The transport network between cities is key in understanding epidemic outbreaks, especially in a vast country like Brazil with 5569 cities spread out over 8.5 million square kilometers. In order to study the COVID-19 spread in Brazil, we built a transport network where each city is a node and the edges are connections by land and air. Our findings have shown that by adding air connections, the average path length substantially decreases (70%) while the clustering coefficient remains almost unchanged, very typical of small-world networks. The airways are shortcuts connecting previously distant cities and hubs, therefore shrinking the distances in the network. Also, the cities with airports are central nodes, which makes them dissemination hotspots and key targets for interventions.

While understanding the time evolution of Covid-19 pandemic is needed to plan economics and tune sanitary policies, a quantitative information of the recurrent epidemic waves is elusive. This work describes a statistical physics study of the subsequent waves in the epidemic spreading of Covid-19 and disclose the frequency components of the epidemic waves pattern over two years in United States, United Kingdom and Japan. These countries have been taken as representative cases of different containment policies such as "Mitigation" (USA and UK) and "Zero Covid" (Japan) policies. The supercritical phases in spreading have been identified by intervals with RIC-index > 0. We have used the wavelet transform of infection and fatality waves to get the spectral analysis showing a dominant component around 130 days. Data of the world dynamic clearly indicates also the crossover to a different phase due to the enforcement of vaccination campaign. In Japan and United Kingdom, we observed the emergence in the infection waves of a long period component (~ 170 days) during vaccination campaign. These results indicate slowing down of the epidemic spreading dynamics due to the vaccination campaign. Finally, we find an intrinsic difference between infection and fatality waves pointing to a non-trivial variation of the lethality due to different gene variants.

Over the last 2 years, the COVID-19 pandemic has stimulated the scientific community by starting a race to develop new vaccines and therapeutic approaches to fight this life-threatening illness. At the same time, the pandemic also evoked an urge for innovative communication strategies to maintain scientific networking and data sharing among investigators. Communication through audiovisual platforms has quickly become a unique tool to sustain scientific interaction, whereas social media has turned into an unmistakable pivotal environment for sharing scientific data and combating misinformation around SARS-CoV-2 infection, prevention, and therapy. Amid this challenging scenario, the scientific community organically established new roles, such as a social media ambassador, a conference-associated role to virtually promote breakthrough science while reconnecting investigators and forging new scientific networks via social media. Moreover, in response to the COVID-19 pandemic, it also became clear the critical need for the scientific community to support efforts to empower flexibility, creativity, and the inclusion of new forms of communication to advance science. Thus, the goal of this brief article is to provide a structured follow-up on the importance for researchers to occupy the internet to promote scientific findings and events, to combat science mistrust by stimulating communication among nonscientists to scientists, and to provide essential strategies for young and senior investigators on how to virtually expand their professional networks within and across research and clinical areas of the cardiovascular field.

While understanding of periodic recurrent waves of Covid-19 epidemics would aid to combat the pandemics, quantitative analysis of data over a two years period from the outbreak, is lacking. The complexity of Covid-19 recurrent waves is related with the concurrent role of i) the containment measures enforced to mitigate the epidemics spreading ii) the rate of viral gene mutations, and iii) the variable immune response of the host implemented by vaccination. This work focuses on the effect of massive vaccination and gene variants on the recurrent waves in a representative case of countries enforcing mitigation and vaccination strategy. The spreading rate is measured by the ratio between the reproductive number Rt(t) and the doubling time Td(t) called RIC-index and the daily fatalities number. The dynamics of the Covid-19 epidemics have been studied by wavelet analysis and represented by a non-linear helicoid vortex in a 3D space where both RIC-index and fatalities change with time. The onset of periodic recurrent waves has been identified by the transition from convergent to divergent trajectories on the helicoid vortex. We report a main period of recurrent waves of 120 days and the elongation of this period after the vaccination campaign.

Contact tracing via digital tracking applications installed on mobile phones is an important tool for controlling epidemic spreading. Its effectivity can be quantified by modifying the standard methodology for analyzing percolation and connectivity of contact networks. We apply this framework to networks with varying degree distributions, numbers of application users, and probabilities of quarantine failures. Further, we study structured populations with homophily and heterophily and the possibility of degree-targeted application distribution. Our results are based on a combination of explicit simulations and mean-field analysis. They indicate that there can be major differences in the epidemic size and epidemic probabilities which are equivalent in the normal susceptible-infectious-recovered (SIR) processes. Further, degree heterogeneity is seen to be especially important for the epidemic threshold but not as much for the epidemic size. The probability that tracing leads to quarantines is not as important as the application adoption rate. Finally, both strong homophily and especially heterophily with regard to application adoption can be detrimental. Overall, epidemic dynamics are very sensitive to all of the parameter values we tested out, which makes the problem of estimating the effect of digital contact tracing an inherently multidimensional problem.

A key factor in the transmission of infectious diseases is the structure of disease transmitting contacts. In the context of the current COVID-19 pandemic and with some data based on the Hungarian population we develop a theoretical epidemic model (susceptible-infected-removed, SIR) on a multilayer network. The layers include the Hungarian household structure, with population divided into children, adults and elderly, as well as schools and workplaces, some spatial embedding and community transmission due to sharing communal spaces, service and public spaces. We investigate the sensitivity of the model (via the time evolution and final size of the epidemic) to the different contact layers and we map out the relation between peak prevalence and final epidemic size. When compared to the classic compartmental model and for the same final epidemic size, we find that epidemics on multilayer network lead to higher peak prevalence meaning that the risk of overwhelming the health care system is higher. Based on our model we found that keeping cliques/bubbles in school as isolated as possible has a major effect while closing workplaces had a mild effect as long as workplaces are of relatively small size.

The structure of complex networks has long been understood to play a role in transmission and spreading phenomena on a graph. Such networks form an important part of the structure of society, including transportation networks. As society fights to control the COVID-19 pandemic, an important question is how to choose the optimum balance between the full opening of transport networks and the control of epidemic spread. In this work we investigate the interplay between network dismantling and epidemic spread rate as a proxy for the imposition of travel restrictions to control disease spread. For network dismantling we focus on the weighted and unweighted forms of metrics that capture the topological and informational structure of the network. Our results indicate that there is benefit to a directed approach to imposing travel restrictions, but we identify that more detailed models of the transport network are necessary for definitive results.

Recent human activity has profoundly transformed Earth biomes on a scale and at rates that are unprecedented. Given the central role of symbioses in ecosystem processes, functions, and services throughout the Earth biosphere, the impacts of human-driven change on symbioses are critical to understand. Symbioses are not merely collections of organisms, but co-evolved partners that arise from the synergistic combination and action of different genetic programs. They function with varying degrees of permanence and selection as emergent units with substantial potential for combinatorial and evolutionary innovation in both structure and function. Following an articulation of operational definitions of symbiosis and related concepts and characteristics of the Anthropocene, we outline a basic typology of anthropogenic change (AC) and a conceptual framework for how AC might mechanistically impact symbioses with select case examples to highlight our perspective. We discuss surprising connections between symbiosis and the Anthropocene, suggesting ways in which new symbioses could arise due to AC, how symbioses could be agents of ecosystem change, and how symbioses, broadly defined, of humans and "farmed" organisms may have launched the Anthropocene. We conclude with reflections on the robustness of symbioses to AC and our perspective on the importance of symbioses as ecosystem keystones and the need to tackle anthropogenic challenges as wise and humble stewards embedded within the system.

While the mathematical laws of uncontrolled epidemic spreading are well known, the statistical physics of coronavirus epidemics with containment measures is currently lacking. The modelling of available data of the first wave of the Covid-19 pandemic in 2020 over 230 days, in different countries representative of different containment policies is relevant to quantify the efficiency of these policies to face the containment of any successive wave. At this aim we have built a 3D phase diagram tracking the simultaneous evolution and the interplay of the doubling time,T_d, and the reproductive number,R_tmeasured using the methodological definition used by the Robert Koch Institute. In this expanded parameter space three different main phases,supercritical,criticalandsubcriticalare identified. Moreover, we have found that in thesupercriticalregime withR_t> 1 the doubling time is smaller than 40 days. In this phase we have established the power law relation betweenT_dand (R_t- 1)^-νwith the exponentνdepending on the definition of reproductive number. In thesubcriticalregime whereR_t< 1 andT_d> 100 days, we have identified arrested metastable phases whereT_dis nearly constant.

The control of Covid 19 epidemics by public health policy in Italy during the first and the second epidemic waves has been driven by using reproductive number Rt(t) to identify the supercritical (percolative), the subcritical (arrested), separated by the critical regime. Here we show that to quantify the Covid-19 spreading rate with containment measures there is a need of a 3D expanded parameter space phase diagram built by the combination of Rt(t) and doubling time Td(t). In this space we identify the Covid-19 dynamics in Italy and its administrative Regions. The supercritical regime is mathematically characterized by (i) the power law of Td vs. [Rt(t) - 1] and (ii) the exponential behaviour of Td vs. time, either in the first and in the second wave. The novel 3D phase diagram shows clearly metastable states appearing before and after the second wave critical regime. for loosening quarantine and tracing of actives cases. The metastable states are precursors of the abrupt onset of a next nascent wave supercritical regime. This dynamic description allows epidemics predictions needed by policymakers interested to point to the target "zero infections" with the elimination of SARS-CoV-2, using the Finding mobile Tracing policy joint with vaccination-campaign, in order to avoid the emergence of recurrent new variants of SARS-CoV-2 virus, accompined by recurrent long lockdowns, with large economical losses, and large number of fatalities.