arXiv subjects

Eleonora Messina

Publications and source records attributed to Eleonora Messina.

6 recordsLinked to original sources

arXiv2026

EPITIME: A Computational Framework for Integral Epidemic Models with Structure-Preserving Discretizations

We present EPITIME (EPidemic Integral models TIMe profile Explorer), a computational framework for the simulation of two classes of integral epidemic models: an age of infection model and an information dependent behavioural model. The framework combines structure preserving Non-Standard Finite Difference discretizations with modular implementations in MATLAB and Python, together with routines for parameter handling, input validation, performance assessment, and graphical interaction. The proposed methods preserve key qualitative properties of the continuous problems, including positivity, boundedness, invariant regions, and correct long term behaviour, independently of the time step. We outline the numerical schemes for both model classes and their main analytical properties, including first order convergence. We then describe the software architecture and illustrate its use through numerical experiments on asymptotic behaviour, inverse reconstruction of an infectivity kernel from COVID 19 incidence data, and behavioural dynamics under different memory kernels. Overall, EPITIME provides a reliable and accessible computational environment for the numerical study of renewal epidemic models.

q-bio.QM↗

arXiv2024

Modified Patankar Linear Multistep methods for production-destruction systems

Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the resulting discretizations retain, with no restrictions on the step size, the positivity of the solution and the linear invariant of the continuous-time system. Moreover, we provide results on arbitrarily high order of convergence and we introduce an embedding technique for the Patankar weight denominators to achieve it.

math.NA↗

arXiv2024

An integral renewal equation approach to behavioural epidemic models with information index

We propose an integral model describing an epidemic of an infectious disease. The model is behavioural in the sense that the constitutive law for the force of infection includes a distributed delay, called "information index", that describes the opinion-driven human behavioural changes. The information index, in turn, contains a memory kernel to mimic how the individuals maintain memory of the past values of the infection. We obtain sufficient conditions for the endemic equilibrium to be locally stable. In particular, we show that when the infectivity function is represented by an exponential distribution, stability is guaranteed by the weak Erlang memory kernel. However, through numerical simulations, we show that self-sustained oscillations may arise when the memory is more focused in the disease's past history, as exemplified by the strong Erlang kernel. We also show the model solutions in cases of different infectivity functions describing infectious diseases like influenza and SARS.

math.DS↗

arXiv2022

The effect of time discretization on the solution of parabolic PDEs with ANNs

We investigate the resolution of parabolic PDEs via Extreme Learning Machine (ELMs) Neural Networks, which have a single hidden layer and can be trained at a modest computational cost as compared with Deep Learning Neural Networks. Our approach addresses the time evolution by applying classical ODEs techniques and uses ELM-based collocation for solving the resulting stationary elliptic problems. In this framework, the $\theta$-method and Backward Difference Formulae (BDF) techniques are investigated on some linear parabolic PDEs that are challeging problems for the stability and accuracy properties of the methods. The results of numerical experiments confirm that ELM-based solution techniques combined with BDF methods can provide high-accuracy solutions of parabolic PDEs.

math.NA↗

arXiv2021

A non-standard numerical scheme for an age-of-infection epidemic model

We propose a numerical method for approximating integro-differential equations arising in age-of-infection epidemic models. The method is based on a non-standard finite differences approximation of the integral term appearing in the equation. The study of convergence properties and the analysis of the qualitative behavior of the numerical solution show that it preserves all the basic properties of the continuous model with no restrictive conditions on the step-length $h$ of integration and that it recovers the continuous dynamic as $h$ tends to zero.

math.NA↗

arXiv2015

A hybrid mathematical model of collective motion under alignment and chemotaxis

In this paper we propose and study a hybrid discrete in continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale model (Cucker and Smale, 2007) was coupled with other cell mechanisms, to describe the cell migration and self-organization in the zebrafish lateral line primordium, we introduce a simplified model in which the coupling between an alignment and chemotaxis mechanism acts on a system of interacting particles. In particular we rely on a hybrid description in which the agents are discrete entities, while the chemoattractant is considered as a continuous signal. The proposed model is then studied both from an analytical and a numerical point of view. From the analytic point of view we prove, globally in time, existence and uniqueness of the solution. Then, the asymptotic behaviour of a linearised version of the system is investigated. Through a suitable Lyapunov functional we show that for $t\rightarrow +\infty$, the migrating aggregate exponentially converges to a state in which all the particles have a same position with zero velocity. Finally, we present a comparison between the analytical findings and some numerical results, concerning the behaviour of the full nonlinear system.

math.CA↗