Deborah Lacitignola

Università degli studi di Cassino e del Lazio Meridionale | UNICAS · Department of Electrical and Information Engineering

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 qualita...

Alloy electrodeposition processes have been experimentally shown to exhibit electrokinetic instability that can lead to compositional heterogeneity in the electrodeposit bulk. Inspired by these experimental evidences we consider the DIB model, a morphochemical reaction-diffusion system introduced in [Bozzini et al., J. Solid State Electr.17, 467–47...

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...

In this study we show that concept of backward bifurcation, borrowed from epidemics, can be fruitfully exploited to shed light on the mechanism underlying the occurrence of hysteresis in marketing and for the strategic planning of adequate tools for its control. We enrich the model introduced in [Gaurav et al., 2019] with the mechanism of self-info...

A SEIR-type model is investigated to evaluate the effects of awareness campaigns in the presence of factors that can induce overexposure to disease. We find that high levels of overexposure can drive system dynamics towards a backward phenomenology and that increasing people awareness through balanced and aware information can be crucial to avoid d...

In this study, the formation of the adult sea urchin shape is rationalized within the Turing's theory paradigm. The emergence of protrusions from the expanding underlying surface is described through a reaction-diffusion model with Gray-Scott kinetics on a growing oblate spheroid. The case of slow exponential isotropic growth is considered. The mod...

This paper focuses on the impact of cross-diffusion for Turing-Hopf instability in a morphochemical model for electrodeposition (DIB) and completes the analysis on the role of cross-diffusion on pattern formation in electrodeposition we recently carried out in [Lacitignola et al. 2018]. We derive and discuss conditions for the destabilization a´ la...

in "Ithaca: Viaggio nella Scienza"

A challenging task in the management of Protected Areas is to control the spread of invasive species, either floristic or faunistic, and the preservation of indigenous endangered species, typically competing for the use of resources in a fragmented habitat. In this paper, we present some mathematical tools that have been recently applied to contain...

Effectively dealing with invasive species is a pervasive problem in environmental management. The damages that stem from invasive species are well known. However, controlling them cost-effectively is an ongoing challenge, and mathematical modeling and optimization are becoming increasingly popular as a tool to assist management. In this paper we in...

We investigate how the Z-type dynamic approach can be applied to control backward bifurcation phenomena in epidemic models. Because of its rich phenomenology, that includes stationary or oscillatory subcritical persistence of the disease, we consider the SIR model introduced by Zhou & Fan in [Nonlinear Analysis: Real World Applications, 13(1), 312-...

We analyze the effects of cross-diffusion on pattern formation in a PDE reaction-diffusion system introduced in Bozzini et al. 2013 to describe metal growth in an electrodeposition process. For this morphochemical model - which refers to the physico-chemical problem of coupling of growth morphology and surface chemistry - we have found that negativ...

The present paper deals with the pattern formation properties of a specific morpho-electrochemical reaction-diffusion model on a sphere. The physico-chemical background to this study is the morphological control of material electrodeposited onto spherical particles. The particular experimental case of interest refers to the optimisation of novel me...

Does it really exist a mathematical beauty of nature? And the revolutionary Turing's idea can be a key to decipher it? In this paper we try to answer these questions by describing the origins, the theoretical basis and the scientific impact of Alan Turing's theory on pattern formation .The picture that emerges is that of a highly topical theory, th...

We apply the Z-control approach to a generalized predator-prey system and consider the specific case of indirect control of the prey population. We derive the associated Z-controlled model and investigate its properties from the point of view of the dynamical systems theory. The key role of the design parameter λ for the successful application of t...

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 ar...

This paper reports on spiral pattern formation in In–Co electrodeposition. We propose an approach to the understanding of this process based on: (i) compositional and chemical-state distribution analysis by high-resolution photoelectron microspectroscopy and (ii) a mathematical model able to capture the morphological features highlighted in the exp...

We focus on the morphochemical reaction-diffusion model introduced in [13] and carry out a nonlinear bifurcation analysis with the aim to characterize the shape and the amplitude of the patterns arising as the result of Turing instability of the physically relevant equilibrium. We perform a weakly non-linear multiple scales analysis, and derive the...

In this paper, we investigate from a theoretical point of view the 2D reaction-diffusion system for electrodeposition coupling morphology and surface chemistry, presented and experimentally validated in Bozzini et al. (2013 J. Solid State Electr.17, 467–479). We analyse the mechanisms responsible for spatio-temporal organization. As a first step, s...

In this paper, we report on the use of high-space resolution soft X-ray fluorescence microspectroscopy for the study of electrodeposited composites containing catalytic ternary metal nanostructures. X-ray fluorescence maps are interpreted in terms of a dynamic mathematical model of the electrodemorphology and metal space distribution, allowing to r...

In this paper we investigate from the numerical point of view the discrete DNA model proposed in [Lacitignola and Saccomandi, Bull. Math. Biol. (2014)] in order to test the robustness of the parametric resonance condition found in the limit of the continuum approximation. To describe more realistically the binding of RNA polymerase to the DNA macro...

In this paper we derive Hopf instability conditions for the morphochemical mathematical model for alloy electrodeposition introduced and experimentally validated in [Bozzini et al., J. Solid State Electr. 17, 467–479 (2013)]. Using normal form theory we show that in the neighborhood of the Hopf bifurcation, essential features of the system dynamics...

We focus on an epidemic model which incorporates a non-linear force of infection and two controls: an imperfect preventive vaccine given to susceptible individuals and therapeutic treatment given to infectious. We study both the cases of constant and non constant controls. In the case of constant controls we perform a qualitative analysis based on...

A nonlinear dynamical system is proposed as a qualitative mathematical model with the twofold aim to reasonably describe the force behavior in a fatiguing sub-maximal contraction and to be possibly employed in assessing muscular activation indexes. The model's properties are studied in terms of its equilibria and their stability properties and the...

We consider a simple mesoscopic model of DNA in which the binding of the RNA polymerase enzyme molecule to the promoter sequence of the DNA is included through a substrate energy term modeling the enzymatic interaction with the DNA strands. We focus on the differential system for solitary waves and derive conditions-in terms of the model parameters...

Three behavioral-epidemic models (i.e., epidemic systems including feedbacks (FB) that the information about an infectious disease has on its spreading) are introduced. Two relevant FB are explicitly considered: the pseudo-rational exemption to vaccination and the information-related changes in contact patterns by healthy subjects. The global stabi...

A challenge to disease control in modern societies is the spread of pseudo-rational exemption to vaccination, as a consequence of a comparison between the steadily declining risk of infection, and the perceived risk of side effects from the vaccine. Here we consider rational exemption in an SEIR model with information dependent vaccination where in...

We consider the case of measles in South Africa to show that an high vaccination coverage may be not enough - alone - to ensure measles eradication. The occurrence of certain epidemic episodes may in fact be encouraged by delays in the treatments or by not adequately fast clinical case management, which may be related to the backward bifurcation ph...

This paper proposes a novel mathematical model for the formation of spatio-temporal patterns in electrodeposition. At variance with classical modelling approaches that are based on systems of reaction–diffusion equations just for chemical species, this model accounts for the coupling between surface morphology and surface composition as a means of...

Alcohol dependence is among the main healthy risky behavior due to the high relevance of negative health and social effect. We study a mathematical model, given by nonlinear ordinary differential equations, describing the spread of high–risk alcohol consumption behavior within a community of individuals. We describe the peer-influence effects on al...

The coupling of surface shape dynamics and surface composition for a material growing by electrodeposition has been found in recent modelling work by the authors, to give rise to a rich morphogenetic scenario. In this paper we concentrate on a systematic description of morphogenesis occurring during metal and alloy electrodeposition. First of all w...

We consider an epidemic model for the dynamics of a vaccine-preventable disease, which incorporates the treatment and an imperfect vaccine given to susceptible individuals. We show that in spite of the simple structure of the model, a backward bifurcation may always occur if the treatment rate is above a threshold value. This occurs regardless of t...

In this paper a reaction-diffusion system for electrochemical material growth processes is considered, including an external sinusoidal forcing term for the PDE equation describing the morphology of the electrodeposit surface profile. The numerical approximation by the Alternating Direction Implicit (ADI) method based on Extended Central Difference...

In this paper we study the numerical approximation of Turing patterns corresponding to steady state solutions of a PDE system of reaction–diffusion equations modeling an electrodeposition process. We apply the Method of Lines (MOL) and describe the semi-discretization by high order finite differences in space given by the Extended Central Differenc...

SIR and SIS epidemic models with information—related changes in contact patterns are introduced. The global stability analysis of the endemic equilibrium is performed by means of the Li–Muldowney geometric approach. Biological implications of the stability conditions are given.

http://www.pfonline.com/articles/ripple-effect-researchers-say-leveling-of-electrodeposits-can-be-achieved-by-applying-a-small-forcing-voltage

Introduction: The numerous physical and hormonal changes occurring during pregnancy may lead to an altered static and dynamic balance causing an increased frequency of musculoskeletal pain at low back level and the risk of falling. Falls are the most common cause of minor injury during pregnancy and the risk of falls is equivalent to that of an eld...

Three behavioral-epidemic models (i.e., epidemic systems including feedbacks (FB) that the information about an infectious disease has on its spreading) are introduced. Two relevant FB are explicitly considered: the pseudo-rational exemption to vaccination and the information-related changes in contact patterns by healthy subjects. The global stabi...

This paper offers an overview of morphogenetic processes going on in metal electrodeposition processes and provides a systematisation of the morphology classes identified experimentally in terms of an electrokinetic theory accounting for charge-transfer and mass-transport rates. In addition, it provides a review of the modelling work by the authors...

Metal plating is a well-assessed and widespread technology. Though being a mature process (Ag plating is in fact the first known application of Volta's battery in 1801, Al electrolysis was used to fabricate Napoleon III's tableware for very special occasions at the imperial French court, present-day decorative- and hard- Cr electrodeposition thrive...

A compartmental epidemic model, introduced by Gumel and Moghadas [1], is considered. The model incorporates a nonlinear incidence rate and an imperfect preventive vaccine given to susceptible individuals. A bifurcation analysis is performed by applying the bifurcation method introduced in [2], which is based on the use of the center manifold theory...

In this paper we consider an analytical and numerical study of a reaction-diffusion system for describing the formation of transition front waves in some electrodeposition (ECD) experiments. Towards this aim, a model accounting for the coupling between morphology and composition of one chemical species adsorbed at the surface of the growing cathode...

We consider a four compartimental tuberculosis model which generalizes the one considered in [4, 17]. We will obtain sufficient conditions for the global stability of the endemic equilibrium. We will use the recent generalization of the Poincaré-Bendixson criterion for systems of n ordinary differential equations, due to M. Li and J. Muldowney [11,...

We consider a four-compartment tuberculosis model including exogenous reinfection. We derive sufficient conditions, in terms of the parameters of the system, which guarantee the occurrence of backward bifurcation. We also discuss the global stability of the endemic state by using a generalization of the Poincaré-Bendixson criterion. An application...

In this paper we present an extension of a mathematical model for the morphological evolution of metal electrodeposits – recently developed by some of the authors – accounting for mass-transport of electroactive species from the bulk of the bath to the cathode surface. The implementation of mass-transport effects is specially necessary for the quan...

'Rational' exemption to vaccination is due to a pseudo-rational comparison between the low risk of infection, and the perceived risk of side effects from the vaccine. Here we consider rational exemption in an SI model with information dependent vaccination where individuals use information on the disease's spread as their information set. Using sui...

¿CUÁLES SON LAS MATEMÁTICAS DE DARWIN? Charles Darwin desarrolló su teoría de la evolución sin utilizar una sola fórmula matemática, circunstancia que aún hoy es objeto de animado debate: ¿son posibles unas matemáticas de la evolución? Y si lo son, ¿qué tipo de matemáticas se necesita? Deborah Lacitignola (Universidad de Cassino, Italia) nos introd...

The dynamics of a structured population model including cannibalism is analyzed. Hopf bifurcation threshold for the cannibalistic attack rate is detected. Linear and nonlinear stability analysis through the Lyapunov Direct Method is also provided. The effects of relevant parameters on the stability are discussed. In particular, cannibalism is found...

We consider the geometric method for global stability due to M. Li and J. Muldowney11 and discuss its applicability to some epidemic models. The method is based on the use of a higher order generalization of the well-known Bendixson criterion.

In this paper a reaction-diffusion system modelling metal growth processes is considered, to investigate - within the electrodeposition context- the formation of morphological patterns in a finite two-dimensional spatial domain. Nonlinear dynamics of the system is studied from both the analytical and numerical points of view. Phase-space analysis i...

In situations with opposing opinions, strong emotions, and high stakes, as it might occur, for instance, in tourism-based social– ecological systems (SESs) between the conflicting interests of mass-tourists and eco-tourists, small events can have large unexpected consequences (Patterson, 2002). This behaviour is called deterministic chaos (Wheeler,...

An SEIR epidemic model with a nonlinear incidence rate is studied. The incidence is assumed to be a convex function with respect to the infective class of a host population. A bifurcation analysis is performed and conditions ensuring that the system exhibits backward bifurcation are provided. The global dynamics is also studied, through a geometric...

In this paper, we consider a general bilinear three dimensional ODE system, whose structure generalizes many mathematical models of biological interest, including many from epidemics. Our main goal is to find sufficient conditions, expressed in terms of the parameters of the system, ensuring that the geometric approach to global stability analysis,...

We study the global behavior of a non-linear susceptible-infectious-removed (SIR)-like epidemic model with a non-bilinear feedback mechanism, which describes the influence of information, and of information-related delays, on a vaccination campaign. We upgrade the stability analysis performed in d'Onofrio et al. [A. d'Onofrio, P. Manfredi, E. Salin...

A bilinear three dimensional ODE system is considered, which generalizes many mathematical models in epidemiology. The global stability problem is investigated through a geometrical approach, due to M. Li and J. Muldowney [8], and based on the use of a higher order generalization of the well-known Bendixson criterion. Global dynamics for the system...

In this paper we deal with a reaction-diffusion system to model the coupling between surface morphology and surface composition, as a means of understanding the formation of morphological patterns found in electrodeposition (ECD). The discussion is restricted to the case of one chemical species adsorbed at the surface of the growing cathode and sou...

Lotka-Volterra systems have played a fundamental role for mathematical modelling in many branches of theoretical biology and proved to describe, at least qualitatively, the essential features of many phenomena, see for example Murray [Murray 2002]. Furthermore models of that kind have been considered successfully also in quite different and less ma...

In the present paper we shall focus on the coupling between surface morphology and surface composition, as a means of understanding the formation of morphological patterns found in electrodeposition (ECD) and, prospectively, as a control strategy of ECD morphology based on manipulations of the surface chemistry (in terms of additive adsorption at t...

The analysis of socio-ecological systems requires new, qualitatively distinct, evaluation schemes and appropriate investigation tools that enable an integrated assessment of ecological, social, and economic factors since human land use is a major force driving land-scape change, landscape dynamics can be better understood in the context of complex...

In this paper we give a contribution to the systematic investigation of cannibalism in predator-prey models commenced since the publication of the paper by Kohlmeier and Ebenhoh in 1995. We present a stage-structured predator-prey model and study its dynamics. We use a Hopf bifurcation analysis to prove that cycles are possible and that cannibalism...

We study the properties of a n2-dimensional Lotka-Volterra system describing competition among species with behaviorally adaptive abilities, in which one species is made ecologically differentiated with respect to the others by carrying capacity and intrinsic growth rate. The case in which one species has a carrying capacity higher than the others...

We study the properties of a n2-dimensional Lotka-Volterra system describing competing species that include behaviorally adaptive abilities. We indicate as behavioral adaptation a mechanism, based on a kind of learning, which is not viewed in the evolutionary sense but is intended to occur over shorter time scales. We consider a competitive adaptiv...

We deal with the global stability for a well-known population-toxicant model. We make use of a geometrical approach to the global stability analysis for ordinary differential equation which is based on the use of a higher-order generalization of the Bendixson's criterion. We obtain sufficient conditions for the global stability of the unique nontri...

We study the properties of an n 2 -dimensional Lotka-Volterra system describing competition among n species, n≥3, with adaptive skills and with one species made ecologically differentiated with respect to the others by carrying capacity and/or intrinsic growth rate. In both cases the symmetry properties of such a system and the existence of a certa...

We study the properties of a n ² -dimensional Lotka–Volterra system describing competition among n different species with adaptive skills, i.e. whose interaction coefficients are time averages of the species level of interaction over their past. Starting by the case of adaptive competition among species all having the same carrying capacities, we f...

Global stability analysis for a basic model describing population growth in a polluted environment is performed by using a geometrical approach based on a higher-order generalization of the Bendixson's criterion. We obtain sufficient conditions for the global stability of the unique non-trivial equilibrium. These conditions are expressed in terms o...