Physics

The emergence of interconnected urban networks is a crucial feature of globalisation processes. Understanding the drivers behind the growth of such networks - in particular urban firm networks -, is essential for the economic resilience of urban systems. We introduce in this paper a generative network model for firm networks at the urban area level including several complementary processes: the economic size of urban areas at origin and destination, industrial sector proximity between firms, the strength of links from the past, as well as the geographical and socio-cultural distance. An empirical network analysis on European firm ownership data confirms the relevance of each of these factors. We then simulate network growth for synthetic systems of cities, unveiling stylized facts such as a transition from a local to a global regime or a maximal integration achieved at an intermediate interaction range. We calibrate the model on the European network, outperforming statistical models and showing a strong role of path-dependency. Potential applications of the model include the study of mitigation policies to deal with exogenous shocks such as economic crisis or potential lockdowns of countries, which we illustrate with an application on stylized scenarios.

In this work we study a simple compartmental model for drinking behavior evolution. The population is divided in 3 compartments regarding their alcohol consumption, namely Susceptible individuals S (nonconsumers), Moderate drinkers M and Risk drinkers R . The transitions among those states are ruled by probabilities. Despite the simplicity of the model, we observed the occurrence of two distinct nonequilibrium phase transitions to absorbing states. One of these states is composed only by Susceptible individuals S , with no drinkers ( M=R=0 ). On the other hand, the other absorbing state is composed only by Risk drinkers R ( S=M=0 ). Between these two steady states, we have the coexistence of the three subpopulations S , M and R . Comparison with abusive alcohol consumption data for Brazil shows a good agreement between the model's results and the database.

Over the past two decades there has been a number of global outbreaks of viral diseases. This has accelerated the efforts to model and forecast the disease spreading, in order to find ways to confine the spreading regionally and between regions. Towards this we have devised a model of geographical spreading of viral infections due to human spatial mobility and adapted it to the latest COVID-19 pandemic. In this the region to be modelled is overlaid with a two-dimensional grid weighted with the population density defined cells, in each of which a compartmental SEIRS system of delay difference equations simulate the local dynamics (microdynamics) of the disease. The infections between cells are stochastic and allow for the geographical spreading of the virus over the two-dimensional space (macrodynamics). This approach allows to separate the parameters related to the biological aspects of the disease from the ones that represent the spatial contagious behaviour through different kinds of mobility of people acting as virus carriers. These provide sufficient information to trace the evolution of the pandemic in different situations. In particular we have applied this approach to three in many ways different countries, Mexico, Finland and Iceland and found that the model is capable of reproducing and predicting the stochastic global path of the pandemic. This study sheds light on how the diverse cultural and socioeconomic aspects of a country influence the evolution of the epidemics and also the efficacy of social distancing and other confinement measures.

We develop an agent-based model to assess the cumulative number of deaths during hypothetical Covid-19-like epidemics for various non-pharmaceutical intervention strategies. We consider local and non-local modes of disease transmission. The first simulates transmission through social contacts in the vicinity of the place of residence while the second through social contacts in public places: schools, hospitals, airports, etc., where many people meet, who live in remote geographic locations. Epidemic spreading is modeled as a discrete-time stochastic process on random geometric networks. We use the Monte-Carlo method in the simulations. The~following assumptions are made. The basic reproduction number is 2.5 and the infectious period lasts approximately ten days. Infections lead to SARS in about one percent of cases, which are likely to lead to respiratory default and death, unless the patient receives an appropriate medical treatment. The~healthcare system capacity is simulated by the availability of respiratory ventilators or intensive care beds. Some parameters of the model, like mortality rates or the number of respiratory ventilators per 100000 inhabitants, are chosen to simulate the real values for the USA and Poland. In the simulations we compare `do-nothing' strategy with mitigation strategies based on social distancing and reducing social mixing. We study epidemics in the pre-vaccine era, where immunity is obtained only by infection. The model applies only to epidemics for which reinfections are rare and can be neglected. The results of the simulations show that strategies that slow the development of an epidemic too much in the early stages do not significantly reduce the overall number of deaths in the long term, but increase the duration of the epidemic. In particular, a~hybrid strategy where lockdown is held for some time and is then completely released, is inefficient.

The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models, including hypergraphs. In this paper, we explore the non-linear dynamics of consensus on hypergraphs, allowing for interactions within hyperedges of any cardinality. After discussing the different ways in which non-linearities can be incorporated in the dynamical model, building on different sociological theories, we explore its mathematical properties and perform simulations to investigate them numerically. After focussing on synthetic hypergraphs, namely on block hypergraphs, we investigate the dynamics on real-world structures, and explore in detail the role of involvement and stubbornness on polarisation.

When making important decisions such as choosing health insurance or a school, people are often uncertain what levels of attributes will suit their true preference. After choice, they might realize that their uncertainty resulted in a mismatch: choosing a sub-optimal alternative, while another available alternative better matches their needs. We study here the overall impact, from a central planner's perspective, of decisions under such uncertainty. We use the representation of Voronoi tessellations to locate all individuals and alternatives in an attribute space. We provide an expression for the probability of correct match, and calculate, analytically and numerically, the average percentage of matches. We test dependence on the level of uncertainty and location. We find overall considerable mismatch even for low uncertainty - a possible concern for policy makers. We further explore a commonly used practice - allocating service representatives to assist individuals' decisions. We show that within a given budget and uncertainty level, the effective allocation is for individuals who are close to the boundary between several Voronoi cells, but are not right on the boundary.

The basic Susceptible-Infected-Recovered (SIR) model is extended to include effects of progressive social awareness, lockdowns and anthropogenic migration. It is found that social awareness can effectively contain the spread by lowering the basic reproduction rate R 0 . Interestingly, the awareness is found to be more effective in a society which can adopt the awareness faster compared to the one having a slower response. The paper also separates the mortality fraction from the clinically recovered fraction and attempts to model the outcome of lockdowns, in absence and presence of social awareness. It is seen that staggered exits from lockdowns are not only economically beneficial but also helps to curb the infection spread. Moreover, a staggered exit strategy with progressive social awareness is found to be the most efficient intervention. The paper also explores the effects of anthropogenic migration on the dynamics of the epidemic in a two-zone scenario. The calculations yield dissimilar evolution of different fractions in different zones. Such models can be convenient to strategize the division of a large zone into smaller sub-zones for a disproportionate imposition of lockdown, or, an exit from one. Calculations are done with parameters consistent with the SARS-COV-2 pathogen in the Indian context.

During the COVID-19 pandemic, the slope of the epidemic curve in Mexico City has been quite unstable. We have predicted that in the case that a fraction of the population above a certain threshold returns to the public space, the negative tendency of the epidemic curve will revert. Such predictions were based on modeling the reactivation of economic activity after lockdown by means of an epidemiological model on a contact network of Mexico City derived from mobile device co-localization. We evaluated the epidemic dynamics considering the tally of active and recovered cases documented in the mexican government's open database. Scenarios were modeled in which different percentages of the population are reintegrated to the public space by scanning values ranging from 5% up to 50%. Null models were built by using data from the Jornada Nacional de Sana Distancia (the Mexican model of elective lockdown) in which there was a mobility reduction of 75% and no mandatory mobility restrictions. We found that a new peak of cases in the epidemic curve was very likely for scenarios in which more than 5% of the population rejoined the public space; The return of more than 50% of the population synchronously will unleash a peak of a magnitude similar to the one that was predicted with no mitigation strategies. By evaluating the tendencies of the epidemic dynamics, the number of new cases registered, new cases hospitalized, and new deaths, we consider that under this scenario, reactivation following only elective measures may not be optimal. Given the need to reactivate economic activities, we suggest to consider alternative measures that allow to diminish the contacts among people returning to the public space. We evaluated that by "encapsulating" reactivated workers may allow a reactivation of a larger fraction of the population without compromising the desired tendency in the epidemic curve.

In this paper we investigate how the modularity of model and real-world social networks affect their robustness and the efficacy of node attack (removal) strategies based on node degree (ID) and node betweenness (IB). We build Barabasi-Albert model networks with different modularity by a new ad hoc algorithm that rewire links forming networks with community structure. We traced the network robustness using the largest connected component (LCC). We find that higher level of modularity decreases the model network robustness under both attack strategies, i.e. model network with higher community structure showed faster LCC disruption when subjected to node removal. Very interesting, we find that when model networks showed non-modular structure or low modularity, the degree-based (ID) is more effective than the betweenness-based node attack strategy (IB). Conversely, in the case the model network present higher modularity, the IB strategies becomes clearly the most effective to fragment the LCC. Last, we investigated how the modularity of the network structure evaluated by the modularity indicator (Q) affect the robustness and the efficacy of the attack strategies in 12 real-world social networks. We found that the modularity Q is negatively correlated with the robustness of the real-world social networks under IB node attack strategy (p-value< 0.001). This result indicates how real-world networks with higher modularity (i.e. with higher community structure) may be more fragile to betwenness-based node attack. The results presented in this paper unveil the role of modularity and community structure for the robustness of networks and may be useful to select the best node attack strategies in network.

The unprecedented behavioural responses of societies have been evidently shaping the COVID-19 pandemic, yet it is a significant challenge to accurately monitor the continuously changing social mixing patterns in real-time. Contact matrices, usually stratified by age, summarise interaction motifs efficiently, but their collection relies on conventional representative survey techniques, which are expensive and slow to obtain. Here we report a data collection effort involving over 2.3% of the Hungarian population to simultaneously record contact matrices through a longitudinal online and sequence of representative phone surveys. To correct non-representative biases characterising the online data, by using census data and the representative samples we develop a reconstruction method to provide a scalable, cheap, and flexible way to dynamically obtain closer-to-representative contact matrices. Our results demonstrate the potential of combined online-offline data collections to understand the changing behavioural responses determining the future evolution of the outbreak, and inform epidemic models with crucial data.