Search

We propose a non-local model for contact guidance and steric hindrance depending on a single external cue, namely the extracellular matrix, that affects in a twofold way the polarization and speed of motion of the cells. We start from a microscopic description of the stochastic processes underlying the cell re-orientation mechanism related to the change of cell speed and direction. Then, we formally derive the corresponding kinetic model that implements exactly the prescribed microscopic dynamics, and, from it, it is possible to deduce the macroscopic limit in the appropriate regime. Moreover, we test our model in several scenarios. In particular, we numerically investigate the minimal microscopic mechanisms that are necessary to reproduce cell dynamics by comparing the outcomes of our model with some experimental results related to breast cancer cell migration. This allows us to validate the proposed modeling approach and to highlight its capability of predicting qualitative cell behaviors in diverse heterogeneous microenvironments. [ABSTRACT FROM AUTHOR]

In the mathematical epidemiology community, there is an increasing interest in shaping the complex interplay between human behaviour and disease spreading. We give a contribution in this direction by illustrating a method to derive behavioural change epidemic models from a stochastic particle description by the means of kinetic equations. We consider a susceptible–infected–removed-like model where contact rates depend on the behavioural patterns adopted across the population. The selection of the social behaviour happens during the interactions between individuals adopting alternative strategies and it is driven by an imitation game dynamics. Agents have a double microscopic state: a discrete label, which denotes the epidemiological compartment to which they belong, and the degree of flexibility of opinion, i.e. a measure of the personal attitude to change opinion and, hence, to switch between the alternative social contact patterns. We derive kinetic evolution equations for the distribution functions of the degree of flexibility of opinion of the individuals for each compartment, whence we obtain macroscopic equations for the densities and average flexibilities of opinion. After providing the basic properties of the macroscopic model, we numerically investigate it by focusing on the impact of the flexibility of opinion on the epidemic course and on the consequent behavioural responses. [ABSTRACT FROM AUTHOR]

In classical epidemic models, a neglected aspect is the heterogeneity of disease transmission and progression linked to the viral load of each infected individual. Here, we investigate the interplay between the evolution of individuals' viral load and the epidemic dynamics from a theoretical point of view. We propose a stochastic particle model describing the infection transmission and the individual physiological course of the disease. Agents have a double microscopic state: a discrete label, that denotes the epidemiological compartment to which they belong and switches in consequence of a Markovian process, and a microscopic trait, measuring their viral load, that changes in consequence of binary interactions or interactions with a background. Specifically, we consider Susceptible–Infected–Removed–like dynamics where infectious individuals may be isolated and the isolation rate may depend on the viral load–sensitivity and frequency of tests. We derive kinetic evolution equations for the distribution functions of the viral load of the individuals in each compartment, whence, via upscaling procedures, we obtain macroscopic equations for the densities and viral load momentum. We perform then a qualitative analysis of the ensuing macroscopic model. Finally, we present numerical tests in the case of both constant and viral load–dependent isolation control. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Boltzmann-type kinetic description of opinion formation on social networks, which takes into account a general connectivity distribution of the individuals. We consider opinion exchange processes inspired by the Sznajd model and related simplifications but we do not assume that individuals interact on a regular lattice. Instead, we describe the structure of the social network statistically, assuming that the number of contacts of a given individual determines the probability that their opinion reaches and influences the opinion of another individual. From the kinetic description of the system, we study the evolution of the mean opinion, whence we find precise analytical conditions under which a polarization switch of the opinions, i.e. a change of sign between the initial and the asymptotic mean opinions, occurs. In particular, we show that a non-zero correlation between the initial opinions and the connectivity of the individuals is necessary to observe polarization switch. Finally, we validate our analytical results through Monte Carlo simulations of the stochastic opinion exchange processes on the social network. This article is part of the theme issue 'Kinetic exchange models of societies and economies'. [ABSTRACT FROM AUTHOR]

The aim of this article is to study the stability of a non-local kinetic model proposed by Loy & Preziosi (2020a) in which the cell speed is affected by the cell population density non-locally measured and weighted according to a sensing kernel in the direction of polarization and motion. We perform the analysis in a |$d$| -dimensional setting. We study the dispersion relation in the one-dimensional case and we show that the stability depends on two dimensionless parameters: the first one represents the stiffness of the system related to the cell turning rate, to the mean speed at equilibrium and to the sensing radius, while the second one relates to the derivative of the mean speed with respect to the density evaluated at the equilibrium. It is proved that for Dirac delta sensing kernels centered at a finite distance, corresponding to sensing limited to a given distance from the cell center, the homogeneous configuration is linearly unstable to short waves. On the other hand, for a uniform sensing kernel, corresponding to uniformly weighting the information collected up to a given distance, the most unstable wavelength is identified and consistently matches the numerical solution of the kinetic equation. [ABSTRACT FROM AUTHOR]