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This paper proposes a model of the dynamics of credit contagion through non-performing loans on financial networks. Credit risk contagion is modeled in the context of the classical SIS (Susceptibles-Infected-Susceptibles) epidemic processes on networks but with a fundamental novelty. In fact, we assume the presence of two different classes of infected agents, and then we differentiate the dynamics of assets subject to idiosyncratic risk from those affected by systemic risk by adopting a SIIS (Susceptible-Infected1-Infected2-Susceptible) model. In the recent literature in this field, the effect of systemic credit risk on the performance of the financial network is a hot topic. We perform numerical simulations intended to explore the roles played by two different network structures on the long-term behavior of assets affected by systemic risk in order to analyze the effect of the topology of the underlying network structure on the spreading of systemic risk on the structure. Random graphs, i.e., the Erd&ouml, s&ndash, R&eacute, nyi model, are considered &ldquo, benchmark&rdquo, network structures while core-periphery structures are often indicated in the literature as idealized structures, although they are able to capture interesting, specific features of real-world financial networks. Moreover, as a matter of comparison, we also perform numerical experiments on small-world networks.

This paper adopts the Kinetic Theory for Active Particles (KTAP) approach to model the dynamics of liquidity profiles on a complex adaptive network system that mimic a stylized financial market. Individual incentives of investors to form or delete a link is driven, in our modelling framework, by stochastic game-type interactions modelling the phenomenology related to policy rules implemented under Basel III, and it is exogeneously and dynamically influenced by a measure of overnight interest rate. The strategic network formation dynamics that emerges from the introduced transition probabilities modelling individual incentives of investors to form or delete links, provides a wide range of measures using which networks might be considered “best” from the point of view of the overall welfare of the system. We use the time evolution of the aggregate degree of connectivity to measure the time evolving network efficiency in two different scenarios, suggesting a first analysis of the stability of the arising and evolving network structures.

A learning dynamics on network is introduced, characterized by binary and multiple nonlinear interactions among the individuals distributed in the different nodes. A particular topology of the network is considered by introducing a leader node which influences all the other “follower” nodes without being influenced in turn. Numerical simulations are provided, particularly focusing on the effect of the network structure and of the nonlinear interactions on the emerging behaviour of the system. It turns out that the leader node always exhibits an autonomous evolution, while the follower nodes may have a regression when the interactions with the leader node are switched off. There is instead a remarkable change in the final configurations of the follower nodes, even if only one of them is connected to the leader: indeed, due to the microscopic interactions among them, all the follower nodes feel a strong “leader effect”.

The complex interactions between human behaviors and social economic sciences is critically analyzed in this paper in view of possible applications of mathematical modeling as an attainable interdisciplinary approach to understand and simulate the aforementioned dynamics. The quest is developed along three steps: Firstly an overall analysis of social and economic sciences indicates the main requirements that a contribution of mathematical modeling should bring to these sciences; subsequently the focus moves to an overview of mathematical tools and to the selection of those which appear, according to the authors bias, appropriate to the modeling; finally, a survey of applications is presented looking ahead to research perspectives.

This paper presents a new approach to the modeling of boundary conditions for first order models of vehicular traffic in highways. The first step consists in deriving a model for the dynamics of the flow of vehicles. Simulations of the parameters lead to a detailed analysis of the qualitative properties of the model. Subsequently, for such model, the statement of initial-boundary value problems is deduced, with domain decomposition, for a tract of highway between tollgates.

We introduce and discuss a dynamics of interaction of risky assets in a portfolio by resorting to methods of statistical mechanics developed to model the evolution of systems whose microscopic state may be augmented by variables which are not mechanical. Statistical methods are applied in the present paper in order to forecast the dynamics of risk/return efficient frontier for equity risk. Specifically, we adopt the methodologies of the kinetic theory for active particles (KTAP) with stochastic game-type interactions and apply the proposed model to a case study analyzing a subset of stocks traded in Milan Stock Exchange. In particular, we evaluate the efficient risk/return frontier within the mean/variance portfolio optimization theory for 13 principal components of the Milan Stock Exchange and apply the proposed kinetic model to forecast its short-term evolution (within one year). The model has the aim to pave the way to many different research perspectives and applications discussed eventually in the paper. In particular, the case of efficient frontier obtained by minimizing the Conditional Value-at-Risk (CVaR) is introduced and a preliminary result is proposed.

In this paper we analyze emergent collective phenomena in the evolution of opinions in a society structured into few interacting nodes of a network. The presented mathematical structure combines two dynamics: a first one on each single node and a second one among the nodes, i.e. in the network. The aim of the model is to analyze the effect of a network structure on a society with respect to opinion dynamics and we show some numerical solutions addressed in this direction, i.e. comparing the emergent behaviors of a consensus-dissent dynamic on a single node when the effect of the network is not considered, with respect to the emergent behaviors when the effect of a network structure linking few interacting nodes is considered. We adopt the framework of the Kinetic Theory for Active Particles (KTAP), deriving a general mathematical structure which allows to deal with nonlinear features of the interactions and representing the conceptual framework toward the derivation of specific models. A specific model is derived from the general mathematical structure by introducing a consensus-dissent dynamics of interactions and a qualitative analysis is given.

In this paper we review methods that allow the construction of a consistent set of models that may describe the interactions between a tumor and the immune system on microscopic, mesoscopic, and macroscopic scales. The presented structures may be a basis for a description on the sub–cellular, cellular, and macroscopic levels. Important open problems are indicated.

The kinetic theory approach is successfully used to model complex phenomena related to social systems, allowing to predict the dynamics and emergent behavior of large populations of agents. In particular, kinetic theory for active particles (KTAP) models are usually analyzed by numerically solving the underlying Boltzmann-type differential equations through ad-hoc implementations. In this paper, we present KAOS: a kinetic theory of active particles modeling and analysis software tool. To the best of our knowledge, KAOS represents the first attempt to design and implement a comprehensive tool that assists the user in all the steps of the modeling process in the framework of the kinetic theories, from the model definition to the representation of transient solutions. To show the KAOS features, we present a new model capturing the competition/cooperation dynamics of a socio-economic system with welfare dynamics, in different socio-political conditions