Marcello Delitala

Marcello Delitala
Politecnico di Torino | polito · DISMA - Department of Mathematical Sciences

Professor

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62
Publications
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Publications

Publications (62)
Article
Biological systems are typically composed of cells heterogeneous for genotype and phenotype, the latter being time-evolving in response to internal or external stimuli. In order to take these aspects into account, we here propose a modelling framework in which a discrete structuring variable distuinguishes cells according to their genotype while a...
Article
We here propose a one-dimensional spatially explicit phenotype-structured model to analyze selected aspects of avascular tumor progression. In particular, our approach distinguishes viable and necrotic cell fractions. The metabolically active part of the disease is, in turn, differentiated according to a continuous trait, that identifies cell varia...
Preprint
Full-text available
Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours, possibly with various degrees of resistance due to immunoediting and microenvironment. Tumours are able to expre...
Article
Full-text available
Hypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spatio-temporal processes that drive the adaptation of tumour cells to hypoxic and acidic microenvironments may open up new avenues of research in oncology and cancer treatm...
Preprint
Full-text available
Hypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spatio-temporal processes that drive the adaptation of tumour cells to hypoxic and acidic microenvironments may open up new avenues of research in oncology and cancer treatm...
Article
Full-text available
Despite the advances in the formulation of different therapies to fight cancer, the design of successful protocols is still a challenging problem. In order to provide some indications on the effectiveness of medical treatments, results from in silico experiments are presented based on a mathematical model comprising two cancer populations competing...
Article
Most models of cancer assume that tumor cells populations, at low densities, grow exponentially to be eventually limited by the available amount of resources such as space and nutrients. However, recent pre-clinical and clinical data of cancer onset or recurrence indicate the presence of a population dynamics in which growth rates increase with cel...
Article
Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours, possibly with various degrees of resistance due to immunoediting and microenvironment. Tumours are able to expre...
Article
Full-text available
Treatment of cancer relies increasingly on combination therapies to overcome cancer resistance, but the design of successful combined protocols is still an open problem. In order to provide some indications on the effectiveness of medical treatments, results from in silico experiments are presented based on a mathematical model comprising two cance...
Article
Drug resistance is one of the major obstacles to a successful treatment of cancer and, in turn, has been recognized to be linked to intratumoral heterogeneity, which increases the probability of the emergence of cancer clones refractory to treatment. Combination therapies have been introduced to overcome resistance, but the design of successful com...
Article
Accumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integro-differential model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Our model takes into account the effects of chemotaxis, adhesive i...
Article
T cells are key players in immune action against the invasion of target cells expressing non-self antigens. During an immune response, antigen-specific T cells dynamically sculpt the antigenic distribution of target cells, and target cells concurrently shape the host's repertoire of antigen-specific T cells. The succession of these reciprocal selec...
Article
Full-text available
How does immunotherapy affect the evolutionary dynamics of cancer cells? Can we enhance the anti-cancer efficacy of T cells by using different types of immune boosters in combination? Bearing these questions in mind, we present a mathematical model of cancer–immune competition under immunotherapy. The model consists of a system of structured equati...
Article
This paper deals with a class of integro-differential equations modeling the dynamics of a market where agents estimate the value of a given traded good. Two basic mechanisms are assumed to concur in value estimation: interactions between agents and sources of public information and herding phenomena. A general well-posedness result is established...
Article
This chapter focuses on selection and resistance to drugs in an integro-differential model describing the dynamics of a cancer cell population exposed to targeted chemotherapies. Mutations, proliferation and competition for resources are assumed to occur under the cytotoxic action of targeted therapeutic agents. The results obtained support the ide...
Chapter
Systems Biology is an interdisciplinary approach to understand biological processes that act on different scales. For example biochemical pathways steer internal cell dynamics, which can lead to cell movement. Cell movement can lead to cancer invasion and cancer invasion can lead to a disease that affects the whole body. To understand such a proces...
Book
This book is devoted to an overview of the status of the art in the study of complex systems, with particular focus on the analysis of systems pertaining to living matter. Both senior scientists and young researchers from diverse and prestigious institutions with a deliberately interdisciplinary cut were invited, in order to compare approaches and...
Article
Predator-prey ecosystems represent, among others, a natural context where evolutionary branching patterns may arise. Moving from this observation, the paper deals with a class of integro-differential equations modeling the dynamics of two populations structured by a continuous phenotypic trait and related by predation. Predators and preys prolifera...
Article
How do we recast the effects of molecular mimicry and genetic alterations affecting the T-cell response against self and non-self antigens into a mathematical model for the development of autoimmune disorders? Bearing this question in mind, we propose a model describing the evolution of a sample composed of immune cells and cells expressing self an...
Article
This paper is devoted to deriving formally the drift–diffusion limit for a kinetic-like model describing the dynamics of a monolayer sample of epithelial and mesenchymal cells, which move via chemotaxis on a flat surface, proliferate, and interact among themselves. The aim is to verify if the macroscopic equations resulting from the underlying mode...
Article
This paper presents a mathematical model for immune response against cancer aimed at reproducing emerging phenomena arising from the interactions between tumor and immune cells. The model is stated in terms of integro-differential equations and describes the dynamics of tumor cells, characterized by heterogeneous antigenic expressions, antigen-pres...
Article
This chapter originated from the idea that carcinogenesis can be considered as a multiscale morphogenetic process. A mathematical framework for modeling cell dynamics in multicellular systems is proposed. This framework is developed on the basis of the formal structures that are offered by the Kinetic Theory for Active Particles. A specific model f...
Article
This paper deals with a class of integro-differential equations arising in evolutionary biology to model the dynamics of specialist and generalist species related by mutualistic interactions. The effects of mutation events, proliferative phenomena and competition are taken into account. Specialist population is assumed to be structured by a continu...
Article
Full-text available
The present study is devoted to modelling the onset and the spread of epidemics. The mathematical approach is based on the generalized kinetic theory for active particles. The modelling includes virus mutations and the role of the immune system. Moreover, the heterogeneous distribution of patients is also taken into account. The structure allows th...
Article
This paper deals with the development of a mathematical model for the in vitro dynamics of malignant hepatocytes exposed to anti-cancer therapies. The model consists of a set of integro-differential equations describing the dynamics of tumor cells under the effects of mutation and competition phenomena, interactions with cytokines regulating cell p...
Article
Full-text available
This review reports the existing literature on traffic flow modelling in the framework of a critical overview which aims to indicate research perspectives. The contents mainly refer to modelling by fluid dynamic and kinetic equations and are arranged in three parts. The first part refers to methodological aspects of mathematical modelling and to th...
Article
This paper deals with some methodological aspects related to the discretization of a class of integro-differential equations modelling the evolution of the probability distribution over the microscopic state of a large system of interacting individuals. The microscopic state includes both mechanical and socio-biological variables. The discretizatio...
Article
The paper presents a model of virus mutations and evolution of epidemics in a system of interacting individuals, where the intensity of the pathology, described by a real discrete positive variable, is heterogeneously distributed, and the virus is in competition with the immune system or therapeutical actions. The model is developed within the fram...
Article
This paper deals with the development of a mathematical model that describes cancer dynamics at the cellular scale. The selected case study concerns colon and rectum cancer, which originates in colorectal crypts. Cells inside the crypts are assumed to be organized according to a compartmental-like arrangement and to be homogeneously mixing. A mathe...
Article
The paper proposes a rigorous method to construct the hyperbolic asymptotic limit of the discrete kinetic theory model of vehicular traffic proposed in [D. Helbing, “Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models”, Eur. Phys. J. B 69, 539–548 (2009)]. A second-order macro...
Article
This paper deals with the modelling of genetic mutations, which occur in almost all cells of a living system. The mutated cells display different stages of cancer progression and are contrasted by the action of the immune system cells. This investigation can be of interest in the evolutionary dynamics of cellular systems since the selective pressur...
Article
In this paper we formulate a discrete version of the bounded confidence model (Deffuant etal. in Adv Complex Syst 3:87–98, 2000; Weisbuch etal. in Complexity 7:55–63, 2002), which is representable as a family of ordinary differential equation systems. Then, we analytically study these systems. We establish the existence of equilibria which correspo...
Article
This paper is a review and critical analysis of the mathematical kinetic theory of active particles applied to the modelling of large living systems made up of interacting entities. The first part of the paper is focused on a general presentation of the mathematical tools of the kinetic theory of active particles. The second part provides a review...
Article
A mathematical framework of the kinetic theory of active particles is derived to couple two interacting systems at different scales. The dynamics at the higher scale is influenced by the lower scale. The analysis is focused on the coupling of multicellular systems in biology to the molecular scale, while the final aim consists in designing mathemat...
Article
This paper deals with a review and critical analysis on the mathematical kinetic theory of active particles applied to the modelling of the very early stage of cancer phenomena, specifically mutations, onset, progression of cancer cells, and their competition with the immune system. The mathematical theory describes the dynamics of large systems of...
Article
This paper deals with the definition of a general framework, inspired by the discrete generalized kinetic theory, suitable for the description of the evolution of opinions within a population in the presence of some external actions. As a conceivable application, a specific model of opinion formation is formulated, relying on the interactions of si...
Article
This paper deals with mathematical modelling, based on the kinetic theory of active particles, of a complex biological living system constituted by different populations of cells. The modelling refers to the competition between immune and tumor cells. Moreover, a qualitative and quantitative analysis is developed to show how the models can describe...
Article
This paper concerns a model of opinion formation in a population of interacting individuals under the influence of external leaders or persuaders, which act in a time periodic fashion. The model is formulated within a general framework inspired to a discrete generalized kinetic approach, which has been developed in Ref. 6. It is expressed by a syst...
Article
Full-text available
This paper deals with the modelling and simulation of traffic flow phenomena at the macroscopic level, based on a suitable development of the Aw-Rascle model, [A. Aw and M. Rascle, SIAM J. Appl. Math. 60, No. 3, 916–938 (2000; Zbl 0957.35086)], and its modification [F. Berthelin et al., Arch. Ration. Mech. Anal. 187, No. 2, 185–220 (2008; Zbl 1153....
Article
The mathematical approach proposed in this paper refers to the modelling of large systems of interacting entities whose microscopic state includes not only mechanical variables (typically position and velocity), but also specific activities of the single entity. Their number is sufficiently large to describe the overall state of the system by a sui...
Article
A conservative social dynamics model is developed within a discrete kinetic framework for active particles, which has been proposed in [M.L. Bertotti, L. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Mod. Meth. Appl. Sci. 14 (2004) 1061–1084]. The model concerns a society in which...
Article
Full-text available
In this paper, we establish and analyze a traffic flow model which describes the formation and dynamics of traffic jams. It consists of a pressureless gas dynamics system under a maximal constraint on the density and is derived through a singular limit of the Aw-Rascle model. From this analysis, we deduce the particular dynamical behavior of cluste...
Article
Following some general ideas on the discrete kinetic and stochastic game theory proposed by one of the Authors in a previous work, this paper develops a discrete velocity mathematical model for vehicular traffic along a one way road. The kinetic scale is chosen because, unlike the macroscopic one, it allows to capture the probabilistic essence of t...
Article
This paper deals with the modelling of vehicular traffic flow by methods of the discrete mathematical kinetic theory. The discretization is developed in the velocity space by a grid adapted to the local density. The discretization overcomes, at least in part, some technical difficulties related to the selection of the correct representation scale,...
Article
This paper deals with the modeling of complex social systems by methods of the mathematical kinetic theory for active particles. Specifically, a recent model by the last two authors is analyzed from the social sciences point of view. The model shows, despite its simplicity, some interesting features. In particular, this paper investigates the abili...
Chapter
Full-text available
Methods of mathematical kinetic theory have been recently developed to describe the collective behavior of large populations of interacting individuals such that their microscopic state is identified not only by a mechanical variable (typically position and velocity), but also by a biological state (or sociobiological state) related to their organi...
Article
This work deals with a family of dynamical systems which were introduced in [M.L. Bertotti, M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods Appl. Sci. 7 (2004) 1061–1084], modelling the evolution of a population of interacting individuals, distinguished by their so...
Article
This paper deals with the modelling of large systems of interacting individuals characterized by a microscopic state which includes both mechanical and socio-biological activities. The first part of the paper is devoted to the derivation and critical analysis of the modelling of microscopic equations and subsequently of the derivation of evolution...
Article
Full-text available
This paper deals with a critical analysis and some developments related to the mathema-tical literature on multiscale modelling of multicellular systems involving tumor immune cells competition at the cellular level. The analysis is focused on the development of mathematical methods of the classical kinetic theory to model the above physical sys-te...
Article
This paper deals with the analysis of a new class of models of population dynamics with kinetic interactions. The content is essentially methodological and is organized in two parts. The first one refers to modeling in the framework of the so-called generalized kinetic (Boltzmann) models. The second part deals with the modeling of microscopic inter...
Article
This paper deals with the modelling of the immune response to the evolution of progressing (corrupted) endothelial cells, i.e. cancer cells. A mathematical model is proposed, on the basis of mathematical methods of the kinetic theory for a large system of interacting cells. Then a qualitative analysis is carried out to prove the existence of the so...
Article
This paper deals with the design of mathematical frameworks for the modeling of traffic flow phenomena by suitable developments of classical models of the kinetic theory. Various types of evolution equations are deduced, and different mathematical structures are proposed toward conceivable applications.
Article
This paper develops a quantitative analysis of the asymptotic behavior of a class of integrodifferential equations modelling the competition between tumor cells and immune cells in the medium of environmental cells'. The analysis is: referred to as a well-defined therapeutical action, namely the possibility of modifying the ability, of neoplastic c...
Article
This paper deals with a critical analysis of the kinetic cellular theory which refers to the modelling of the immune response to the evolution of the progression of endothelial cells which have lost their differentiation and start their evolution towards metastatic states. The first part of the paper deals with the development of a general framewor...

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