Language Statistics at Different Spatial, Temporal, and Grammatical Scales.

In recent decades, the field of statistical linguistics has made significant strides, which have been fueled by the availability of data. Leveraging Twitter data, this paper explores the English and Spanish languages, investigating their rank diversity across different scales: temporal intervals (ranging from 3 to 96 h), spatial radii (spanning 3 km to over 3000 km), and grammatical word ngrams (ranging from 1-grams to 5-grams). The analysis focuses on word ngrams, examining a time period of 1 year (2014) and eight different countries. Our findings highlight the relevance of all three scales with the most substantial changes observed at the grammatical level. Specifically, at the monogram level, rank diversity curves exhibit remarkable similarity across languages, countries, and temporal or spatial scales. However, as the grammatical scale expands, variations in rank diversity become more pronounced and influenced by temporal, spatial, linguistic, and national factors. Additionally, we investigate the statistical characteristics of Twitter-specific tokens, including emojis, hashtags, and user mentions, revealing a sigmoid pattern in their rank diversity function. These insights contribute to quantifying universal language statistics while also identifying potential sources of variation.

Ascertainment rate of SARS-CoV-2 infections from healthcare and community testing in the UK.

The proportion of SARS-CoV-2 infections ascertained through healthcare and community testing is generally unknown and expected to vary depending on natural factors and changes in test-seeking behaviour. Here we use population surveillance data and reported daily case numbers in the United Kingdom to estimate the rate of case ascertainment. We mathematically describe the relationship between the ascertainment rate, the daily number of reported cases, population prevalence, and the sensitivity of PCR and Lateral Flow tests as a function time since exposure. Applying this model to the data, we estimate that 20%-40% of SARS-CoV-2 infections in the UK were ascertained with a positive test with results varying by time and region. Cases of the Alpha variant were ascertained at a higher rate than the wild type variants circulating in the early pandemic, and higher again for the Delta variant and Omicron BA.1 sub-lineage, but lower for the BA.2 sub-lineage. Case ascertainment was higher in adults than in children. We further estimate the daily number of infections and compare this to mortality data to estimate that the infection fatality rate increased by a factor of 3 during the period dominated by the Alpha variant, and declined in line with the distribution of vaccines. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Efficient sentinel surveillance strategies for preventing epidemics on networks.

Surveillance plays a crucial role in preventing emerging infectious diseases from becoming epidemic. In circumstances where it is possible to monitor the infection status of certain people, transport hubs, or hospitals, early detection of the disease allows interventions to be implemented before most of the damage can occur, or at least its impact can be mitigated. This paper addresses the question of which nodes we should select in a network of individuals susceptible to some infectious disease in order to minimize the number of casualties. By simulating disease outbreaks on a collection of empirical and synthetic networks we show that the best strategy depends on topological characteristics of the network. For highly modular or spatially embedded networks it is better to place the sentinels on nodes distributed across different regions. However, if the degree heterogeneity is high, then a strategy that targets network hubs is preferred. We further consider the consequences of having an incomplete sample of the network and demonstrate that the value of new information diminishes as more data is collected. Finally we find further marginal improvements using two heuristics informed by known results in graph theory that exploit the fragmented structure of sparse network data.

The reachability of contagion in temporal contact networks: how disease latency can exploit the rhythm of human behavior.

BACKGROUND: The symptoms of many infectious diseases influence their host to withdraw from social activity limiting their potential to spread. Successful transmission therefore requires the onset of infectiousness to coincide with a time when the host is socially active. Since social activity and infectiousness are both temporal phenomena, we hypothesize that diseases are most pervasive when these two processes are synchronized. METHODS: We consider disease dynamics that incorporate behavioral responses that effectively shorten the infectious period of the pathogen. Using data collected from face-to-face social interactions and synthetic contact networks constructed from empirical demographic data, we measure the reachability of this disease model and perform disease simulations over a range of latent period durations. RESULTS: We find that maximum transmission risk results when the disease latent period (and thus the generation time) are synchronized with human circadian rhythms of 24 h, and minimum transmission risk when latent periods are out of phase with circadian rhythms by 12 h. The effect of this synchronization is present for a range of disease models with realistic disease parameters and host behavioral responses. CONCLUSIONS: The reproductive potential of pathogens is linked inextricably to the host social behavior required for transmission. We propose that future work should consider contact periodicity in models of disease dynamics, and suggest the possibility that disease control strategies may be designed to optimize against the effects of synchronization.

A Metapopulation Model for Preventing the Reintroduction of Bovine Viral Diarrhea Virus to Naïve Herds: Scotland Case Study.

Background: Bovine viral diarrhea (BVD) virus is one of the most problematic infectious pathogens for cattle. Since 2013, a mandatory BVD eradication program has successfully reduced the number of infected cattle living on Scottish farms; however, England remains at high prevalence and presents a risk to Scotland through animal movement. Methods: We analyze cattle movements in the UK from 2008 to 2017 and recorded incidence of BVD in Scotland from 2017 to 2020. To simulate BVD reintroduction into Scotland, we developed an epidemiological model that combines transmission between cattle and animal movements between farms. A total of four control strategies were implemented in the model: no intervention, import restriction, targeted vaccination, and combined strategy. Results: During the course of the eradication scheme, movements into Scotland became increasingly distributed in regions close to the England-Scotland border. The prevalence of BVD in this region decreased at a slower rate than the rest of Scotland during the eradication scheme. Our model showed that the change in the prevalence is expected, given that the change in the patterns of movement and if vaccination is targeted to the border areas that decrease in the prevalence will be seen throughout the whole of Scotland. Conclusion: Scottish farms are susceptible to BVD virus reintroduction through animal imports from non-BVD-free nations with farms in border areas being the most vulnerable. Protecting the border regions provides direct and indirect protection to the rest of Scottish farms by interrupting chains of transmission.

SCoVMod - a spatially explicit mobility and deprivation adjusted model of first wave COVID-19 transmission dynamics.

Background: Mobility restrictions prevent the spread of infections to disease-free areas, and early in the coronavirus disease 2019 (COVID-19) pandemic, most countries imposed severe restrictions on mobility as soon as it was clear that containment of local outbreaks was insufficient to control spread. These restrictions have adverse impacts on the economy and other aspects of human health, and it is important to quantify their impact for evaluating their future value. Methods: Here we develop Scotland Coronavirus transmission Model (SCoVMod), a model for COVID-19 in Scotland, which presents unusual challenges because of its diverse geography and population conditions. Our fitted model captures spatio-temporal patterns of mortality in the first phase of the epidemic to a fine geographical scale. Results: We find that lockdown restrictions reduced transmission rates down to an estimated 12\% of its pre-lockdown rate. We show that, while the timing of COVID-19 restrictions influences the role of the transmission rate on the number of COVID-related deaths, early reduction in long distance movements does not. However, poor health associated with deprivation has a considerable association with mortality; the Council Area (CA) with the greatest health-related deprivation was found to have a mortality rate 2.45 times greater than the CA with the lowest health-related deprivation considering all deaths occurring outside of carehomes. Conclusions: We find that in even an early epidemic with poor case ascertainment, a useful spatially explicit model can be fit with meaningful parameters based on the spatio-temporal distribution of death counts. Our simple approach is useful to strategically examine trade-offs between travel related restrictions and physical distancing, and the effect of deprivation-related factors on outcomes.

Social fluidity mobilizes contagion in human and animal populations.

Humans and other group-living animals tend to distribute their social effort disproportionately. Individuals predominantly interact with a small number of close companions while maintaining weaker social bonds with less familiar group members. By incorporating this behavior into a mathematical model, we find that a single parameter, which we refer to as social fluidity, controls the rate of social mixing within the group. Large values of social fluidity correspond to gregarious behavior, whereas small values signify the existence of persistent bonds between individuals. We compare the social fluidity of 13 species by applying the model to empirical human and animal social interaction data. To investigate how social behavior influences the likelihood of an epidemic outbreak, we derive an analytical expression of the relationship between social fluidity and the basic reproductive number of an infectious disease. For species that form more stable social bonds, the model describes frequency-dependent transmission that is sensitive to changes in social fluidity. As social fluidity increases, animal-disease systems become increasingly density-dependent. Finally, we demonstrate that social fluidity is a stronger predictor of disease outcomes than both group size and connectivity, and it provides an integrated framework for both density-dependent and frequency-dependent transmission.

Spontaneous divergence of disease status in an economic epidemiological game.

We introduce a game inspired by the challenges of disease management in livestock farming and the transmission of endemic disease through a trade network. Success in this game comes from balancing the cost of buying new stock with the risk that it will be carrying some disease. When players follow a simple memory-based strategy we observe a spontaneous separation into two groups corresponding to players with relatively high, or low, levels of infection. By modelling the dynamics of both the disease and the formation and breaking of trade relationships, we derive the conditions for which this separation occurs as a function of the transmission rate and the threshold level of acceptable disease for each player. When interactions in the game are restricted to players that neighbour each other in a small-world network, players tend to have similar levels of infection as their neighbours. We conclude that success in economic-epidemiological systems can originate from misfortune and geographical circumstances as well as by innate differences in personal attitudes towards risk.

Ant colonies maintain social homeostasis in the face of decreased density.

Interactions lie at the heart of social organization, particularly in ant societies. Interaction rates are presumed to increase with density, but there is little empirical evidence for this. We manipulated density within carpenter ant colonies of the species Camponotus pennsylvanicus by quadrupling nest space and by manually tracking 6.9 million ant locations and over 3200 interactions to study the relationship between density, spatial organization and interaction rates. Colonies divided into distinct spatial regions on the basis of their underlying spatial organization and changed their movement patterns accordingly. Despite a reduction in both overall and local density, we did not find the expected concomitant reduction in interaction rates across all colonies. Instead, we found divergent effects across colonies. Our results highlight the remarkable organizational resilience of ant colonies to changes in density, which allows them to sustain two key basic colony life functions, that is food and information exchange, during environmental change.

Separating temporal and topological effects in walk-based network centrality.

The recently introduced concept of dynamic communicability is a valuable tool for ranking the importance of nodes in a temporal network. Two metrics, broadcast score and receive score, were introduced to measure the centrality of a node with respect to a model of contagion based on time-respecting walks. This article examines the temporal and structural factors influencing these metrics by considering a versatile stochastic temporal network model. We analytically derive formulas to accurately predict the expectation of the broadcast and receive scores when one or more columns in a temporal edge-list are shuffled. These methods are then applied to two publicly available data sets and we quantify how much the centrality of each individual depends on structural or temporal influences. From our analysis, we highlight two practical contributions: a way to control for temporal variation when computing dynamic communicability and the conclusion that the broadcast and receive scores can, under a range of circumstances, be replaced by the row and column sums of the matrix exponential of a weighted adjacency matrix given by the data.

Memory and burstiness in dynamic networks.

A discrete-time random process is described, which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time t is given by a fixed probability x, is modified to include a memory effect where the event probability is increased proportionally to the number of events that occurred within a given amount of time preceding t. For small values of x the interevent time distribution follows a power law with exponent -2-x. We consider a dynamic network where each node forms, and breaks connections according to this process. The value of x for each node depends on the fitness distribution, ρ(x), from which it is drawn; we find exact solutions for the expectation of the degree distribution for a variety of possible fitness distributions, and for both cases where the memory effect either is, or is not present. This work can potentially lead to methods to uncover hidden fitness distributions from fast changing, temporal network data, such as online social communications and fMRI scans.