Epidemic control by social distancing and vaccination: Optimal strategies and remarks on the COVID-19 Italian response policy.

After the many failures in the control of the COVID-19 pandemic, identifying robust principles of epidemic control will be key in future preparedness. In this work, we propose an optimal control model of an age-of-infection transmission model under a two-phase control regime where social distancing is the only available control tool in the first phase, while the second phase also benefits from the arrival of vaccines. We analyzed the problem by an ad-hoc numerical algorithm under a strong hypothesis implying a high degree of prioritization to the protection of health from the epidemic attack, which we termed the "low attack rate" hypothesis.

Multiple pandemic waves vs multi-period/multi-phasic epidemics: Global shape of the COVID-19 pandemic.

The overall course of the COVID-19 pandemic in Western countries has been characterized by complex sequences of phases. In the period before the arrival of vaccines, these phases were mainly due to the alternation between the strengthening/lifting of social distancing measures, with the aim to balance the protection of health and that of the society as a whole. After the arrival of vaccines, this multi-phasic character was further emphasized by the complicated deployment of vaccination campaigns and the onset of virus' variants.

Parameter Estimation of an Epidemic Model with State Constraints.

We consider a mathematical model with five compartments relevant to depict the feature of a certain type of epidemic transmission. We aim to identify some system parameters by means of a minimization problem for a functional involving available measurements for observable compartments, which we treat by an optimal control technique with a state constraint imposed by realistic considerations. The proof of the maximum principle is done by passing to the limit in the conditions of optimality for an appropriate approximating problem.

The steady state of epidermis: mathematical modeling and numerical simulations.

We consider a model with age and space structure for the epidermis evolution. The model, previously presented and analyzed with respect to the suprabasal epidermis, includes different types of cells (proliferating cells, differentiated cells, corneous cells, and apoptotic cells) moving with the same velocity, under the constraint that the local volume fraction occupied by the cells is constant in space and time. Here, we complete the model proposing a mechanism regulating the cell production in the basal layer and we focus on the stationary case of the problem, i.

A control problem for a cross-diffusion system in a nonhomogeneous medium.

We study a model, motivated by a bioremediation process, describing a cross-diffusion movement of a bacteria population b attracted by a chemoattractant signal c, in a nonhomogeneous stratified medium with n layers. We assume that this reaction-diffusion process is characterized by a low rate of degradation and a low diffusion coefficient of the chemoattractant, expressed in the model by a small parameter ϵ. The model consists of n systems of nonlinear parabolic equations with transmission conditions between layers.

An age-structured model of epidermis growth.

We propose a model with age and space structure for the evolution of the supra-basal epidermis. The model includes different types of cells: proliferating cells, differentiated cells, corneous cells, and apoptotic cells. We assume that all cells move with the same velocity and that the local volume fraction, occupied by the cells is constant in space and time.

Acoustic radiation force imaging sonoelastography for noninvasive staging of liver fibrosis.

Aim: To investigate the diagnostic accuracy of acoustic radiation force impulse (ARFI) imaging as a noninvasive method for the assessment of liver fibrosis in chronic hepatitis C (CHC) patients.

Methods: We performed a prospective blind comparison of ARFI elastography, APRI index and FibroMax in a consecutive series of patients who underwent liver biopsy for CHC in University Hospital Bucharest. Histopathological staging of liver fibrosis according to the METAVIR scoring system served as the reference.