Technology has become part of today’s life. It constitutes a fundamental aspect the environment also for older people who are not familiar with most new technologies. Is their use technology based on certain abilities and is this related such factors as income, lack alternatives, past performance, or availability equipment? Methods The MOBILATE 2000 database survey conducted in 5 European countries was aimed at enhancement out-of-home mobility people. project offers data describing...

Abstract We present an epidemic model capable of describing key features the Covid-19 pandemic. While capturing several qualitative properties virus spreading, it allows to compute basic reproduction number, number deaths due and various other statistics. Numerical integrations are used illustrate adherence evolutions described by specific well known real In particular, this is consistent with relevance quarantine, shows dramatic role care houses accounts for increase in death toll when...

We extend the classical Lighthill–Whitham–Richards (LWR) traffic model allowing different maximal speeds for vehicles. Then we add a uniform bound on speed. The result, presented in this paper, is new macroscopic displaying two phases based nonsmooth $2\times2$ system of conservation laws. This compared with other models same type current literature, as well kinetic one. Moreover, establish rigorous connection between microscopic follow-the-leader ordinary differential equations and continuum model.

Elderly people whose physical strength and sensory abilities are waning often in particular need of a car order to deal with daily demands join social or cultural activities. However, the number pensioner households that own varies greatly according region, age, gender size household. This article first describes access older private cars predominant modes transport used by them urban rural areas six European regions five countries. In second part, authors analyse importance driving compared...

We consider the Cauchy problem for an $n\times n$ strictly hyperbolic system of balance laws $u_t+f(u)_x=g(x,u)$, $x\in\mathbb{R}$, $t>0$, $\|g(x,\cdot)\|_{\mathbf{C}^2}\leq\tilde{M}(x)\in\mathbf{L}^1$, endowed with initial data $u(0,.)=u_o\in\mathbf{L}^1\cap\mathbf{BV}(\mathbb{R};\mathbb{R}^n)$. Each characteristic field is assumed to be genuinely nonlinear or linearly degenerate and nonresonant source, i.e., $|\lambda_i(u)|\geq c>0$ all $i\in\{1,\dots,n\}$. Assuming that $\mathbf{L}^1$...

To analyse dietary habits and explore the role of socioeconomic status in a sample elderly Italians.

We present an epidemic model capable of describing key features the Covid-19 pandemic. While capturing several qualitative properties virus spreading, it allows to compute basic reproduction number, number deaths due and various other statistics. Numerical integrations are used illustrate relevance quarantine role care houses.

We present a traffic flow model consisting of gluing between the Lighthill-Whitham and Richards macroscopic with first order microscopic follow leader model. The basic analytical properties this are investigated. Existence uniqueness proved, as well estimates on dependence solutions from initial data. Moreover, numerical integrations show some qualitative features model, in particular transfer information among regions where different models used.

We present a unified framework ensuring well posedness and providing stability estimates to class of Initial – Boundary Value Problems for renewal equations comprising variety biological or epidemiological models. This versatility is achieved considering fairly general possibly non linear and/or local interaction terms, allowing both low regularity assumptions independent variables with without boundary. In particular, these results also apply, instance, model the spreading Covid like...

Nowadays, traffic monitoring systems have access to real time data, e.g. through GPS devices. We propose a new model able take into account these data and, hence, describe the effects of unpredictable accidents. The well-posedness this is proved and numerical integrations show qualitative features resulting solutions. As further motivation for use we that inverse problem Lighthill–Whitham Richards (LWR) ill-posed.

We present two frameworks for the description of traffic, both consisting in coupling systems different types. First, we consider Free--Congested model [7,11], where a scalar conservation law is coupled with $2\times2$ system. Then, micro- and macroscopic models, former system ordinary differential equations latter usual LWR law, see [10]. A comparison between also provided.

This paper deals with the Cauchy Problem for a PDE-ODE model, where system of two conservation laws, namely Two-Phase macroscopic model proposed in [13], is coupled an ordinary differential equation describing trajectory autonomous vehicle (AV), which aims to control traffic flow.Under suitable assumptions, we prove global time existence result.

We extend the Phase Transition model for traffic proposed in [8], by Colombo, Marcellini, and Rascle to network case. More precisely, we consider Riemann problem such a system at general junction with $n$ incoming $m$ outgoing roads. propose solver which conserves both number of cars maximal speed each vehicle, is key feature model. For special junctions, prove that well defined.

We consider the initial boundary value problem for phase transition traffic model introduced in [9], which is a macroscopic based on 2×2 system of conservation laws. prove existence solutions by means wave-front tracking technique, provided data and conditions have finite total variation.

We introduce a formalism to deal with the microscopic modeling of vehicular traffic on road network. Traffic each is unidirectional, and dynamics vehicle described by follow-the-leader model. From mathematical point view, this amounts defining system ODEs an arbitrary A general existence uniqueness result provided, while priorities at junctions are shown hinder stability solutions. investigate occurrence Braess paradox in time-dependent setting within The emergence Nash equilibria...

<p style='text-indent:20px;'>We present a new epidemic model highlighting the roles of immunization time and concurrent use different vaccines in vaccination campaign. To this aim, we introduce intra-compartmental dynamics, procedure that can be extended to various other situations, as detailed through specific case studies considered herein, where dynamics <i>within</i> compartments are influence whole evolution.</p>

This paper is devoted to the extension full $3\times3$ Euler system of basic analytical properties equations governing a fluid flowing in duct with varying section. First, we consider Cauchy problem for pipeline consisting 2 ducts joined at junction. Then, this result extended more complex pipes. A key assumption these theorems boundedness total variation pipe's We provide explicit examples show that bound necessary.