Spatially extended SHAR epidemiological framework of infectious disease transmission

Mathematical models play an important role in epidemiology. The inclusion of a spatial component in epidemiological models is especially important to understand and address many relevant ecological and public health questions, e.g., when wanting to differentiate transmission patterns across geographical regions or when considering spatially heterogeneous intervention measures. However, the introduction of spatial effects can have significant consequences on the observed model dynamics and hence must be carefully analyzed and interpreted. Cellular automata epidemiological models typically rely on simplified computational grids but can provide valuable insight into the spatial dynamics of transmission within a population by suitably accounting for the connections between individuals in the considered community. In this paper, we describe a stochastic cellular automata disease model based on an extension of the traditional Susceptible-Infected-Recovered (SIR) compartmentalization of the population, namely, the Susceptible-Hospitalized-Asymptomatic-Recovered (SHAR) formulation, in which infected individuals either present a severe form of the disease, thus requiring hospitalization, or belong to the so-called mild/asymptomatic class. The critical transmission threshold is derived analytically in the nonspatial SHAR formulation, and this generalizes previously obtained theoretical results for the SIR model. We present simulation results discussing the effect of key model parameters and of spatial correlations on model outputs and propose an algorithm for tracking the evolution of infection clusters within the considered population. Focusing on the role of import and criticality on the overall dynamics, we conclude that the current spatial setting increases the critical transmission threshold in comparison to the nonspatial model.Fil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Cusimano, Nicole. Basque Center For Applied Mathematics; EspañaFil: Stollenwerk, Nico. Basque Center For Applied Mathematics; EspañaFil: Aguiar, Maíra. Basque Center For Applied Mathematics; Españ

Parameter estimation and measurement of social inequality in a kinetic model forwealth distribution

This paper deals with the modeling of wealth distribution considering a society with non-constant population and non-conservative wealth trades. The modeling approach is based on the kinetic theory of active particles, where individuals are distinguished by a scalar variable (the activity) which expresses their social state. A qualitative analysis of the model focusing on asymptotic behaviors and measurement of inequality through the Gini coefficient is presented. Finally, some specific case-studies are proposed in order to carry out numerical experiments to validate our model, characterize societies and investigate emerging behaviors.Fil: Buffa, Bruno Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Torres, German Ariel. Instituto de Modelado e Innovación Tecnológica (Consejo Nacional de Investigaciones Científicas y Técnicas - Universidad Nacional del Nordeste); Argentina. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentin

Credit risk contagion and systemic risk on networks

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 Erdös-Rényi model, are considered "benchmark" 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.Fil: Dolfin, Marina. University Of Messina. Department of Engineering; ItaliaFil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Limosani, Michele. University Of Messina. Department Of Economics; ItaliaFil: Xibilia, Maria Gabriella. University Of Messina. Department Of Engineering; Itali

A multiscale network-based model of contagion dynamics: Heterogeneity, spatial distancing and vaccination

Lockdown and vaccination policies have been the major concern in the last year in order to contain the SARS-CoV-2 infection during the COVID-19 pandemic. In this paper, we present a model able to evaluate alternative lockdown policies and vaccination strategies. Our approach integrates and refines the multiscale model proposed by Bellomo et al., 2020, analyzing alternative network structures and bridging two perspectives to study complexity of living systems. Inside different matrices of contacts we explore the impact of closures of distinct nodes upon the overall contagion dynamics. Social distancing is shown to be more effective when targeting the reduction of contacts among and inside the most vulnerable nodes, namely hospitals/nursing homes. Moreover, our results suggest that school closures alone would not significantly affect the infection dynamics and the number of deaths in the population. Finally, we investigate a scenario with immunization in order to understand the effectiveness of targeted vaccination policies towards the most vulnerable individuals. Our model agrees with the current proposed vaccination strategy prioritizing the most vulnerable segment of the population to reduce severe cases and deaths.Fil: Aguiar, Maíra. Università Di Trento; Italia. Basque Center For Applied Mathematics (bcam); España. Ikerbasque, Basque Foundation For Science; EspañaFil: Dosi, Giovanni. Sant'anna Scuola Universitaria Superiore Pisa; ItaliaFil: Knopoff, Damián Alejandro. Universidad Nacional de Córdoba; Argentina. Basque Center For Applied Mathematics; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Virgillito, Maria Enrica. Sant'anna Scuola Universitaria Superiore Pisa; Itali

From particles to firms: On the kinetic theory of climbing up evolutionary landscapes

This paper constitutes the first attempt to bridge the evolutionary theory in economics and the theory of active particles in mathematics. It seeks to present a kinetic model for an evolutionary formalization of economic dynamics. The new derived mathematical representation intends to formalize the processes of learning and selection as the two fundamental drivers of evolutionary environments [G. Dosi, M.-C. Pereira and M.-E. Virgillito, The footprint of evolutionary processes of learning and selection upon the statistical properties of industrial dynamics, Ind. Corp. Change, 26 (2017) 187-210]. To coherently represent the aforementioned properties, the kinetic theory of active particles [N. Bellomo, A. Bellouquid, L. Gibelli and N. Outada, A Quest Towards a Mathematical Theory of Living Systems (Birkhäuser-Springer, 2017)] is here further developed, including the complex interaction of two hierarchical functional subsystems. Modeling and simulations enlighten the predictive ability of the approach. Finally, we outline the potential avenues for future research.Fil: Bellomo, Nicola. Universidad de Granada; España. Politecnico di Torino; ItaliaFil: Dosi, Giovanni. Sant'anna Scuola Universitaria Superiore Pisa; ItaliaFil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Virgillito, Maria Enrica. Sant'anna Scuola Universitaria Superiore Pisa; Itali

Explaining coexistence of nitrogen fixing and non-fixing rhizobia in legume-rhizobia mutualism using mathematical modeling

In the mutualism established between legumes and soil bacteria known as rhizobia, bacteria from soil infect plants roots and reproduce inside root nodules where they fix atmospheric N2 for plant nutrition, receiving carbohydrates in exchange. Host-plant sanctions against non N2 fixing, cheating bacterial symbionts have been proposed to act in the legume-Rhizobium symbiosis, to preserve the mutualistic relationship. Sanctions include decreased rhizobial survival in nodules occupied by cheating rhizobia. Previously, a simple population model experimentally based showed that the coexistence of fixing and cheating rhizobia strains commonly found in field conditions is possible, and that the inclusion of sanctions leads to the extinction of cheating strains in soil. Here, we extend the previous model to include other factors that could complicate the sanction scenario, like horizontal transmission of symbiotic plasmids, turning non-nodulating strains into nodulating rhizobia, and competition between fixing and cheating strains for nodulation. In agreement with previous results, we show that plant populations persist even in the presence of cheating rhizobia without incorporating any sanction against the cheater populations in the model, under the realistic assumption that plants can at least get some amount of fixed N2 from the effectively mutualistic rhizobia occupying some nodules. Inclusion of plant sanctions leads to the unrealistic extinction of cheater strains in soil. Our results agree with increasing experimental evidence and theoretical work showing that mutualisms can persist in presence of cheating partners.Fil: Moyano, Gabriel Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Marco, Diana Elizabeth. Universidad Nacional de Córdoba. Facultad de Cs.exactas Físicas y Naturales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Knopoff, Damián Alejandro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Torres, German Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; ArgentinaFil: Turner, Cristina Vilma. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin

Further steps in the modeling of behavioural crowd dynamics, good news for safe handling: Comment on "Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management"

Fil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin

On the modeling of migration phenomena on small networks

This paper deals with the modeling of migration phenomena in a small network of nations, with the aim of investigating the influence that the wealth and the welfare policies have on this phenomena. The modeling approach is based on the kinetic theory of active particles, while individuals over the network are distinguished by a scalar variable (the activity) which expresses their social state. The dynamics is induced both by the communication of individuals over the network and by the welfare policy within each nation, which is expressed in terms of competitive and altruistic interactions. The evolution of the discrete probability distribution over the social state is described by a system of nonlinear ordinary differential equations. The existence and uniqueness of the solution is discussed and some specific case-studies are proposed in order to carry out simulations and to investigate the emerging behaviors.Fil: Knopoff, Damián Alejandro. Universidad Nacional de Cordoba. Facultad de Matematica, Astronomia y Fisica. Seccion Matematica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentin

Looking for fairer societies, can hard sciences help?: Comment on “Modeling human behavior in economics and social science” by Marina Dolfin, Leone Leonida and Nisrine Outada

Fil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin

A kinetic model for horizontal transfer and bacterial antibiotic resistance

This paper presents a mathematical model for bacterial growth, mutations, horizontal transfer and development of antibiotic resistance. The model is based on the so-called kinetic theory for active particles that is able to capture the main complexity features of the system. Bacterial and immune cells are viewed as active particles whose microscopic state is described by a scalar variable. Particles interact among them and the temporal evolution of the system is described by a generalized distribution function over the microscopic state. The model is derived and tested in a couple of case studies in order to confirm its ability to describe one of the most fundamental problems of modern medicine, namely bacterial resistance to antibiotics.Fil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Sánchez Sansó, Juan M.. Hospital Misericordia Nuevo Siglo; Argentin