Due to the recent evolution of the COVID-19 outbreak, the scientific community is making efforts to analyse models for understanding the present situation and for predicting future scenarios. In this paper, we propose a forced Susceptible-Exposed-Infected-Recovered-Dead (fSEIRD) differential model for the analysis and forecast of the COVID-19 spread in Italian regions, using the data from the Italian Protezione Civile (Italian Civil Protection Department) from 24/02/2020. In this study, we investigate an adaptation of fSEIRD by proposing two different piecewise time-dependent infection rate functions to fit the current epidemic data affected by progressive movement restriction policies put in place by the Italian government. The proposed models are flexible and can be quickly adapted to monitor various epidemic scenarios. Results on the regions of Lombardia and Emilia-Romagna confirm that the proposed models fit the data very accurately and make reliable predictions.
The inversion of two-dimensional NMR data is an ill-posed problem related to the numerical computation of the inverse Laplace transform. In this paper we present the 2DUPEN algorithm that extends the Uniform Penalty (UPEN) algorithm [Borgia, Brown, Fantazzini, Journal of Magnetic Resonance, 1998] to two-dimensional data. The UPEN algorithm, defined for the inversion of one-dimensional NMR relaxation data, uses Tikhonov-like regularization and optionally non-negativity constraints in order to implement locally adapted regularization. In this paper, we analyze the regularization properties of this approach. Moreover, we extend the one-dimensional UPEN algorithm to the two-dimensional case and present an efficient implementation based on the Newton Projection method. Without any a-priori information on the noise norm, 2DUPEN automatically computes the locally adapted regularization parameters and the distribution of the unknown NMR parameters by using variable smoothing. Results of numerical experiments on simulated and real data are presented in order to illustrate the potential of the proposed method in reconstructing peaks and flat regions with the same accuracy.
Due to the recent diffusion of COVID-19 outbreak, the scientific community is making efforts in analysing models for understanding the present situation and predicting future scenarios. In this paper, we propose a Susceptible-Infected-Exposed-Recovered-Dead (SEIRD) differential model [Weitz J. S. and Dushoff J., Scientific reports, 2015] for the analysis and forecast of the COVID-19 spread in Italian regions, using the data from the Italian Protezione Civile from February 24th 2020. In this study, we investigate an adaptation of SEIRD that takes into account the actual policies of the Italian government, consisting of modelling the infection rate as a time-dependent function (SEIRD(rm)). Preliminary results on Lombardia and Emilia-Romagna regions confirm that SEIRD(rm) fits the data more accurately than the original SEIRD model with constant rate infection parameter. Moreover, the increased flexibility in the choice of the infection rate function makes it possible to better control the predictions due to the lockdown policy. 12 the outbreak containment. 13 We consider here deterministic compartmental models, based on a system of initial 14 value problems of Ordinary Differential Equations. This theory has been studied since 15 the beginning of the century by W.O. Kermack and A. G. MacKendrick [3] who 16proposed the basic Susceptible-Infected-Removed (SIR) model. The SIR model and its 17 later modifications, such as Susceptible-Exposed-Infected-Removed (SEIR) [4] were later 18 introduced in the study of outbreaks diffusion. These models split the population into 19 : medRxiv preprint groups, compartments, and reproduce their behaviour by formalising their reciprocal 20 interactions. For example, the SIR model groups are Susceptible who can catch the 21 disease, Infected who have the disease and can spread it, and Removed those who have 22 either had the disease or are recovered, immune or isolated until recovery. The SEIR 23 model proposed by Chowell et al. [5] also considers the Exposed group: containing 24 individuals who are in the incubation period. 25The evolution of the Infected group depends on a critical parameter, usually denoted 26 as R0, representing the basic reproductive rate and it measures of how transferable a 27 disease is. This quantity determines whether the infection will spread exponentially, die 28 out, or remain constant. When R 0 > 1 the epidemic is spreading.
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