Nonlinear bias toward complex contagion in uncertain transmission settings.

Current epidemics in the biological and social domains are challenging the standard assumptions of mathematical contagion models. Chief among them are the complex patterns of transmission caused by heterogeneous group sizes and infection risk varying by orders of magnitude in different settings, like indoor versus outdoor gatherings in the COVID-19 pandemic or different moderation practices in social media communities. However, quantifying these heterogeneous levels of risk is difficult, and most models typically ignore them. Here, we include these features in an epidemic model on weighted hypergraphs to capture group-specific transmission rates. We study analytically the consequences of ignoring the heterogeneous transmissibility and find an induced superlinear infection rate during the emergence of a new outbreak, even though the underlying mechanism is a simple, linear contagion. The dynamics produced at the individual and group levels are therefore more similar to complex, nonlinear contagions, thus blurring the line between simple and complex contagions in realistic settings. We support this claim by introducing a Bayesian inference framework to quantify the nonlinearity of contagion processes. We show that simple contagions on real weighted hypergraphs are systematically biased toward the superlinear regime if the heterogeneity of the weights is ignored, greatly increasing the risk of erroneous classification as complex contagions. Our results provide an important cautionary tale for the challenging task of inferring transmission mechanisms from incidence data. Yet, it also paves the way for effective models that capture complex features of epidemics through nonlinear infection rates.

Multidisciplinary learning through collective performance favors decentralization.

Many models of learning in teams assume that team members can share solutions or learn concurrently. However, these assumptions break down in multidisciplinary teams where team members often complete distinct, interrelated pieces of larger tasks. Such contexts make it difficult for individuals to separate the performance effects of their own actions from the actions of interacting neighbors. In this work, we show that individuals can overcome this challenge by learning from network neighbors through mediating artifacts (like collective performance assessments). When neighbors' actions influence collective outcomes, teams with different networks perform relatively similarly to one another. However, varying a team's network can affect performance on tasks that weight individuals' contributions by network properties. Consequently, when individuals innovate (through "exploring" searches), dense networks hurt performance slightly by increasing uncertainty. In contrast, dense networks moderately help performance when individuals refine their work (through "exploiting" searches) by efficiently finding local optima. We also find that decentralization improves team performance across a battery of 34 tasks. Our results offer design principles for multidisciplinary teams within which other forms of learning prove more difficult.

Compressing the Chronology of a Temporal Network with Graph Commutators.

Studies of dynamics on temporal networks often represent the network as a series of "snapshots," static networks active for short durations of time. We argue that successive snapshots can be aggregated if doing so has little effect on the overlying dynamics. We propose a method to compress network chronologies by progressively combining pairs of snapshots whose matrix commutators have the smallest dynamical effect. We apply this method to epidemic modeling on real contact tracing data and find that it allows for significant compression while remaining faithful to the epidemic dynamics.

Network analysis of patterns and relevance of enteric pathogen co-infections among infants in a diarrhea-endemic setting.

Despite significant progress in recent decades toward ameliorating the excess burden of diarrheal disease globally, childhood diarrhea remains a leading cause of morbidity and mortality in low-and-middle-income countries (LMICs). Recent large-scale studies of diarrhea etiology in these populations have revealed widespread co-infection with multiple enteric pathogens, in both acute and asymptomatic stool specimens. We applied methods from network science and ecology to better understand the underlying structure of enteric co-infection among infants in two large longitudinal birth cohorts in Bangladesh. We used a configuration model to establish distributions of expected random co-occurrence, based on individual pathogen prevalence alone, for every pathogen pair among 30 enteropathogens detected by qRT-PCR in both diarrheal and asymptomatic stool specimens. We found two pairs, Enterotoxigenic E. coli (ETEC) with Enteropathogenic E. coli (EPEC), and ETEC with Campylobacter spp., co-infected significantly more than expected at random (both pairs co-occurring almost 4 standard deviations above what one could expect due to chance alone). Furthermore, we found a general pattern that bacteria-bacteria pairs appear together more frequently than expected at random, while virus-bacteria pairs tend to appear less frequently than expected based on model predictions. Finally, infants co-infected with leading bacteria-bacteria pairs had more days of diarrhea in the first year of life compared to infants without co-infection (p-value <0.0001). Our methods and results help us understand the structure of enteric co-infection which can guide further work to identify and eliminate common sources of infection or determine biologic mechanisms that promote co-infection.

The response of Canada's clinical health research ecosystem to the COVID-19 pandemic.

BACKGROUND: The response of Canada's research community to the COVID-19 pandemic provides a unique opportunity to examine the country's clinical health research ecosystem. We sought to describe patterns of enrolment across Canadian Institutes of Health Research (CIHR)-funded studies on COVID-19. METHODS: We identified COVID-19 studies funded by the CIHR and that enrolled participants from Canadian acute care hospitals between January 2020 and April 2023. We collected information on study-and site-level variables from study leads, site investigators, and public domain sources. We described and evaluated factors associated with cumulative enrolment. RESULTS: We obtained information for 23 out of 26 (88%) eligible CIHR-funded studies (16 randomized controlled trials [RCTs] and 7 cohort studies). The 23 studies were managed by 12 Canadian and 3 international coordinating centres. Of 419 Canadian hospitals, 97 (23%) enrolled a total of 28 973 participants - 3876 in RCTs across 78 hospitals (median cumulative enrolment per hospital 30, interquartile range [IQR] 10-61), and 25 097 in cohort studies across 62 hospitals (median cumulative enrolment per hospital 158, IQR 6-348). Of 78 hospitals recruiting participants in RCTs, 13 (17%) enrolled 50% of all RCT participants, whereas 6 of 62 hospitals (9.7%) recruited 54% of participants in cohort studies. INTERPRETATION: A minority of Canadian hospitals enrolled the majority of participants in CIHR-funded studies on COVID-19. This analysis sheds light on the Canadian health research ecosystem and provides information for multiple key partners to consider ways to realize the full research potential of Canada's health systems.

Adaptive staffing can mitigate essential worker disease and absenteeism in an emerging epidemic.

Essential worker absenteeism has been a pressing problem in the COVID-19 pandemic. Nearly 20% of US hospitals experienced staff shortages, exhausting replacement pools and at times requiring COVID-positive healthcare workers to remain at work. To our knowledge there are no data-informed models examining how different staffing strategies affect epidemic dynamics on a network in the context of rising worker absenteeism. Here we develop a susceptible-infected-quarantined-recovered adaptive network model using pair approximations to gauge the effects of worker replacement versus redistribution of work among remaining healthy workers in the early epidemic phase. Parameterized with hospital data, the model exhibits a time-varying trade-off: Worker replacement minimizes peak prevalence in the early phase, while redistribution minimizes final outbreak size. Any "ideal" strategy requires balancing the need to maintain a baseline number of workers against the desire to decrease total number infected. We show that one adaptive strategy-switching from replacement to redistribution at epidemic peak-decreases disease burden by 9.7% and nearly doubles the final fraction of healthy workers compared to pure replacement.

Superspreading events in the transmission dynamics of SARS-CoV-2: Opportunities for interventions and control.

Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), the etiological agent of the Coronavirus Disease 2019 (COVID-19) disease, has moved rapidly around the globe, infecting millions and killing hundreds of thousands. The basic reproduction number, which has been widely used-appropriately and less appropriately-to characterize the transmissibility of the virus, hides the fact that transmission is stochastic, often dominated by a small number of individuals, and heavily influenced by superspreading events (SSEs). The distinct transmission features of SARS-CoV-2, e.g., high stochasticity under low prevalence (as compared to other pathogens, such as influenza), and the central role played by SSEs on transmission dynamics cannot be overlooked. Many explosive SSEs have occurred in indoor settings, stoking the pandemic and shaping its spread, such as long-term care facilities, prisons, meat-packing plants, produce processing facilities, fish factories, cruise ships, family gatherings, parties, and nightclubs. These SSEs demonstrate the urgent need to understand routes of transmission, while posing an opportunity to effectively contain outbreaks with targeted interventions to eliminate SSEs. Here, we describe the different types of SSEs, how they influence transmission, empirical evidence for their role in the COVID-19 pandemic, and give recommendations for control of SARS-CoV-2.

Temporal and Probabilistic Comparisons of Epidemic Interventions.

Forecasting disease spread is a critical tool to help public health officials design and plan public health interventions. However, the expected future state of an epidemic is not necessarily well defined as disease spread is inherently stochastic, contact patterns within a population are heterogeneous, and behaviors change. In this work, we use time-dependent probability generating functions (PGFs) to capture these characteristics by modeling a stochastic branching process of the spread of a disease over a network of contacts in which public health interventions are introduced over time. To achieve this, we define a general transmissibility equation to account for varying transmission rates (e.g. masking), recovery rates (e.g. treatment), contact patterns (e.g. social distancing) and percentage of the population immunized (e.g. vaccination). The resulting framework allows for a temporal and probabilistic analysis of an intervention's impact on disease spread, which match continuous-time stochastic simulations that are much more computationally expensive. To aid policy making, we then define several metrics over which temporal and probabilistic intervention forecasts can be compared: Looking at the expected number of cases and the worst-case scenario over time, as well as the probability of reaching a critical level of cases and of not seeing any improvement following an intervention. Given that epidemics do not always follow their average expected trajectories and that the underlying dynamics can change over time, our work paves the way for more detailed short-term forecasts of disease spread and more informed comparison of intervention strategies.

Localization, epidemic transitions, and unpredictability of multistrain epidemics with an underlying genotype network.

Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modelling community to focus on the complexity of other factors such as population structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics. Here, we introduce a disease model with an underlying genotype network to account for two important mechanisms. One, the disease can mutate along network pathways as it spreads in a host population. Two, the genotype network allows us to define a genetic distance between strains and therefore to model the transcendence of immunity often observed in real world pathogens. We study the emergence of epidemics in this model, through its epidemic phase transitions, and highlight the role of the genotype network in driving cyclicity of diseases, large scale fluctuations, sequential epidemic transitions, as well as localization around specific strains of the associated pathogen. More generally, our model illustrates the richness of behaviours that are possible even in well-mixed host populations once we consider strain diversity and go beyond the "one disease equals one pathogen" paradigm.

Universal Nonlinear Infection Kernel from Heterogeneous Exposure on Higher-Order Networks.

The collocation of individuals in different environments is an important prerequisite for exposure to infectious diseases on a social network. Standard epidemic models fail to capture the potential complexity of this scenario by (1) neglecting the higher-order structure of contacts that typically occur through environments like workplaces, restaurants, and households, and (2) assuming a linear relationship between the exposure to infected contacts and the risk of infection. Here, we leverage a hypergraph model to embrace the heterogeneity of environments and the heterogeneity of individual participation in these environments. We find that combining heterogeneous exposure with the concept of minimal infective dose induces a universal nonlinear relationship between infected contacts and infection risk. Under nonlinear infection kernels, conventional epidemic wisdom breaks down with the emergence of discontinuous transitions, superexponential spread, and hysteresis.

Social Confinement and Mesoscopic Localization of Epidemics on Networks.

Recommendations around epidemics tend to focus on individual behaviors, with much less efforts attempting to guide event cancellations and other collective behaviors since most models lack the higher-order structure necessary to describe large gatherings. Through a higher-order description of contagions on networks, we model the impact of a blanket cancellation of events larger than a critical size and find that epidemics can suddenly collapse when interventions operate over groups of individuals rather than at the level of individuals. We relate this phenomenon to the onset of mesoscopic localization, where contagions concentrate around dominant groups.

Immunization strategies in networks with missing data.

Network-based intervention strategies can be effective and cost-efficient approaches to curtailing harmful contagions in myriad settings. As studied, these strategies are often impractical to implement, as they typically assume complete knowledge of the network structure, which is unusual in practice. In this paper, we investigate how different immunization strategies perform under realistic conditions-where the strategies are informed by partially-observed network data. Our results suggest that global immunization strategies, like degree immunization, are optimal in most cases; the exception is at very high levels of missing data, where stochastic strategies, like acquaintance immunization, begin to outstrip them in minimizing outbreaks. Stochastic strategies are more robust in some cases due to the different ways in which they can be affected by missing data. In fact, one of our proposed variants of acquaintance immunization leverages a logistically-realistic ongoing survey-intervention process as a form of targeted data-recovery to improve with increasing levels of missing data. These results support the effectiveness of targeted immunization as a general practice. They also highlight the risks of considering networks as idealized mathematical objects: overestimating the accuracy of network data and foregoing the rewards of additional inquiry.

Syntrophy emerges spontaneously in complex metabolic systems.

Syntrophy allows a microbial community as a whole to survive in an environment, even though individual microbes cannot. The metabolic interdependence typical of syntrophy is thought to arise from the accumulation of degenerative mutations during the sustained co-evolution of initially self-sufficient organisms. An alternative and underexplored possibility is that syntrophy can emerge spontaneously in communities of organisms that did not co-evolve. Here, we study this de novo origin of syntrophy using experimentally validated computational techniques to predict an organism's viability from its metabolic reactions. We show that pairs of metabolisms that are randomly sampled from a large space of possible metabolism and viable on specific primary carbon sources often become viable on new carbon sources by exchanging metabolites. The same biochemical reactions that are required for viability on primary carbon sources also confer viability on novel carbon sources. Our observations highlight a new and important avenue for the emergence of metabolic adaptations and novel ecological interactions.

Modeling the impact of school reopening on SARS-CoV-2 transmission using contact structure data from Shanghai.

BACKGROUND: Mathematical modeling studies have suggested that pre-emptive school closures alone have little overall impact on SARS-CoV-2 transmission, but reopening schools in the background of community contact reduction presents a unique scenario that has not been fully assessed. METHODS: We adapted a previously published model using contact information from Shanghai to model school reopening under various conditions. We investigated different strategies by combining the contact patterns observed between different age groups during both baseline and "lockdown" periods. We also tested the robustness of our strategy to the assumption of lower susceptibility to infection in children under age 15 years. RESULTS: We find that reopening schools for all children would maintain a post-intervention R0 < 1 up to a baseline R0 of approximately 3.3 provided that daily contacts among children 10-19 years are reduced to 33% of baseline. This finding was robust to various estimates of susceptibility to infection in children relative to adults (up to 50%) and to estimates of various levels of concomitant reopening in the rest of the community (up to 40%). However, full school reopening without any degree of contact reduction in the school setting returned R0 virtually back to baseline, highlighting the importance of mitigation measures. CONCLUSIONS: These results, based on contact structure data from Shanghai, suggest that schools can reopen with proper precautions during conditions of extreme contact reduction and during conditions of reasonable levels of reopening in the rest of the community.

Asymmetric percolation drives a double transition in sexual contact networks.

Zika virus (ZIKV) exhibits unique transmission dynamics in that it is concurrently spread by a mosquito vector and through sexual contact. Due to the highly asymmetric durations of infectiousness between males and females-it is estimated that males are infectious for periods up to 10 times longer than females-we show that this sexual component of ZIKV transmission behaves akin to an asymmetric percolation process on the network of sexual contacts. We exactly solve the properties of this asymmetric percolation on random sexual contact networks and show that this process exhibits two epidemic transitions corresponding to a core-periphery structure. This structure is not present in the underlying contact networks, which are not distinguishable from random networks, and emerges because of the asymmetric percolation. We provide an exact analytical description of this double transition and discuss the implications of our results in the context of ZIKV epidemics. Most importantly, our study suggests a bias in our current ZIKV surveillance, because the community most at risk is also one of the least likely to get tested.

The risk of sustained sexual transmission of Zika is underestimated.

Pathogens often follow more than one transmission route during outbreaks-from needle sharing plus sexual transmission of HIV to small droplet aerosol plus fomite transmission of influenza. Thus, controlling an infectious disease outbreak often requires characterizing the risk associated with multiple mechanisms of transmission. For example, during the Ebola virus outbreak in West Africa, weighing the relative importance of funeral versus health care worker transmission was essential to stopping disease spread. As a result, strategic policy decisions regarding interventions must rely on accurately characterizing risks associated with multiple transmission routes. The ongoing Zika virus (ZIKV) outbreak challenges our conventional methodologies for translating case-counts into route-specific transmission risk. Critically, most approaches will fail to accurately estimate the risk of sustained sexual transmission of a pathogen that is primarily vectored by a mosquito-such as the risk of sustained sexual transmission of ZIKV. By computationally investigating a novel mathematical approach for multi-route pathogens, our results suggest that previous epidemic threshold estimates could under-estimate the risk of sustained sexual transmission by at least an order of magnitude. This result, coupled with emerging clinical, epidemiological, and experimental evidence for an increased risk of sexual transmission, would strongly support recent calls to classify ZIKV as a sexually transmitted infection.

Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm.

Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the efficiency of current algorithms. We show that algorithms believed to require O ( log  N ) or even O ( 1 ) operations per update-where N is the number of nodes-display instead a polynomial scaling for networks that are either dense or sparse and heterogeneous. This significantly affects the required computation time for simulations on large networks. To circumvent the issue, we propose a node-based method combined with a composition and rejection algorithm, a sampling scheme that has an average-case complexity of O [ log ( log  N ) ] per update for general networks. This systematic approach is first set-up for Markovian dynamics, but can also be adapted to a number of non-Markovian processes and can enhance considerably the study of a wide range of dynamics on networks.

Edge fires drive the shape and stability of tropical forests.

In tropical regions, fires propagate readily in grasslands but typically consume only edges of forest patches. Thus, forest patches grow due to tree propagation and shrink by fires in surrounding grasslands. The interplay between these competing edge effects is unknown, but critical in determining the shape and stability of individual forest patches, as well the landscape-level spatial distribution and stability of forests. We analyze high-resolution remote-sensing data from protected Brazilian Cerrado areas and find that forest shapes obey a robust perimeter-area scaling relation across climatic zones. We explain this scaling by introducing a heterogeneous fire propagation model of tropical forest-grassland ecotones. Deviations from this perimeter-area relation determine the stability of individual forest patches. At a larger scale, our model predicts that the relative rates of tree growth due to propagative expansion and long-distance seed dispersal determine whether collapse of regional-scale tree cover is continuous or discontinuous as fire frequency changes.

Complex dynamics of synergistic coinfections on realistically clustered networks.

We investigate the impact of contact structure clustering on the dynamics of multiple diseases interacting through coinfection of a single individual, two problems typically studied independently. We highlight how clustering, which is well known to hinder propagation of diseases, can actually speed up epidemic propagation in the context of synergistic coinfections if the strength of the coupling matches that of the clustering. We also show that such dynamics lead to a first-order transition in endemic states, where small changes in transmissibility of the diseases can lead to explosive outbreaks and regions where these explosive outbreaks can only happen on clustered networks. We develop a mean-field model of coinfection of two diseases following susceptible-infectious-susceptible dynamics, which is allowed to interact on a general class of modular networks. We also introduce a criterion based on tertiary infections that yields precise analytical estimates of when clustering will lead to faster propagation than nonclustered networks. Our results carry importance for epidemiology, mathematical modeling, and the propagation of interacting phenomena in general. We make a call for more detailed epidemiological data of interacting coinfections.

The timing and targeting of treatment in influenza pandemics influences the emergence of resistance in structured populations.

Antiviral resistance in influenza is rampant and has the possibility of causing major morbidity and mortality. Previous models have identified treatment regimes to minimize total infections and keep resistance low. However, the bulk of these studies have ignored stochasticity and heterogeneous contact structures. Here we develop a network model of influenza transmission with treatment and resistance, and present both standard mean-field approximations as well as simulated dynamics. We find differences in the final epidemic sizes for identical transmission parameters (bistability) leading to different optimal treatment timing depending on the number initially infected. We also find, contrary to previous results, that treatment targeted by number of contacts per individual (node degree) gives rise to more resistance at lower levels of treatment than non-targeted treatment. Finally we highlight important differences between the two methods of analysis (mean-field versus stochastic simulations), and show where traditional mean-field approximations fail. Our results have important implications not only for the timing and distribution of influenza chemotherapy, but also for mathematical epidemiological modeling in general. Antiviral resistance in influenza may carry large consequences for pandemic mitigation efforts, and models ignoring contact heterogeneity and stochasticity may provide misleading policy recommendations.