A Macroscopic Mathematical Model For Cell Migration Assays Using A Real-Time Cell Analysis

Experiments of cell migration and chemotaxis assays have been classically performed in the so-called Boyden Chambers. A recent technology, xCELLigence Real Time Cell Analysis, is now allowing to monitor the cell migration in real time. This technology measures impedance changes caused by the gradual increase of electrode surface occupation by cells during the course of time and provide a Cell Index which is proportional to cellular morphology, spreading, ruffling and adhesion quality as well as cell number. In this paper we propose a macroscopic mathematical model, based on \emph{advection-reaction-diffusion} partial differential equations, describing the cell migration assay using the real-time technology. We carried out numerical simulations to compare simulated model dynamics with data of observed biological experiments on three different cell lines and in two experimental settings: absence of chemotactic signals (basal migration) and presence of a chemoattractant. Overall we conclude that our minimal mathematical model is able to describe the phenomenon in the real time scale and numerical results show a good agreement with the experimental evidences

Analysis of a model for waterborne diseases with Allee effect on bacteria

A limitation of current modeling studies in waterborne diseases (one of the leading causes of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs model with bacterial growth inducing Allee effect. We adopt an adequate functional response to significantly express the shape of indirect transmission. The existence and stability of biologically meaningful equilibria is investigated through a detailed discussion of both backward and Hopf bifurcations. The sensitivity analysis of the basic reproduction number is performed. Numerical simulations confirming the obtained results in two different scenarios are shown

A “pay-how-you-drive” car insurance approach through cluster analysis

As discussed in the recent literature, several innovative car insurance concepts are proposed in order to gain advantages both for insurance companies and for drivers. In this context, the “pay-how-you-drive” paradigm is emerging, but it is not thoroughly discussed and much less implemented. In this paper, we propose an approach in order to identify the driver behavior exploring the usage of unsupervised machine learning techniques. A real-world case study is performed to evaluate the effectiveness of the proposed solution. Furthermore, we discuss how the proposed model can be adopted as risk indicator for car insurance companies

Modelli stocastici per la dinamica di neuroni singoli e accoppiati: aspetti computazionali, simulazioni e risultati asintotici

Questa tesi ripercorre i modelli storicamente proposti per lo studio della trasmissione del segnale sinaptico, soffermandosi in particolare sui modelli stocastici. A partire dall'identificazione fondamentale dell'istante in cui un potenziale di azione viene generato con il tempo di "primo passaggio" per il processo stocastico che descrive la dinamica del potenziale di membrana, vengono presentati il classico modello LIF ed alcune sue estensioni da noi proposte, sia nel caso di un singolo neurone che di una coppia di neuroni interagenti. Per questi modelli sono stati ottenuti risultati teorici e stime asintotiche; sono poi stati realizzati ed implementati algoritmi numerici per la simulazione degli spari e la determinazione della densità del tempo di primo passaggio come soluzione di una equazione integrale. Infine è stato realizzato un pacchetto software per la generazione di tempi di primo passaggio per processi di diffusione gaussiani attraverso soglie sufficientemente regolari

Traveling Band Solutions in a System Modeling Hunting Cooperation

A classical Lotka–Volterra model with the logistical growth of prey-and-hunting cooperation in the functional response of predators to prey was extended by introducing advection terms, which included the velocities of animals. The effect of velocity on the kinetics of the problem was analyzed. In order to examine the band behavior of species over time, traveling wave solutions were introduced, and conditions for the coexistence of both populations and/or extinction were found. Numerical simulations illustrating the obtained results were performed

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered. The conditions for the onset of cross-diffusion-driven instability are obtained by linear stability analysis. The technique of multiple time scales is employed to deduce the amplitude equation near Turing bifurcation threshold by choosing the cross-diffusion coefficient as a bifurcation parameter. The stability analysis of these amplitude equations leads to the identification of various Turing patterns driven by the cross-diffusion, which are also investigated through numerical simulations

A Preliminary Investigation of a Single Shock Impact on Italian Mortality Rates Using STMF Data: A Case Study of COVID-19

Mortality shocks, such as pandemics, threaten the consolidated longevity improvements, confirmed in the last decades for the majority of western countries. Indeed, just before the COVID-19 pandemic, mortality was falling for all ages, with a different behavior according to different ages and countries. It is indubitable that the changes in the population longevity induced by shock events, even transitory ones, affecting demographic projections, have financial implications in public spending as well as in pension plans and life insurance. The Short Term Mortality Fluctuations (STMF) data series, providing data of all-cause mortality fluctuations by week within each calendar year for 38 countries worldwide, offers a powerful tool to timely analyze the effects of the mortality shock caused by the COVID-19 pandemic on Italian mortality rates. This dataset, recently made available as a new component of the Human Mortality Database, is described and techniques for the integration of its data with the historical mortality time series are proposed. Then, to forecast mortality rates, the well-known stochastic mortality model proposed by Lee and Carter in 1992 is first considered, to be consistent with the internal processing of the Human Mortality Database, where exposures are estimated by the Lee–Carter model; empirical results are discussed both on the estimation of the model coefficients and on the forecast of the mortality rates. In detail, we show how the integration of the yearly aggregated STMF data in the HMD database allows the Lee–Carter model to capture the complex evolution of the Italian mortality rates, including the higher lethality for males and older people, in the years that follow a large shock event such as the COVID-19 pandemic. Finally, we discuss some key points concerning the improvement of existing models to take into account mortality shocks and evaluate their impact on future mortality dynamics

Stochastic modeling of the firing activity of coupled neurons periodically driven

A stochastic model for describing the firing activity of a couple of interacting neurons subject to time-dependent stimuli is proposed. Two stochastic differential equations suitably coupled and including periodic terms to represent stimuli imposed to one or both neurons are considered to describe the problem. We investigate the first passage time densities through specified firing thresholds for the involved time non-homogeneous Gauss-Markov processes. We provide simulation results and numerical approximations of the firing densities. Asymptotic behaviors of the first passage times are also given

A discrete kinetic approximation for the incompressible Navier-Stokes equations

In this paper we introduce a new class of numerical schemes for the incompressible Navier-Stokes equations, which are inspired by the theory of discrete kinetic schemes for compressible fluids. For these approximations it is possible to give a stability condition, based on a discrete velocities version of the Boltzmann H-theorem. Numerical tests are performed to investigate their convergence and accuracy