Physics

Containment measures implemented by some countries to suppress the spread of COVID-19 have resulted in a slowdown of the epidemic characterized by time series of daily infections plateauing over extended periods of time. We prove that such a dynamical pattern is compatible with critical Susceptible-Infected-Removed (SIR) dynamics. In traditional analyses of the critical SIR model, the critical dynamical regime is started from a single infected node. The application of containment measures to an ongoing epidemic, however, has the effect to make the system enter in its critical regime with a number of infected individuals potentially large. We describe how such non-trivial starting conditions affect the critical behavior of the SIR model. We perform a theoretical and large-scale numerical investigation of the model. We show that the expected outbreak size is an increasing function of the initial number of infected individuals, while the expected duration of the outbreak is a non-monotonic function of the initial number of infected individuals. Also, we precisely characterize the magnitude of the fluctuations associated with the size and duration of the outbreak in critical SIR dynamics with non-trivial initial conditions. Far from heard immunity, fluctuations are much larger than average values, thus indicating that predictions of plateauing time series may be particularly challenging.

We introduce a theoretical framework that highlights the impact of physical distancing variables such as human mobility and physical proximity on the evolution of epidemics and, crucially, on the reproduction number. In particular, in response to the coronavirus disease (CoViD-19) pandemic, countries have introduced various levels of 'lockdown' to reduce the number of new infections. Specifically we use a collisional approach to an infection-age structured model described by a renewal equation for the time homogeneous evolution of epidemics. As a result, we show how various contributions of the lockdown policies, namely physical proximity and human mobility, reduce the impact of SARS-CoV-2 and mitigate the risk of disease resurgence. We check our theoretical framework using real-world data on physical distancing with two different data repositories, obtaining consistent results. Finally, we propose an equation for the effective reproduction number which takes into account types of interactions among people, which may help policy makers to improve remote-working organizational structure.

Epidemic spread on networks is one of the most studied dynamics in network science and has important implications in real epidemic scenarios. Nonetheless, the dynamics of real epidemics and how it is affected by the underline structure of the infection channels are still not fully understood. Here we apply the SIR model and study analytically and numerically the epidemic spread on a recently developed spatial modular model imitating the structure of cities in a country. The model assumes that inside a city the infection channels connect many different locations, while the infection channels between cities are less and usually directly connect only a few nearest neighbor cities in a two-dimensional plane. We find that the model experience two epidemic transitions. The first lower threshold represents a local epidemic spread within a city but not to the entire country and the second higher threshold represents a global epidemic in the entire country. Based on our analytical solution we proposed several control strategies and how to optimize them. We also show that while control strategies can successfully control the disease, early actions are essentials to prevent the disease global spread.

The challenges presented by the COVID-19 epidemic have created a renewed interest in the development of new methods to combat infectious diseases. A prominent property of the SARS-CoV-2 transmission is the significant fraction of asymptomatic transmission. This may influence the effectiveness of the standard contact tracing procedure for quarantining potentially infected individuals. However, the effects of asymptomatic transmission on the epidemic threshold of epidemic spreading on networks are largely unknown. Here we study the critical percolation transition in a simple epidemic network model in the presence of a recursive contact tracing algorithm for instant quarantining. We find that, above a certain fraction of asymptomatic transmission, standard contact tracing loses its ability to suppress spreading below the epidemic threshold. However, we also find that recursive contact tracing opens a possibility to contain epidemics with a large fraction of asymptomatic or presymptomatic transmission. In particular, we calculate the required fraction of network nodes participating in the contact tracing for networks with arbitrary degree distributions and for varying recursion depths and discuss the influence of recursion depth and asymptomatic rate on the epidemic percolation phase transition. We test and illustrate our theoretical results using numerical simulations on infection trees and networks. We anticipate recursive contact tracing to provide a basis for digital, app-based contact tracing tools that extend the efficiency of contact tracing to diseases with a large fraction of asymptomatic transmission.

We assess the epidemic situation caused by SARS-CoV-2 using Tsallis' proposal for determining the occurrence of the peak, and also the Susceptible-Infected-Recovered-Asymptomatic-Symptomatic and Dead (\textbf{SIRASD}) compartmental model. Using these two models, we determine a range of probable peak dates and study several social distancing scenarios during the epidemic. Due to the socioeconomic situation and the conflictive political climate, we take for our study the case of Bolivia, where a national election was originally scheduled to occur on September 6th and recently rescheduled on October 18th. For this, we analyze both electoral scenarios and show that such an event can largely affect the epidemic's dynamics.

Understanding the spatiotemporal road network accessibility during a hurricane evacuation, the level of ease of residents in an area in reaching evacuation destination sites through the road network, is a critical component of emergency management. While many studies have attempted to measure road accessibility (either in the scope of evacuation or beyond), few have considered both dynamic evacuation demand and characteristics of a hurricane. This study proposes a methodological framework to achieve this goal. In an interval of every six hours, the method first estimates the evacuation demand in terms of number of vehicles per household in each county subdivision by considering the hurricane's wind radius and track. The closest facility analysis is then employed to model evacuees' route choices towards the predefined evacuation destinations. The potential crowdedness index (PCI), a metric capturing the level of crowdedness of each road segment, is then computed by coupling the estimated evacuation demand and route choices. Finally, the road accessibility of each sub-county is measured by calculating the reciprocal of the sum of PCI values of corresponding roads connecting evacuees from the sub-county to the designated destinations. The method is applied to the entire state of Florida during Hurricane Irma in September 2017. Results show that I-75 and I-95 northbound have a high level of congestion, and sub-counties along the northbound I-95 suffer from the worst road accessibility. In addition, this research performs a sensitivity analysis for examining the impacts of different choices of behavioral response curves on accessibility results.

Estimating a massive drive time matrix between locations is a practical but challenging task. The challenges include availability of reliable road network (including traffic) data, programming expertise, and access to high-performance computing resources. This research proposes a method for estimating a nationwide drive time matrix between ZIP code areas in the U.S.--a geographic unit at which many national datasets such as health information are compiled and distributed. The method (1) does not rely on intensive efforts in data preparation or access to advanced computing resources, (2) uses algorithms of varying complexity and computational time to estimate drive times of different trip lengths, and (3) accounts for both interzonal and intrazonal drive times. The core design samples ZIP code pairs with various intensities according to trip lengths and derives the drive times via Google Maps API, and the Google times are then used to adjust and improve some primitive estimates of drive times with low computational costs. The result provides a valuable resource for researchers.

Emergency evacuation of patients from a hospital can be challenging in the event of a fire. Most emergency evacuation studies are based on the assumption that pedestrians are ambulant and can egress by themselves. However, this is often not the case during emergency evacuations in healthcare facilities such as hospitals and nursing homes. To investigate emergency evacuations in such healthcare facilities, we performed a series of controlled experiments to study the dynamics of patient beds in horizontal movement. We considered a patient bed because it is one of the commonly used devices to transport patients within healthcare facilities. Through a series of controlled experiments, we examined the change of velocity in corner turning movements and speed reductions in multiple trips between both ends of a straight corridor. Based on the experimental results, we then developed a mathematical model of total evacuation time prediction for a patient bed horizontally moving in a healthcare facility. Factoring uncertainty in the horizontal movement, we produced the probability distribution of movement duration and estimated the probability that an evacuation can be safely performed within certain amount of time. In addition, we predicted that the evacuation time would be longer than the prediction results from an existing model which assumes constant movement speed. Our results from the model demonstrated good agreement with our experimental results.

Epidemic data show the existence of a region of quasi-linear growth (strolling period) of infected cases extending in between waves. We demonstrate that this constitutes evidence for the existence of near time-scale invariance that is neatly encoded via complex fixed points in the epidemic Renormalisation Group approach. As a result we achieve a deeper understanding of multiple wave dynamics and its inter-wave strolling regime. Our results are tested and calibrated against the COVID-19 pandemic data. Because of the simplicity of our approach that is organised around symmetry principles our discovery amounts to a paradigm shift in the way epidemiological data are mathematically modelled.

Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions going beyond pairwise models, such as graphs, in which all the interactions are considered as involving only two individuals at a time. Hypergraphs respond to this need, providing a mathematical representation of a system allowing from pairs to larger groups. In this work, through the use of different hypergraphs, we study how group interactions influence the evolution of cooperation in a structured population, by analyzing the evolutionary dynamics of the public goods game. Here we show that, likewise network reciprocity, group interactions also promote cooperation. More importantly, by means of an invasion analysis in which the conditions for a strategy to survive are studied, we show how, in heterogeneously-structured populations, reciprocity among players is expected to grow with the increasing of the order of the interactions. This is due to the heterogeneity of connections and, particularly, to the presence of individuals standing out as hubs in the population. Our analysis represents a first step towards the study of evolutionary dynamics through higher-order interactions, and gives insights into why cooperation in heterogeneous higher-order structures is enhanced. Lastly, it also gives clues about the co-existence of cooperative and non-cooperative behaviors related to the structural properties of the interaction patterns.