A behavioural modelling approach to assess the impact of COVID-19 vaccine hesitancy.

We introduce a compartmental epidemic model to describe the spread of COVID-19 within a population, assuming that a vaccine is available, but vaccination is not mandatory. The model takes into account vaccine hesitancy and the refusal of vaccination by individuals, which take their decision on vaccination based on both the present and past information about the spread of the disease. Theoretical analysis and simulations show that voluntary vaccination can certainly reduce the impact of the disease but is unable to eliminate it.

On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies.

Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a major simplification consists in assuming that the infectious period is exponentially distributed, then implying that the chance of recovery is independent on the time since infection. Here, we first attempt to investigate the consequences of relaxing this assumption on the performances of time-variant disease control strategies by using optimal control theory.

Two-temperature Navier-Stokes equations for a polyatomic gas derived from kinetic theory.

A polyatomic gas with slow relaxation of the internal modes is considered, and the Navier-Stokes equations with two temperatures, the translational and internal temperatures, are derived for such a gas on the basis of the ellipsoidal-statistical (ES) model of the Boltzmann equation for a polyatomic gas, proposed by Andries et al. [Eur. J.

Glioma invasion and its interplay with nervous tissue and therapy: A multiscale model.

A multiscale mathematical model for glioma cell migration and proliferation is proposed, taking into account a possible therapeutic approach. Starting with the description of processes occurring at the subcellular level, the equation for the mesoscopic level is formulated and a macroscopic model is derived, via parabolic limit and Hilbert expansions in the moment equations. After the model set up and the study of the well-posedness of this macroscopic setting, we investigate the role of the fibers in the tumor dynamics.

Optimal control of epidemic size and duration with limited resources.

The total number of infections (epidemic size) and the time needed for the infection to go extinct (epidemic duration) represent two of the main indicators for the severity of infectious disease epidemics in human and livestock. However, few attempts have been made to address the problem of minimizing at the same time the epidemic size and duration from a theoretical point of view by using optimal control theory. Here, we investigate the multi-objective optimal control problem aiming to minimize, through either vaccination or isolation, a suitable combination of epidemic size and duration when both maximum control effort and total amount of resources available during the entire epidemic period are limited.

Time-optimal control strategies in SIR epidemic models.

We investigate the time-optimal control problem in SIR (Susceptible-Infected-Recovered) epidemic models, focusing on different control policies: vaccination, isolation, culling, and reduction of transmission. Applying the Pontryagin's Minimum Principle (PMP) to the unconstrained control problems (i.e.

React or wait: which optimal culling strategy to control infectious diseases in wildlife.

We applied optimal control theory to an SI epidemic model to identify optimal culling strategies for diseases management in wildlife. We focused on different forms of the objective function, including linear control, quadratic control, and control with limited amount of resources. Moreover, we identified optimal solutions under different assumptions on disease-free host dynamics, namely: self-regulating logistic growth, Malthusian growth, and the case of negligible demography.

How different two almost identical action potentials can be: a model study on cardiac repolarization.

Spatial heterogeneity in the properties of ion channels generates spatial dispersion of ventricular repolarization, which is modulated by gap junctional coupling. However, it is possible to simulate conditions in which local differences in excitation properties are electrophysiologically silent and only play a role in pathological states. We use a numerical procedure on the Luo-Rudy phase 1 model of the ventricular action potential (AP1) in order to find a modified set of model parameters which generates an action potential profile (AP2) almost identical to AP1.

Kinetic Bhatnagar-Gross-Krook model for fast reactive mixtures and its hydrodynamic limit.

A recently proposed consistent Bhatnagar-Gross-Krook-type approach for reversible bimolecular chemical reactions, well suited to deal with collision dominated gas mixtures in which mechanical and chemical relaxation times are of the same order of magnitude (fast reactions), is discussed. The model recovers essential features of the chemical process such as mass action law at equilibrium and reactive H theorem. The hydrodynamic limit, at both Euler and Navier-Stokes levels, is derived by a Chapman-Enskog procedure, in terms of the relevant hydrodynamic variables, and compared to the corresponding limits holding in the nonreactive and in the slowly reactive cases.

Effects of predation efficiencies on the dynamics of a tritrophic food chain.

In this paper the dynamics of a tritrophic food chain (resource, consumer, top predator) is investigated, with particular attention not only to equilibrium states but also to cyclic behaviours that the system may exhibit. The analysis is performed in terms of two bifurcation parameters, denoted by p and q, which measure the efficiencies of the interaction processes. The persistence of the system is discussed, characterizing in the (p; q) plane the regions of existence and stability of biologically significant steady states and those of existence of limit cycles.

Modelling of predator-prey trophic interactions. Part II: three trophic levels.

A general class of lumped parameter models describing the local dynamics of a tri-trophic chain in a controlled environment is analyzed in detail. The trophic functions characterizing the interactions are defined only by some properties and allow us to treat both prey-dependent and ratio-dependent models in a unified manner. Conditions for existence and stability of extinction and coexistence equilibrium states are determined.

Effect of input resistance voltage-dependency on DC estimate of membrane capacitance in cardiac myocytes.

The measure of membrane capacitance (C(m)) in cardiac myocytes is of primary importance as an index of their size in physiological and pathological conditions, and for the understanding of their excitability. Although a plethora of very accurate methods has been developed to access C(m) value in single cells, cardiac electrophysiologists still use, in the majority of laboratories, classical direct current techniques as they have been established in the early days of cardiac cellular electrophysiology. These techniques are based on the assumption that cardiac membrane resistance (R(m)) is constant, or changes negligibly, in a narrow potential range around resting potential.

Modelling of predator-prey trophic interactions. Part I: two trophic levels.

A class of lumped parameter models to describe the local dynamics in a controlled environment of a two-trophic chain is considered. The class is characterized by a trophic function (functional response of predator to the abundance of prey) depending on the ratio of prey biomass x and a linear function of predator biomass y: f(qx/[(1-rho)k + rhoy]), where q is the efficiency of the predation process, k is a reference biomass, and rho (0 < or = rho < or = 1) specifies the predation model. The trophic function is defined only by some properties determining its shape.

[The efficacy of oral treatment with flecainide for paroxysmal atrial fibrillation: correlation with plasma concentration].

In the acute treatment of paroxysmal atrial fibrillation several drugs can be used. The aim of our work was to assess the efficacy of a single oral dose of flecainide in the conversion to sinus rhythm by correlating this data with flecainide plasma concentration. We have considered 37 patients affected by paroxysmal atrial fibrillation (for more than 8 hours) randomly assigned to the following two groups: group A, 19 patients, mean age 44.