Concurrency-Induced Transitions in Epidemic Dynamics on Temporal Networks

Fixation probability in evolutionary dynamics on switching temporal networks

Population structure has been known to substantially affect evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of selection, and those that suppress the spreading of fitter mutants are called suppressors of selection. Research in the past two decades has found various families of amplifiers while suppressors still remain somewhat elusive. It has also been discovered that most networks are amplifiers of selection under the birth-death updating combined with uniform initialization, which is a standard condition assumed widely in the literature. In the present study, we extend the birth-death processes to temporal (i.e., time-varying) networks. For the sake of tractability, we restrict ourselves to switching temporal networks, in which the network structure deterministically alternates between two static networks at constant time intervals or stochastically in a Markovian manner. We show that, in a majority of cases, switching networks are less amplifying than both of the two static networks constituting the switching networks. Furthermore, most small switching networks, i.e., networks on six nodes or less, are suppressors, which contrasts to the case of static networks.

Strategy evolution on dynamic networks

Models of strategy evolution on static networks help us understand how population structure can promote the spread of traits like cooperation. One key mechanism is the formation of altruistic spatial clusters, where neighbors of a cooperative individual are likely to reciprocate, which protects prosocial traits from exploitation. However, most real-world interactions are ephemeral and subject to exogenous restructuring, so that social networks change over time. Strategic behavior on dynamic networks is difficult to study, and much less is known about the resulting evolutionary dynamics. Here we provide an analytical treatment of cooperation on dynamic networks, allowing for arbitrary spatial and temporal heterogeneity. We show that transitions among a large class of network structures can favor the spread of cooperation, even if each individual social network would inhibit cooperation when static. Furthermore, we show that spatial heterogeneity tends to inhibit cooperation, whereas temporal heterogeneity tends to promote it. Dynamic networks can have profound effects on the evolution of prosocial traits, even when individuals have no agency over network structures.

Staged HIV transmission and treatment in a dynamic model with long-term partnerships

The transmission dynamics of HIV are closely tied to the duration and overlap of sexual partnerships. We develop an autonomous population model that can account for the possibilities of an infection from either a casual sexual partner or a long-term partner who was either infected at the start of the partnership or has been newly infected since the onset of the partnership. The impact of the long-term partnerships on the rate of infection is captured by calculating the expected values of the rate of infection from these extended contacts. The model includes three stages of infectiousness: acute, chronic, and virally suppressed. We calculate HIV incidence and the fraction of new infections attributed to casual contacts and long-term partnerships allowing for variability in condom usage, the effect of achieving and maintaining viral suppression, and early intervention by beginning HAART during the acute phase of infection. We present our results using data on MSM HIV transmission from the CDC in the U.S. While the acute stage is the most infectious, the majority of the new infections will be transmitted by long-term partners in the chronic stage when condom use is infrequent as is common in long-term relationships. Time series analysis of the solution, as well as parameter sensitivity analysis, are used to determine effective intervention strategies.

Contact network analysis of COVID-19 Delta variant outbreak in urban China -based on 2,050 confirmed cases in Xi'an, China

BACKGROUND

The purpose of this paper is to study how the Delta variant spread in a China city, and to what extent the non-pharmaceutical prevention measures of local government be effective by reviewing the contact network of COVID-19 cases in Xi'an, China.

METHODS

We organize the case reports of the Shaanxi Health Commission into a database by text coding and convert them into a network matrix. Then we construct a dynamic contact network for the corresponding analysis and calculate network indicators. we analyze the cases' dynamic contact network structure and intervals between diagnosis time and isolation time by using data visualization, network analysis method, and Ordinary Least Square (OLS) regression.

RESULTS

The contact network for this outbreak in Xi'an is very sparse, with a density of less than 0.0001. The contact network is a scale-free network. The average degree centrality is 0.741 and the average PageRank score is 0.0005. The network generated from a single source of infection contains 1371 components. We construct three variables of intervals and analyze the trend of intervals during the outbreak. The mean interval (interval 1) between case diagnosis time and isolation time is - 3.9 days. The mean of the interval (interval 2) between the infector's diagnosis time and the infectee's diagnosis time is 4.2 days. The mean of the interval (interval 3) between infector isolation time and infectee isolation time is 2.9 days. Among the three intervals, only interval 1 has a significant positive correlation with degree centrality.

CONCLUSIONS

By integrating COVID-19 case reports of a Chinese city, we construct a contact network to analyze the dispersion of the outbreak. The network is a scale-free network with multiple hidden pathways that are not detected. The intervals of patients in this outbreak decreased compared to the beginning of the outbreak in 2020. City lockdown has a significant effect on the intervals that can affect patients' network centrality. Our study highlights the value of case report text. By linking different reports, we can quickly analyze the spread of the epidemic in an urban area.

Concurrency measures in the era of temporal network epidemiology: a review

Diseases spread over temporal networks of interaction events between individuals. Structures of these temporal networks hold the keys to understanding epidemic propagation. One early concept of the literature to aid in discussing these structures is concurrency-quantifying individuals' tendency to form time-overlapping 'partnerships'. Although conflicting evaluations and an overabundance of operational definitions have marred the history of concurrency, it remains important, especially in the area of sexually transmitted infections. Today, much of theoretical epidemiology uses more direct models of contact patterns, and there is an emerging body of literature trying to connect methods to the concurrency literature. In this review, we will cover the development of the concept of concurrency and these new approaches.

Analysis of dynamic contact network of patients with COVID-19 in Shaanxi Province of China

The spread of COVID-19 is closely related to the structure of human social networks. Based on 237 cases, by using epidemiological retrospective statistics, data visualization, and social network analysis methods, this paper summarized characteristics of patients with COVID-19 in Shaanxi, China, and analyzed these patients' dynamic contact network structure. The study found that there are many clustered infections through strong ties, about one-third of cases are caused by relatives' infection. In early stages of the epidemic, imported cases were the most, and in the later stages, local infection cases were the most. The infected people were mostly middle-aged men. Symptoms of imported cases occurred on average of 3 days after they arrived, and medical measures were taken 5 days later on average. All cases showed symptoms in less than 2 days on average and were then taken to medical treatment. The contact network can be divided into multiple disconnected components. The largest component has 12 patients. The average degree centrality in the network is 0.987, average betweenness degree is 0, average closeness degree is 0.452, and average PageRank index is 0.0042. The number of contacts of patients is unevenly distributed in the network.

Concurrency and reachability in treelike temporal networks

Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes and links appear and disappear. We focus on the effects of accessibility, whether there is a temporally consistent path from one node to another, and reachability, the density of the corresponding accessibility graph representation of the temporal network. The level of reachability thus inherently limits the possible extent of any spreading process on the temporal network. We study reachability in terms of the overall levels of temporal concurrency between edges and the structural cohesion of the network agglomerating over all edges. We use simulation results and develop heterogeneous mean-field model predictions for random networks to better quantify how the properties of the underlying temporal network regulate reachability.

Containing misinformation spreading in temporal social networks

Many researchers from a variety of fields, including computer science, network science, and mathematics, have focused on how to contain the outbreaks of Internet misinformation that threaten social systems and undermine societal health. Most research on this topic treats the connections among individuals as static, but these connections change in time, and thus social networks are also temporal networks. Currently, there is no theoretical approach to the problem of containing misinformation outbreaks in temporal networks. We thus propose a misinformation spreading model for temporal networks and describe it using a new theoretical approach. We propose a heuristic-containing (HC) strategy based on optimizing the final outbreak size that outperforms simplified strategies such as those that are random-containing and targeted-containing. We verify the effectiveness of our HC strategy on both artificial and real-world networks by performing extensive numerical simulations and theoretical analyses. We find that the HC strategy dramatically increases the outbreak threshold and decreases the final outbreak threshold.

A sexually transmitted infection model with long-term partnerships in homogeneous and heterogenous populations

Population models for sexually transmitted infections frequently use a transmission model that assumes an inherent partnership length of zero. However, in a population with long-term partnerships, the infection status of the partners, the length of the partnership, and the exclusivity of the partnership significantly affect the rate of infection. We develop an autonomous population model that can account for the possibilities of an infection from either a casual sexual partner or a longtime partner who was either infected at the start of the partnership or was newly infected. The impact of the long-term partnerships on the rate of infection is captured by calculating the expected values of the rate of infection from these extended contacts. We present a new method to evaluate partner acquisition rates for casual or long-term partnerships which produces in a more realistic number of lifetime sexual partners. Results include a SI model with different infectiousness levels for the transmission of HIV and HSV-2 with acute and chronic/latent infection stages for homogeneous (MSM) and heterogeneous (WSM-MSW) groups. The accompanying reproduction number and sensitivity studies highlight the impact of both casual and long-term partnerships on infection spread. We construct an autonomous set of equations that handle issues usually ignored by autonomous equations and handled only through simulations or in a non-autonomous form. The autonomous formulation of the model allows for simple numerical computations while incorporating a combination of random instantaneous contacts between individuals and prolonged contacts between specific individuals.

Diffusion in networks and the virtue of burstiness

Whether an idea, information, or infection diffuses throughout a society depends not only on the structure of the network of interactions, but also on the timing of those interactions. People are not always available to interact with others, and people differ in the timing of when they are active. Some people are active for long periods and then inactive for long periods, while others switch more frequently from being active to inactive and back. We show that maximizing diffusion in classic contagion processes requires heterogeneous activity patterns across agents. In particular, maximizing diffusion comes from mixing two extreme types of people: those who are stationary for long periods of time, changing from active to inactive or back only infrequently, and others who alternate frequently between being active and inactive.

Epidemic spreading in modular time-varying networks

We investigate the effects of modular and temporal connectivity patterns on epidemic spreading. To this end, we introduce and analytically characterise a model of time-varying networks with tunable modularity. Within this framework, we study the epidemic size of Susceptible-Infected-Recovered, SIR, models and the epidemic threshold of Susceptible-Infected-Susceptible, SIS, models. Interestingly, we find that while the presence of tightly connected clusters inhibits SIR processes, it speeds up SIS phenomena. In this case, we observe that modular structures induce a reduction of the threshold with respect to time-varying networks without communities. We confirm the theoretical results by means of extensive numerical simulations both on synthetic graphs as well as on a real modular and temporal network.