Percolation of temporal hierarchical mobility networks during COVID-19.

Percolation theory is essential for understanding disease transmission patterns on the temporal mobility networks. However, the traditional approach of the percolation process can be inefficient when analysing a large-scale, dynamic network for an extended period. Not only is it time-consuming but it is also hard to identify the connected components. Recent studies demonstrate that spatial containers restrict mobility behaviour, described by a hierarchical topology of mobility networks. Here, we leverage crowd-sourced, large-scale human mobility data to construct temporal hierarchical networks composed of over 175 000 block groups in the USA. Each daily network contains mobility between block groups within a Metropolitan Statistical Area (MSA), and long-distance travels across the MSAs. We examine percolation on both levels and demonstrate the changes of network metrics and the connected components under the influence of COVID-19. The research reveals the presence of functional subunits even with high thresholds of mobility. Finally, we locate a set of recurrent critical links that divide components resulting in the separation of core MSAs. Our findings provide novel insights into understanding the dynamical community structure of mobility networks during disruptions and could contribute to more effective infectious disease control at multiple scales. This article is part of the theme issue 'Data science approaches to infectious disease surveillance'.

Resilience Analysis of Australian Electricity and Gas Transmission Networks

Given they are two critical infrastructure areas, the security of electricity and gas networks is highly important due to potential multifaceted social and economic impacts. Unexpected errors or sabotage can lead to blackouts, causing a significant loss for the public, businesses, and governments. Climate change and an increasing number of consequent natural disasters (e.g., bushfires and floods) are other emerging network resilience challenges. In this paper, we used network science to examine the topological resilience of national energy networks with two case studies of Australian gas and electricity networks. To measure the fragility and resilience of these energy networks, we assessed various topological features and theories of percolation. We found that both networks follow the degree distribution of power-law and the characteristics of a scale-free network. Then, using these models, we conducted node and edge removal experiments. The analysis identified the most critical nodes that can trigger cascading failure within the network upon a fault. The analysis results can be used by the network operators to improve network resilience through various mitigation strategies implemented on the identified critical nodes.

Mobility strategies based on percolation theory to avoid disease spread: COVID-19

Human mobility is an important factor in the spatial propagation of infectious diseases. On the other hand, the control strategies based on mobility restrictions are generally unpopular and costly. These high social and economic costs make it very important to design global protocols where the cost is minimized and effects maximized. In this work, we calculate the percolation threshold of the spread in a network of a disease. In particular, we found the number of roads to close and regions to isolate in the Puebla State, Mexico, to avoid the global spread of COVID-19. Computational simulations taking into account the proposed strategy show a potential reduction of 94% of infections. This methodology can be used in broader and different areas to help in the design of health policies.

Household bubbles and COVID-19 transmission: insights from percolation theory.

In the era of social distancing to curb the spread of COVID-19, bubbling is the combining of two or more households to create an exclusive larger group. The impact of bubbling on COVID-19 transmission is challenging to quantify because of the complex social structures involved. We developed a network description of households in the UK, using the configuration model to link households. We explored the impact of bubbling scenarios by joining together households of various sizes. For each bubbling scenario, we calculated the percolation threshold, that is, the number of connections per individual required for a giant component to form, numerically and theoretically. We related the percolation threshold to the household reproduction number. We find that bubbling scenarios in which single-person households join with another household have a minimal impact on network connectivity and transmission potential. Ubiquitous scenarios where all households form a bubble are likely to lead to an extensive transmission that is hard to control. The impact of plausible scenarios, with variable uptake and heterogeneous bubble sizes, can be mitigated with reduced numbers of contacts outside the household. Bubbling of households comes at an increased risk of transmission; however, under certain circumstances risks can be modest and could be balanced by other changes in behaviours. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Epidemics, the Ising-model and percolation theory: A comprehensive review focused on Covid-19.

We revisit well-established concepts of epidemiology, the Ising-model, and percolation theory. Also, we employ a spin S = 1/2 Ising-like model and a (logistic) Fermi-Dirac-like function to describe the spread of Covid-19. Our analysis show that: (i) in many cases the epidemic curve can be described by a Gaussian-type function; (ii) the temporal evolution of the accumulative number of infections and fatalities follow a logistic function; (iii) the key role played by the quarantine to block the spread of Covid-19 in terms of an interacting parameter between people. In the frame of elementary percolation theory, we show that: (i) the percolation probability can be associated with the probability of a person being infected with Covid-19; (ii) the concepts of blocked and non-blocked connections can be associated, respectively, with a person respecting or not the social distancing. Yet, we make a connection between epidemiological concepts and well-established concepts in condensed matter Physics.