Multiscale biological tissue models and flux-limited chemotaxis for multicellular growing systems

This paper deals with the derivation of macroscopic tissue models from the underlying description delivered by a class of equations that models binary mixtures of multicellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modi¯cation of the biological functions and proliferative and destructive events. The asymptotic analysis deals with suitable parabolic and hyperbolic limits, and is speci¯cally focused on the modeling of the chemotaxis phenomena

Multiscale biological tissue models and flux-limited chemotaxis for multicellular growing systems

This paper deals with the derivation of macroscopic tissue models from the underlying description delivered by a class of equations that models binary mixtures of multicellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modi¯cation of the biological functions and proliferative and destructive events. The asymptotic analysis deals with suitable parabolic and hyperbolic limits, and is speci¯cally focused on the modeling of the chemotaxis phenomen

On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state

We show that a pair of conjectures raised in [11] concerning the construction of normal solutions to the relativistic Boltzmann equation are valid. This ensures that the results in [11] hold for any range of positive temperatures and that the relativistic Euler system under the kinetic equation of state is hyperbolic and the speed of sound cannot overcome $c/\sqrt{3}$.Comment: 6 pages. Abridged version; full version to appear in Commun. Pure Appl. Ana

Fixed Point Results for Generalized Chatterjea Type Contractive Conditions in Partially Ordered -Metric Spaces

In the framework of ordered -metric spaces, fixed points of maps that satisfy the generalized ( , )-Chatterjea type contractive conditions are obtained. The results presented in the paper generalize and extend several well known comparable results in the literature

A multiscale model of virus pandemic: Heterogeneous interactive entities in a globally connected world

This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called SARS–CoV–2 Severe Acute Respiratory Syndrome, corona virus n.2. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from the small scale of the virus itself and cells, to the large scale of individuals and further up to the collective behaviour of populations. An interdisciplinary vision is developed thanks to the contributions of epidemiologists, immunologists and economists as well as those of mathematical modellers. The first part of the contents is devoted to understanding the complex features of the system and to the design of a modelling rationale. The modelling approach is treated in the second part of the paper by showing both how the virus propagates into infected individuals, successfully and not successfully recovered, and also the spatial patterns, which are subsequently studied by kinetic and lattice models. The third part reports the contribution of research in the fields of virology, epidemiology, immune competition, and economy focussed also on social behaviours. Finally, a critical analysis is proposed looking ahead to research perspectives.publishedVersionFil: Bellomo, Nicola. Universidad de Granada. Departamento de Matemática Aplicada; España.Fil: Bingham, Richard. University of York. Departments of Mathematics and Biology. Cross-disciplinary Centre for Systems Analysis; United Kingdom.Fil: Chaplain, Mark A. J. University of St Andrews. School of Mathematics and Statistics; Scotland.Fil: Dosi, Giovanni. Scuola Superiore Sant’Anna. Institute of Economics and EMbeDS; Italia.Fil: Forni, Guido. Accademia Nazionale dei Lincei; Italia.Fil: Knopoff, Damian A. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.Fil: Knopoff, Damian A. Consejo Nacional de Investigaciones Científicas y Técnicas de Argentina. Centro de Investigacion y Estudios de Matematica; Argentina.Fil: Lowengrub, John. University California Irvine. Department of Mathematics; United States.Fil: Twarock, Reidun. University of York. Departments of Mathematics and Biology. Cross-disciplinary Centre for Systems Analysis; United Kingdom.Fil: Virgillito, Maria Enrica.Scuola Superiore Sant’Anna. Institute of Economics and EMbeDS; Italia

Kinetic Theory Approach to Modeling of Cellular Repair Mechanisms under Genome Stress

Under acute perturbations from outer environment, a normal cell can trigger cellular self-defense mechanism in response to genome stress. To investigate the kinetics of cellular self-repair process at single cell level further, a model of DNA damage generating and repair is proposed under acute Ion Radiation (IR) by using mathematical framework of kinetic theory of active particles (KTAP). Firstly, we focus on illustrating the profile of Cellular Repair System (CRS) instituted by two sub-populations, each of which is made up of the active particles with different discrete states. Then, we implement the mathematical framework of cellular self-repair mechanism, and illustrate the dynamic processes of Double Strand Breaks (DSBs) and Repair Protein (RP) generating, DSB-protein complexes (DSBCs) synthesizing, and toxins accumulating. Finally, we roughly analyze the capability of cellular self-repair mechanism, cellular activity of transferring DNA damage, and genome stability, especially the different fates of a certain cell before and after the time thresholds of IR perturbations that a cell can tolerate maximally under different IR perturbation circumstances

Mathematical models for immunology:current state of the art and future research directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years