to propose future states in the Markov chain. Splitting schemes are numerical integrators for Hamiltonian problems that may advantageously replace the St ̈ormer-Verlet method within HMC methodology. In this paper a family of stable methods for univariate and multivariate Gaussian distributions, taken as guide-problems for more realistic situations, is proposed. Differently from similar methods proposed in the recent literature, the considered schemes are featured by null expectation of the random variable representing the energy error. The effectiveness of the novel procedures is shown for bivariate and multivariate test cases taken from the literature.

We generalize the nonstandard Euler and Heun schemes in order to provide explicit geometric numerical integrators for biochemical systems, here denoted as GeCo schemes, that preserve both positivity of the solutions and linear invariants. We relax the request on the order convergence of the denominator function for the first-order approximation and we let it depend on the step size also throughout the solution approximating values. The first-order variant is exact on a two-dimensional linear test problem. Moreover, we introduce a class of modified mGeCo(alpha) schemes and, by tuning the parameter alpha >= 1, we improve the numerical performance of GeCo integrators on some examples taken from the literature. A numerical comparison with BBKS and mBBKSschemes, which are implicit integrators, positive and conserve linear invariants, show the gain in efficiency of both GeCo and mGeCo(alpha) procedures as they generate similar errors with an explicit functional form. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.