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. The outputs of the model were also compared with the data from the Italian COVID-19 experience to provide a crude assessment of the goodness of the enacted interventions prior to the onset of the Omicron variant.

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. To cope with this multi-phasic character, we propose a theoretical approach to the modeling of overall pandemic courses, that we term multi-period/multi-phasic, based on a specific definition of phase. This allows a unified and parsimonious representation of complex epidemic courses even when vaccination and virus' variants are considered, through sequences of weak ergodic renewal equations that become fully ergodic when appropriate conditions are met. Specific hypotheses on epidemiological and intervention parameters allow reduction to simple models. The framework suggest a simple, theory driven, approach to data explanation that allows an accurate reproduction of the overall course of the COVID-19 epidemic in Italy since its beginning (February 2020) up to omicron onset, confirming the validity of the concept.

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 proof of the estimates for the dual approximating system requires a more challenging treatment since the trajectories are not absolutely continuous, but only with bounded variation. These allow to pass to the limit to obtain the conditions of optimality for the primal problem and lead to a singular dual backward system with a generalized solution in the sense of measure. As far as we know, this approach developed here for the identification of parameters in an epidemic model considering a state constraint related to the actions undertaken for the disease containment was not addressed in the literature and represents a novel issue in this paper.

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.e. on the case corresponding to the normal status of the skin. A numerical scheme to compute the solution of the model is proposed and its convergence is studied. Simulations are provided for realistic values of the parameters, showing the possibility of reproducing the structure of both "thin" and "thick" epidermis.

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. We prove a global-in-time solution for the asymptotic model setup with respect to the small parameter of the problem, for arbitrarily large initial data. Next, we deal with the control problem focusing mainly on the reduction of the chemoattractant concentration, by acting upon the initial distribution of the bacteria population b0. To this end, we prove the existence of a solution to the control problem and determine the optimality conditions.

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. This hypothesis, based on experimental evidence, allows us to determine a constitutive equation for the cell velocity. We focus on the stationary case of the problem, that takes the form of a quasi-linear evolution problem of first order, and we investigate conditions under which there is a solution.

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. A total of 74 patients underwent ARFI elastography, APRI index, FibroMax and successful liver biopsy. RESULTS: The noninvasive tests had a good correlation with the liver biopsy results. The most powerful test in predicting fibrosis was ARFI elastography. The diagnostic accuracy of ARFI elastography, expressed as area under receiver operating characteristic curve (AUROC) had a validity of 90.2% (95% CI AUROC = 0.831-0.972, P < 0.001) for the diagnosis of significant fibrosis (F >or= 2). ARFI sonoelastography predicted even better F3 or F4 fibrosis (AUROC = 0.993, 95% CI = 0.979-1). CONCLUSION: ARFI elastography had very good accuracy for the assessment of liver fibrosis and was superior to other noninvasive methods (APRI Index, FibroMax) for staging liver fibrosis.