Random Networks with Tunable Degree Distribution and Clustering

We present an algorithm for generating random networks with arbitrary degree distribution and Clustering (frequency of triadic closure). We use this algorithm to generate networks with exponential, power law, and poisson degree distributions with variable levels of clustering. Such networks may be used as models of social networks and as a testable null hypothesis about network structure. Finally, we explore the effects of clustering on the point of the phase transition where a giant component forms in a random network, and on the size of the giant component. Some analysis of these effects is presented.Comment: 9 pages, 13 figures corrected typos, added two references, reorganized reference

COVID-19 Scenario Projections: The Emergence of Omicron in the US

On November 24, 2021, South African scientists announced the rapid spread of a new SARS-CoV-2 variant. Within days, the WHO named the variant Omicron and classified it as a variant of concern (VOC). As of December 15, 2021, many of Omicron's epidemiological characteristics remain uncertain, including its intrinsic transmissibility, ability to evade vaccine-acquired and infection-acquired immunity, and severity. To support situational awareness and planning in the United States, we simulated the emergence and spread of Omicron in the US across a range of plausible scenarios. Using a stochastic compartmental model that tracks population-level immunity against the Delta and Omicron variants derived from infections, primary vaccines, and booster vaccines, we project COVID-19 cases, hospitalizations and deaths over a six month period beginning on December 1, 2021 under 18 different scenarios.Integrative Biolog

COVID-19 Scenario Projections: The Emergence of Omicron in the US - January 2022

As of January 6, 2021, the highly-transmissible SARS-CoV-2 Omicron variant is driving the largest COVID-19 wave in the US to date. The numbers of new cases and hospitalizations continue to rise, straining healthcare systems around the country. On December 16, 2021, we posted projections for the emergence of the Omicron variant under 18 plausible scenarios [1]. At that time, many of Omicron's epidemiological characteristics were uncertain. Recent studies suggest that the Omicron variant is more transmissible, more immune evasive, and less severe than the Delta variant. In this report, we present updated scenario projections that reflect our current understanding of Omicron transmission and severity in the US. Using a stochastic compartmental model that tracks population-level immunity against the Delta and Omicron variants derived from infections, primary vaccines, and booster vaccines, we project COVID-19 cases, hospitalizations, and deaths over a six month period beginning on January 1, 2022 under eight different scenarios.Integrative Biolog

Omicron scenario projections for the Austin-Round Rock MSA

The ongoing COVID-19 surge is straining healthcare systems in the Austin-Round Rock Metropolitan area. As of January 21, 2022, COVID-19 hospital admissions have reached record numbers and the total number of COVID-19 patients in hospitals and ICUs continue to rise. To support response efforts and public risk awareness, we used a data-driven mathematical model to simulate the continued spread of the Omicron variant in the Austin-Round Rock MSA area from January 22, 2022 to June 21, 2022 under four plausible scenarios. Our projections suggest that the 7-day rolling average of reported new cases in the five-county MSA likely peaked on January 9, 2022 at a value 6,109.Integrative Biolog

Disease Surveillance on Complex Social Networks

As infectious disease surveillance systems expand to include digital, crowd-sourced, and social network data, public health agencies are gaining unprecedented access to high-resolution data and have an opportunity to selectively monitor informative individuals. Contact networks, which are the webs of interaction through which diseases spread, determine whether and when individuals become infected, and thus who might serve as early and accurate surveillance sensors. Here, we evaluate three strategies for selecting sensors—sampling the most connected, random, and friends of random individuals—in three complex social networks—a simple scale-free network, an empirical Venezuelan college student network, and an empirical Montreal wireless hotspot usage network. Across five different surveillance goals—early and accurate detection of epidemic emergence and peak, and general situational awareness—we find that the optimal choice of sensors depends on the public health goal, the underlying network and the reproduction number of the disease (R0). For diseases with a low R0, the most connected individuals provide the earliest and most accurate information about both the onset and peak of an outbreak. However, identifying network hubs is often impractical, and they can be misleading if monitored for general situational awareness, if the underlying network has significant community structure, or if R0 is high or unknown. Taking a theoretical approach, we also derive the optimal surveillance system for early outbreak detection but find that real-world identification of such sensors would be nearly impossible. By contrast, the friends-of-random strategy offers a more practical and robust alternative. It can be readily implemented without prior knowledge of the network, and by identifying sensors with higher than average, but not the highest, epidemiological risk, it provides reasonably early and accurate information

Harnessing case isolation and ring vaccination to control Ebola.

As a devastating Ebola outbreak in West Africa continues, non-pharmaceutical control measures including contact tracing, quarantine, and case isolation are being implemented. In addition, public health agencies are scaling up efforts to test and deploy candidate vaccines. Given the experimental nature and limited initial supplies of vaccines, a mass vaccination campaign might not be feasible. However, ring vaccination of likely case contacts could provide an effective alternative in distributing the vaccine. To evaluate ring vaccination as a strategy for eliminating Ebola, we developed a pair approximation model of Ebola transmission, parameterized by confirmed incidence data from June 2014 to January 2015 in Liberia and Sierra Leone. Our results suggest that if a combined intervention of case isolation and ring vaccination had been initiated in the early fall of 2014, up to an additional 126 cases in Liberia and 560 cases in Sierra Leone could have been averted beyond case isolation alone. The marginal benefit of ring vaccination is predicted to be greatest in settings where there are more contacts per individual, greater clustering among individuals, when contact tracing has low efficacy or vaccination confers post-exposure protection. In such settings, ring vaccination can avert up to an additional 8% of Ebola cases. Accordingly, ring vaccination is predicted to offer a moderately beneficial supplement to ongoing non-pharmaceutical Ebola control efforts

The Impact of Imitation on Vaccination Behavior in Social Contact Networks

Previous game-theoretic studies of vaccination behavior typically have often assumed that populations are homogeneously mixed and that individuals are fully rational. In reality, there is heterogeneity in the number of contacts per individual, and individuals tend to imitate others who appear to have adopted successful strategies. Here, we use network-based mathematical models to study the effects of both imitation behavior and contact heterogeneity on vaccination coverage and disease dynamics. We integrate contact network epidemiological models with a framework for decision-making, within which individuals make their decisions either based purely on payoff maximization or by imitating the vaccination behavior of a social contact. Simulations suggest that when the cost of vaccination is high imitation behavior may decrease vaccination coverage. However, when the cost of vaccination is small relative to that of infection, imitation behavior increases vaccination coverage, but, surprisingly, also increases the magnitude of epidemics through the clustering of nonvaccinators within the network. Thus, imitation behavior may impede the eradication of infectious diseases. Calculations that ignore behavioral clustering caused by imitation may significantly underestimate the levels of vaccination coverage required to attain herd immunity

Effects of Heterogeneous and Clustered Contact Patterns on Infectious Disease Dynamics

The spread of infectious diseases fundamentally depends on the pattern of contacts between individuals. Although studies of contact networks have shown that heterogeneity in the number of contacts and the duration of contacts can have far-reaching epidemiological consequences, models often assume that contacts are chosen at random and thereby ignore the sociological, temporal and/or spatial clustering of contacts. Here we investigate the simultaneous effects of heterogeneous and clustered contact patterns on epidemic dynamics. To model population structure, we generalize the configuration model which has a tunable degree distribution (number of contacts per node) and level of clustering (number of three cliques). To model epidemic dynamics for this class of random graph, we derive a tractable, low-dimensional system of ordinary differential equations that accounts for the effects of network structure on the course of the epidemic. We find that the interaction between clustering and the degree distribution is complex. Clustering always slows an epidemic, but simultaneously increasing clustering and the variance of the degree distribution can increase final epidemic size. We also show that bond percolation-based approximations can be highly biased if one incorrectly assumes that infectious periods are homogeneous, and the magnitude of this bias increases with the amount of clustering in the network. We apply this approach to model the high clustering of contacts within households, using contact parameters estimated from survey data of social interactions, and we identify conditions under which network models that do not account for household structure will be biased

Erratic Flu Vaccination Emerges from Short-Sighted Behavior in Contact Networks

The effectiveness of seasonal influenza vaccination programs depends on individual-level compliance. Perceptions about risks associated with infection and vaccination can strongly influence vaccination decisions and thus the ultimate course of an epidemic. Here we investigate the interplay between contact patterns, influenza-related behavior, and disease dynamics by incorporating game theory into network models. When individuals make decisions based on past epidemics, we find that individuals with many contacts vaccinate, whereas individuals with few contacts do not. However, the threshold number of contacts above which to vaccinate is highly dependent on the overall network structure of the population and has the potential to oscillate more wildly than has been observed empirically. When we increase the number of prior seasons that individuals recall when making vaccination decisions, behavior and thus disease dynamics become less variable. For some networks, we also find that higher flu transmission rates may, counterintuitively, lead to lower (vaccine-mediated) disease prevalence. Our work demonstrates that rich and complex dynamics can result from the interaction between infectious diseases, human contact patterns, and behavior