Deborah Lacitignola - Academia.edu (original) (raw)

Papers by Deborah Lacitignola

Mathematical Biosciences, 216: 9-16 (2008)

We study the global behavior of a non-linear susceptible-infectious-removed (SIR)-like epidemic m... more 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. (Theor. Popul. Biol., 71, 2007) and, at same time, give a special example of application of the geometric method for global stability, due to Li and Muldowney. Numerical investigations are provided to show how the stability properties depend on the interplay between some relevant parameters of the model.

This paper offers an overview of morphogenetic processes going on in metal electrodeposition proc... more 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 masstransport rates. In addition, it provides a review of the modelling work by the authors, based on a reaction-diffusion system coupling morphology with surface chemistry of the growing metal and briefly describes the experimental validation of the model.

A bilinear three dimensional ODE system is considered, which generalizes many mathematical models... more 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 is completely determined.

Ecological Modelling, 2015

Nonlinear Analysis: Modelling and Control

A compartmental epidemic model, introduced by Gumel and Moghadas [1], is considered. The model in... more 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. Conditions ensuring the occurrence of backward bifurcation are derived. The obtained results are numerically validated and then discussed from both the mathematical and the epidemiological perspective.

Note di Matematica

We consider a four compartimental tuberculosis model which generalizes the one considered in [4, ... more 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, 12, 14]. Their approach, sometimes quoted as geometric approach to global stability, has been (and currently is being) extensively applied to the study of the global behavior of mathematical models of biological interest. The majority of applications refer to epidemic models, as SIR, SEIR, SEIS, SEIRS models (see, e.g., [1, 5, 9, 13, 16, 18]) altough applications to other population dy-namics context may be found, [3, 6]. In a recent analysis on general three dimensional systems, [7, 8], it has been shown that the mathematical structure of SEIR-like systems appears to be particularly suitable for the applications of the method. Applicatio...

X-Ray Spectrometry, 2015

In this paper, we report on the use of high-space resolution soft X-ray fluorescence microspectro... more 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 electrode morphology and metal space distribution, allowing to reproduce the observed space patterns and electrochemical transients by assigning an appropriate set of electrokinetic parameters. The discussed materials-science case is the electrochemical growth of a Mn-Mg-Cu-polypyrrole nanocomposite electrocatalyst materialfree of expensive Pt and environmentally unfriendly Cowith promising performance for fuel-cell oxygen electrodes. The synergy of high-resolution compositional mapping with electrokinetic modelling not only provides the general rationale for quantitative use of potentially large compositional distribution datasets but also yields unprecedented insight into the specific catalyst synthesis process. The expounded application is just a prototypical case study of a more general approach, which can be employed for the understanding of electrochemical material science processes, both in situ and ex situ, as well as for the characterisation of the corresponding products, with no other limitations in principle than X-ray transmission and beam damage.

Ag-Bi [35, 36] Ag-Cd [23][24][25] Ag-In [2,[26][27][28][29][30][31] Ag-Sn [41]

Acta Applicandae Mathematicae, 2014

In this paper we derive Hopf instability conditions for the morphochemical mathematical model for... more 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 are captured by a specific Complex Ginzburg-Landau Equation (CGLE). The derived CGLE yields analytical results on the existence and stability of spiral waves. Moreover, the arising of spiral instability is discussed in terms of the relevant system parameters and the related phenomenology is investigated numerically. To face with the numerical approximation of the spiral structures and of their longtime oscillating behavior we apply an Alternatig Direction Implicit (ADI) method based on high order finite differences in space.

International Journal of Biomathematics, 2014

ABSTRACT A nonlinear dynamical system is proposed as a qualitative mathematical model with the tw... more ABSTRACT 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 existence of the fatigue equilibrium is ensured as the only system's attractor in the feasibility range of the parameters. Suitable mathematical indicators — related to the dynamical properties of resilience and reactivity — are introduced to characterize the asymptotic and the transient system's behavior. The practical impact of the analytical results is elucidated and a connection is established between the introduced mathematical indicators and muscle functionality indexes as rate of force development, task failure time and complete restore time. Experimental validation with handgrip force signal at high load and possible practical applications are also presented.

In this paper a reaction-diffusion system for electrochemical material growth processes is consid... more 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 Formulas (ECDF) of order p = 4 in space is applied to investigate the way the variation of the frequency of the superimposed voltage sinusoid affects Turing pattern scenarios corresponding to steady state solutions of the unforced model. The ADI-ECDF method, introduced in [20] for the approximation of Turing patterns in the unforced case, is shown to be efficient from the computational point of view also to track oscillating Turing patterns for long-time simulations. In particular, the proposed method allows to identify a critical frequency range where the ripple effect arises, that is spots & worms patterns, related to the buildup of roughness in the material growth process, are suppressed and spatially homogeneous steady state solutions are attained. Such results have been validated by comparison with original experimental results on the growth of silver chloride films.

Waves and Stability in Continuous Media - Proceedings of the 15th Conference on WASCOM 2009, 2010

±=/(*).(1) where/: D~* R&amp;amp;amp;quot;, D CR&amp;amp;amp;quot; open set and/€... more ±=/(*).(1) where/: D~* R&amp;amp;amp;quot;, D CR&amp;amp;amp;quot; open set and/€ C:(D), A Bendixson criterion for (1) is a condition satisfied by the field/which precludes the existence of nonconstant periodic solutions. In the planar case (n= 2), classical Bendixson criteria are inequalities as, eg: div (a/)&amp;amp;amp;lt; 0, where a {x) is some scalar-valued function (Dulac criterion). This approach is no longer valid when n&amp;amp;amp;gt; 3.

Modeling the Interplay Between Human Behavior and the Spread of Infectious Diseases, 2012

ABSTRACT

Mathematical Biosciences and Engineering, 2010

In this paper a reaction-diffusion system modelling metal growth processes is considered, to inve... more In this paper a reaction-diffusion system modelling metal growth processes is considered, to investigate -within the electrodeposition contextthe 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 is provided and initiation of spatial patterns induced by diffusion is shown to occur in a suitable region of the parameter space. Investigations aimed at establishing the role of some relevant chemical parameters on stability and selection of solutions are also provided. By the numerical approximation of the equations, simulations are presented which turn out to be in good agreement with experiments for the electrodeposition of Au-Cu and Au-Cu-Cd alloys.