Physics

Assessing the economic impact of COVID-19 pandemic and public health policies is essential for a rapid recovery. In this paper, we analyze the impact of mobility contraction on furloughed workers and excess deaths in Italy. We provide a link between the reduction of mobility and excess deaths, confirming that the first countrywide lockdown has been effective in curtailing the COVID-19 epidemics. Our analysis points out that a mobility contraction of 10% leads to a mortality reduction of 5% whereas it leads to an increase of 50% in full time equivalent furloughed workers. Based on our results, we propose a prioritizing policy for the most advanced stage of the COVID-19 vaccination campaign, considering the unemployment risk of the healthy active population. Keywords: COVID-19 mortality; Furlough schemes; Economic impact of lockdowns; Vaccination rollout: Unemployment risk

This paper introduces a mathematical framework for determining second surge behavior of COVID-19 cases in the United States. Within this framework, a flexible algorithmic approach selects a set of turning points for each state, computes distances between them, and determines whether each state is in (or over) a first or second surge. Then, appropriate distances between normalized time series are used to further analyze the relationships between case trajectories on a month-by-month basis. Our algorithm shows that 31 states are experiencing second surges, while 4 of the 10 largest states are still in their first surge, with case counts that have never decreased. This analysis can aid in highlighting the most and least successful state responses to COVID-19.

In the wake of the COVID-19 pandemic many countries implemented containment measures to reduce disease transmission. Studies using digital data sources show that the mobility of individuals was effectively reduced in multiple countries. However, it remains unclear whether these reductions caused deeper structural changes in mobility networks, and how such changes may affect dynamic processes on the network. Here we use movement data of mobile phone users to show that mobility in Germany has not only been reduced considerably: Lockdown measures caused substantial and long-lasting structural changes in the mobility network. We find that long-distance travel was reduced disproportionately strongly. The trimming of long-range network connectivity leads to a more local, clustered network and a moderation of the "small-world" effect. We demonstrate that these structural changes have a considerable effect on epidemic spreading processes by "flattening" the epidemic curve and delaying the spread to geographically distant regions.

We propose an epidemiological model that includes the mobility patterns of the individuals, in the spirit to those considered in (Barmak, 2011, 2016) and (Medus, 2011). We assume that people move around in a city of 120x120 blocks with 300 inhabitants in each block. The mobility pattern is associated to a complex network in which nodes represent blocks while the links represent the traveling path of the individuals. We implemented three confinement strategies in order to mitigate the disease spreading: 1) global confinement, 2) partial restriction to mobility, and 3) localized confinement. In the first case, it was observed that a global isolation policy prevents the massive outbreak of the disease. In the second case, a partial restriction to mobility could lead to a massive contagion if this was not complemented with sanitary measures such as the use of masks and social distancing. Finally, a local isolation policy was proposed, conditioned to the health status of each block. It was observed that this mitigation strategy was able to contain and even reduce the outbreak of the disease by intervening in specific regions of the city according to their level of contagion. It was also observed that this strategy is capable of controlling the epidemic in the case that a certain proportion of those infected are asymptomatic.

Schelling and Sakoda prominently proposed computational models suggesting that strong ethnic residential segregation can be the unintended outcome of a self-reinforcing dynamic driven by choices of individuals with rather tolerant ethnic preferences. There are only few attempts to apply this view to school choice, another important arena in which ethnic segregation occurs. In the current paper, we explore with an agent-based theoretical model similar to those proposed for residential segregation, how ethnic tolerance among parents can affect the level of school segregation. More specifically, we ask whether and under which conditions school segregation could be reduced if more parents hold tolerant ethnic preferences. We move beyond earlier models of school segregation in three ways. First, we model individual school choices using a random utility discrete choice approach. Second, we vary the pattern of ethnic segregation in the residential context of school choices systematically, comparing residential maps in which segregation is unrelated to parents' level of tolerance to residential maps reflecting their ethnic preferences. Thirdly, we introduce heterogeneity in tolerance levels among parents belonging to the same group. Our simulation experiments suggest that ethnic school segregation can be a very robust phenomenon, occurring even when about half of the population prefers mixed to segregated schools. However, we also identify a sweet spot in the parameter space in which a larger proportion of tolerant parents makes the biggest difference. This is the case when the preference for nearby schools weighs heavily in parents' utility function and the residential map is only moderately segregated. Further experiments are presented that unravel the underlying mechanisms.

Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems, and societal cohesiveness. One of the essential features that create complex network vulnerability to failure propagation is the dependency among their components, exposing entire systems to significant risks from destabilizing hazards such as human attacks, natural disasters or internal breakdowns. Developing realistic models for cascading failures as well as strategies to halt and mitigate the failure propagation can point to new approaches to restoring and strengthening real-world networks. In this review, we summarize recent progress on models developed based on physics and complex network science to understand the mechanisms, dynamics and overall impact of cascading failures. We present models for cascading failures in single networks and interdependent networks and explain how different dynamic propagation mechanisms can lead to an abrupt collapse and a rich dynamic behavior. Finally, we close the review with novel emerging strategies for containing cascades of failures and discuss open questions that remain to be addressed.

We analyze mobility changes following the implementation of containment measures aimed at mitigating the spread of COVID-19 in Bogotá, Colombia. We characterize the mobility network before and during the pandemic and analyze its evolution and changes between January and July 2020. We then link the observed mobility changes to socioeconomic conditions, estimating a gravity model to assess the effect of socioeconomic conditions on mobility flows. We observe an overall reduction in mobility trends, but the overall connectivity between different areas of the city remains after the lockdown, reflecting the mobility network's resilience. We find that the responses to lockdown policies depend on socioeconomic conditions. Before the pandemic, the population with better socioeconomic conditions shows higher mobility flows. Since the lockdown, mobility presents a general decrease, but the population with worse socioeconomic conditions shows lower decreases in mobility flows. We conclude deriving policy implications.

Heavy-tailed networks, which have degree distributions characterised by slower than exponentially bounded tails, are common in many different situations. Some interesting cases, where heavy tails are characterised by inverse powers λ in the range 1<λ<2, arise for associative knowledge networks, and semantic and linguistic networks. In these cases, the differences between the networks are often delicate, calling for robust methods to characterise the differences. Here, we introduce a method for comparing networks using a density matrix based on q-generalised adjacency matrix kernels. It is shown that comparison of networks can then be performed using the q-generalised Kullback-Leibler divergence. In addition, the q-generalised divergence can be interpreted as a q-generalised free energy, which enables the thermodynamic-like macroscopic description of the heavy-tailed networks. The viability of the q-generalised adjacency kernels and the thermodynamic-like description in characterisation of complex networks is demonstrated using a simulated set of networks, which are modular and heavy-tailed with a degree distribution of inverse power law in the range 1<λ<2 .

Since the beginning of the epidemic, daily reports of CoViD-19 cases, hospitalizations, and deaths from around the world have been publicly available. This paper describes methods to characterize broad features of the spread of the disease, with relatively long periods of constant transmission rates, using a new population modeling framework based on discrete-time difference equations. Comparative parameters are chosen for their weak dependence on model assumptions. Approaches for their point and interval estimation, accounting for additional sources of variance in the case data, are presented. These methods provide a basis to quantitatively assess the impact of changes to social distancing policies using publicly available data. As examples, data from Ontario and German states are analyzed using this framework. German case data show a small increase in transmission rates following the relaxation of lock-down rules on May 6, 2020. By combining case and death data from Germany, the mean and standard deviation of the time from infection to death are estimated.

Infectious diseases typically spread over a contact network with millions of individuals, whose sheer size is a tremendous challenge to analysing and controlling an epidemic outbreak. For some contact networks, it is possible to group individuals into clusters. A high-level description of the epidemic between a few clusters is considerably simpler than on an individual level. However, to cluster individuals, most studies rely on equitable partitions, a rather restrictive structural property of the contact network. In this work, we focus on Susceptible-Infected-Susceptible (SIS) epidemics, and our contribution is threefold. First, we propose a geometric approach to specify all networks for which an epidemic outbreak simplifies to the interaction of only a few clusters. Second, for the complete graph and any initial viral state vectors, we derive the closed-form solution of the nonlinear differential equations of the N-Intertwined Mean-Field Approximation (NIMFA) of the SIS process. Third, by relaxing the notion of equitable partitions, we derive low-complexity approximations and bounds for epidemics on arbitrary contact networks. Our results are an important step towards understanding and controlling epidemics on large networks.