Publications (33) View all
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Article: Cluster formation in opinion dynamics: a qualitative analysis
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ABSTRACT: 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 correspond to opinion profiles displaying a finite number of isolated clusters. We prove the asymptotic stability of some of these equilibria and show that they represent the asymptotic trend of the solutions of the systems under consideration. For a particular case, we also characterize the initial profiles that lead to different cluster configurations. Mathematics Subject Classification (2000)34C60-34D05-34D20-91F99 KeywordsOpinion formation-Bounded confidence model-Dynamical systems-Qualitative analysisZeitschrift für angewandte Mathematik und Physik ZAMP 04/2012; 61(4):583-602. · 0.95 Impact Factor -
Article: A mathematical model for the dynamics of cancer hepatocytes under therapeutic actions.
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ABSTRACT: 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 proliferation as well as the action of cytotoxic drugs and targeted therapeutic agents. Asymptotic analysis and simulations, developed with an exploratory aim, are addressed to enlighten the role played by the biological phenomena under consideration in the dynamics of hepatocellular carcinoma, with particular reference to the intra-tumor heterogeneity and the response to therapies. The obtained results suggest that cancer progression selects for highly proliferative clones. Moreover, it seems that intra-tumor heterogeneity makes targeted therapeutic agents to be less effective than cytotoxic drugs and a joint action of these two classes of agents may mutually increase their efficacy. Finally, it is highlighted how targeted therapeutic agents might act as an additional selective pressure leading to the selection for the most fitting, and then most resistant, cancer clones.Journal of Theoretical Biology 12/2011; 297:88-102. · 2.21 Impact Factor -
Article: Asymptotic limits of a discrete Kinetic Theory model of vehicular traffic.
Appl. Math. Lett. 01/2011; 24:672-678. -
Article: A mathematical model for progression and heterogeneity in colorectal cancer dynamics.
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ABSTRACT: 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 mathematical model for cancer progression is proposed here. This model describes the generation of multiple clonal sub-populations of cells at different progression stages in a single crypt. Asymptotic analysis and simulations are developed with an exploratory aim. The obtained results offer some insights into the role played by mutation, proliferation and differentiation phenomena on cancer dynamics. In particular, the acquisition of an additional growing power and a reduction for cellular differentiation seem more likely to be the driving force behind carcinogenesis rather than an increase in the mutation rate. The mutation rate instead seems to affect progression dynamics and intra-tumor heterogeneity. The role played by cells, at different differentiation stages, in the onset and progression of colorectal cancer is highlighted. The results support the fact that stem cells play a key role in cancer development and the idea that transit-amplifying cells could also take on an active role in carcinogenesis.Theoretical Population Biology 01/2011; 79(4):130-8. · 1.65 Impact Factor -
Article: On the modelling of genetic mutations and immune system competition
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ABSTRACT: 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 pressure on the mutated cells exerted by the immune system is analyzed. The proposed mathematical model is developed by means of the tools of the kinetic theory of active particles. Numerical simulations, obtained considering different values of the parameters in the model, show different emerging behaviors that are typical of the cancer-immune system competition.Computers & Mathematics with Applications 01/2011; 61(9):2362-2375. · 1.75 Impact Factor
