Interacting social processes on interconnected networks

We propose and study a model for the interplay between two different dynamical processes -one for opinion formation and the other for decision making- on two interconnected networks A and B. The opinion dynamics on network A corresponds to that of the M-model, where the state of each agent can take one of four possible values (S = -2,-1, 1, 2), describing its level of agreement on a given issue. The likelihood to become an extremist (S = ±2) or a moderate (S = ±1) is controlled by a reinforcement parameter r ≥ 0. The decision making dynamics on network B is akin to that of the Abrams-Strogatz model, where agents can be either in favor (S = +1) or against (S = -1) the issue. The probability that an agent changes its state is proportional to the fraction of neighbors that hold the opposite state raised to a power β. Starting from a polarized case scenario in which all agents of network A hold positive orientations while all agents of network B have a negative orientation, we explore the conditions under which one of the dynamics prevails over the other, imposing its initial orientation. We find that, for a given value of β, the two-network system reaches a consensus in the positive state (initial state of network A) when the reinforcement overcomes a crossover value r∗(β), while a negative consensus happens for r ∗(β). In the r - β phase space, the system displays a transition at a critical threshold βc, from a coexistence of both orientations for β c to a dominance of one orientation for β > βc. We develop an analytical mean-field approach that gives an insight into these regimes and shows that both dynamics are equivalent along the crossover line (r∗, β∗).Facultad de Ciencias ExactasInstituto de Física de Líquidos y Sistemas Biológico

Interacting social processes on interconnected networks

We propose and study a model for the interplay between two different dynamical processes -one for opinion formation and the other for decision making- on two interconnected networks A and B. The opinion dynamics on network A corresponds to that of the M-model, where the state of each agent can take one of four possible values (S = -2,-1, 1, 2), describing its level of agreement on a given issue. The likelihood to become an extremist (S = ±2) or a moderate (S = ±1) is controlled by a reinforcement parameter r ≥ 0. The decision making dynamics on network B is akin to that of the Abrams-Strogatz model, where agents can be either in favor (S = +1) or against (S = -1) the issue. The probability that an agent changes its state is proportional to the fraction of neighbors that hold the opposite state raised to a power β. Starting from a polarized case scenario in which all agents of network A hold positive orientations while all agents of network B have a negative orientation, we explore the conditions under which one of the dynamics prevails over the other, imposing its initial orientation. We find that, for a given value of β, the two-network system reaches a consensus in the positive state (initial state of network A) when the reinforcement overcomes a crossover value r∗(β), while a negative consensus happens for r ∗(β). In the r - β phase space, the system displays a transition at a critical threshold βc, from a coexistence of both orientations for β c to a dominance of one orientation for β > βc. We develop an analytical mean-field approach that gives an insight into these regimes and shows that both dynamics are equivalent along the crossover line (r∗, β∗).Facultad de Ciencias ExactasInstituto de Física de Líquidos y Sistemas Biológico

An epidemic model for COVID-19 transmission in Argentina: Exploration of the alternating quarantine and massive testing strategies

The COVID-19 pandemic has challenged authorities at different levels of government administration aroundthe globe. When faced with diseases of this severity, it is useful for the authorities to have prediction tools to estimate in advance the impact on the health system as well as the human, material, and economic resources that will be necessary. In this paper, we construct an extended Susceptible?Exposed?Infected?Recovered modelthat incorporates the social structure of Mar del Plata, the 4◦ most inhabited city in Argentina and head ofthe Municipality of General Pueyrredón. Moreover, we consider detailed partitions of infected individualsaccording to the illness severity, as well as data of local health resources, to bring predictions closer to thelocal reality. Tuning the corresponding epidemic parameters for COVID-19, we study an alternating quarantinestrategy: a part of the population can circulate without restrictions at any time, while the rest is equally dividedinto two groups and goes on successive periods of normal activity and lockdown, each one with a durationof days. We also implement a random testing strategy with a threshold over the population. We found that = 7 is a good choice for the quarantine strategy since it reduces the infected population and, conveniently,it suits a weekly schedule. Focusing on the health system, projecting from the situation as of September 30,we foresee a difficulty to avoid saturation of the available ICU, given the extremely low levels of mobility thatwould be required. In the worst case, our model estimates that four thousand deaths would occur, of which30% could be avoided with proper medical attention. Nonetheless, we found that aggressive testing wouldallow an increase in the percentage of people that can circulate without restrictions, and the medical facilitiesto deal with the additional critical patients would be relatively low.Fil: Vassallo, Lautaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Pérez, Ignacio Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Alvarez Zuzek, Lucila G.. University Of Georgetown; Estados UnidosFil: Amaya, Julián. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Torres, Marcos F.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Valdez, Lucas Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: la Rocca, Cristian Ernesto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Braunstein, Lidia Adriana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentin

Epidemics in partially overlapped multiplex networks

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction $q$ of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted $T$. We also theoretically determine the dependence of the epidemic threshold on the fraction $q > 0$ of shared nodes in a system composed of two layers. We find that in the limit of $q \to 0$ the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.Comment: 13 pages, 4 figure

Dependence of the epidemic threshold of the SIR model with the overlapping fraction and topology of the layers.

<p>Phase diagram in the plane for two Erdös-Rényi layers with and different values of . The black full lines correspond to obtained theoretically from Eq. (3) for from top to bottom. The limit corresponds to a disease spreading in layer A when it is isolated and the limit represents the fully overlapped multiplex network. Colored regions correspond to the epidemic-free phase for each value of , while the region above corresponds to the epidemic-phase.</p

Potentials <i>V</i>_<i>A</i> and <i>V</i>_<i>B</i> as in Fig 5, but for volatility values <i>β</i> = <i>α</i> = 1.78 (left panel) and <i>β</i> = 3 (right panel).

<p>Plots in the left panel correspond to the crossover point, a symmetric case where the system remains disordered, while plots in the right panel show the negative consensus regime III.</p

Average magnetization at the steady state 〈<i>m</i>_<i>A</i>〉 (circles) and 〈<i>m</i>_<i>B</i>〉 (diamonds) in networks<i>A</i> and <i>B</i>, respectively, as a function of <i>β</i>, for<i>r</i> = 0.25.

<p>Below the critical threshold <i>β_c</i> ≃ 0.86 the system remains in a disordered state where both + and − orientations coexist (Regime I), while above <i>β_c</i> the system reaches an ordered state of consensus (Regimes II and III). The point <i>β</i>* denotes the crossover between Regimes II and III, characterized by a positive and negative consensus, respectively. Numerical results correspond to two DR random networks of degree <i>μ</i> = 5 and size <i>N</i> = 2048 each, averaged over 10⁴ independent realizations.</p

Effect of the overlapping fraction in the SIR epidemic threshold on individual layers.

<p>Fraction of recovered individuals vs the transmissibility in the steady state of the SIR model. The values were obtained theoretically from Eq. (4) for two Erdös-Rényi layers with , and different overlapping fraction values. In orange circles , in green squares , in blue triangles and in violet diamonds . In the upper panel we plot and in the bottom panel we plot . The arrows indicate the threshold and are used as a guide to show that is the same for and . The black full lines denote (up) and (down) when both networks are isolated and .</p

Reinforcement-volatility (<i>r</i> − <i>β</i>) phase diagram on a log-linear scale for a two-network system with the same parameters as in Fig 2.

<p>Solid circles correspond to the crossover points (<i>r</i>*, <i>β</i>*) between network-A and network-B dominance regions, while the dashed line represents the transition point <i>β_c</i> ≃ 0.86 between coexistence and consensus.</p