Phase lag in epidemics on a network of cities

Beijing's central role in global artificial intelligence research

Nations worldwide are mobilizing to harness the power of Artificial Intelligence (AI) given its massive potential to shape global competitiveness over the coming decades. Using a dataset of 2.2 million AI papers, we study inter-city citations, collaborations, and talent migrations to uncover dependencies between Eastern and Western cities worldwide. Beijing emerges as a clear outlier, as it has been the most impactful city since 2007, the most productive since 2002, and the one housing the largest number of AI scientists since 1995. Our analysis also reveals that Western cities cite each other far more frequently than expected by chance, East-East collaborations are far more common than East-West or West-West collaborations, and migration of AI scientists mostly takes place from one Eastern city to another. We then propose a measure that quantifies each city's role in bridging East and West. Beijing's role surpasses that of all other cities combined, making it the central gateway through which knowledge and talent flow from one side to the other. We also track the center of mass of AI research by weighing each city's geographic location by its impact, productivity, and AI workforce. The center of mass has moved thousands of kilometers eastward over the past three decades, with Beijing's pull increasing each year. These findings highlight the eastward shift in the tides of global AI research, and the growing role of the Chinese capital as a hub connecting researchers across the globe.

Intrinsic noise, Delta-Notch signalling and delayed reactions promote sustained, coherent, synchronized oscillations in the presomitic mesoderm

Using a stochastic individual-based modelling approach, we examine the role that Delta-Notch signalling plays in the regulation of a robust and reliable somite segmentation clock. We find that not only can Delta-Notch signalling synchronize noisy cycles of gene expression in adjacent cells in the presomitic mesoderm (as is known), but it can also amplify and increase the coherence of these cycles. We examine some of the shortcomings of deterministic approaches to modelling these cycles and demonstrate how intrinsic noise can play an active role in promoting sustained oscillations, giving rise to noise-induced quasi-cycles. Finally, we explore how translational/transcriptional delays can result in the cycles in neighbouring cells oscillating in anti-phase and we study how this effect relates to the propagation of noise-induced stochastic waves.

The problem of detrending when analysing potential indicators of disease elimination

As we strive towards the elimination of many burdensome diseases, the question of when intervention efforts may cease is increasingly important. It can be very difficult to know when prevalences are low enough that the disease will die out without further intervention, particularly for diseases that lack accurate tests. The consequences of stopping an intervention prematurely can put back elimination efforts by decades. Critical slowing down theory predicts that as a dynamical system moves through a critical transition, deviations from the steady state return increasingly slowly. We study two potential indicators of disease elimination predicted by this theory, and investigate their response using a simple stochastic model. We compare our dynamical predictions to simulations of the fluctuation variance and coefficient of variation as the system moves through the transition to elimination. These comparisons demonstrate that the primary challenge facing the analysis of early warning signs in timeseries data is that of accurately 'detrending' the signal, in order to preserve the statistical properties of the fluctuations. We show here that detrending using the mean of even just four realisations of the process can give a significant improvement when compared to using a moving window average. Taking this idea further, we consider a 'metapopulation' model of an endemic disease, in which infection spreads in various separated areas with some movement between the subpopulations. We successfully predict the behaviour of both variance and the coefficient of variation in a metapopulation by using information from the other subpopulations to detrend the system.

Correlations between stochastic endemic infection in multiple interacting subpopulations

Heterogeneity plays an important role in the emergence, persistence and control of infectious diseases. Metapopulation models are often used to describe spatial heterogeneity, and the transition from random- to heterogeneous-mixing is made by incorporating the interaction, or coupling, within and between subpopulations. However, such couplings are difficult to measure explicitly; instead, their action through the correlations between subpopulations is often all that can be observed. We use moment-closure methods to investigate how the coupling and resulting correlation are related, considering systems of multiple identical interacting populations on highly symmetric complex networks: the complete network, the k-regular tree network, and the star network. We show that the correlation between the prevalence of infection takes a relatively simple form and can be written in terms of the coupling, network parameters and epidemiological parameters only. These results provide insight into the effect of metapopulation network structure on endemic disease dynamics, and suggest that detailed case-reporting data alone may be sufficient to infer the strength of between population interaction and hence lead to more accurate mathematical descriptions of infectious disease behaviour.

Correlations between stochastic epidemics in two interacting populations

It is increasingly apparent that heterogeneity in the interaction between individuals plays an important role in the dynamics, persistence, evolution and control of infectious diseases. In epidemic modelling two main forms of heterogeneity are commonly considered: spatial heterogeneity due to the segregation of populations and heterogeneity in risk at the same location. The transition from random-mixing to heterogeneous-mixing models is made by incorporating the interaction, or coupling, within and between subpopulations. However, such couplings are difficult to measure explicitly; instead, their action through the correlations between subpopulations is often all that can be observed. Here, using moment-closure methodology supported by stochastic simulation, we investigate how the coupling and resulting correlation are related. We focus on the simplest case of interactions, two identical coupled populations, and show that for a wide range of parameters the correlation between the prevalence of infection takes a relatively simple form. In particular, the correlation can be approximated by a logistic function of the between population coupling, with the free parameter determined analytically from the epidemiological parameters. These results suggest that detailed case-reporting data alone may be sufficient to infer the strength of between population interaction and hence lead to more accurate mathematical descriptions of infectious disease behaviour.

Periodicity, synchronization and persistence in pre-vaccination measles

We investigate the relationship between periodicity, synchronization and persistence of measles through simulations of geographical spread on the British Isles. We show that the establishment of areas of biennial periodicity depends on the interplay between human mobility and local population size and that locations undergoing biennial cycles tend to be, on average, synchronized in phase. We show however that occurrences of opposition of phase are actually quite common and correspond to stable dynamics. We also show that persistence is strictly related to circulation of the disease in the highly populated area of London and that this ensures survival of the disease even when human mobility drops to extremely low levels.

Intertangled stochastic motifs in networks of excitatory-inhibitory units

A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust internode correlations that persist at large distances. Antiphase synchrony at small frequencies is resolved on adjacent nodes and found to promote the spontaneous generation of long-ranged stochastic patterns that invade the network as a whole. These patterns are lacking under the idealized deterministic scenario, and could provide hints on how living systems implement and handle a large gallery of delicate computational tasks.

Stochastic epidemic dynamics on extremely heterogeneous networks

Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many contacts. We derive a two-dimensional diffusion model for the full temporal behavior of the stochastic susceptible-infectious-recovered (SIR) model on such a network, by making use of a time-scale separation in the deterministic limit of the dynamics. This low-dimensional process is an accurate approximation to the full model in the limit of large populations, even for cases when the time-scale separation is not too pronounced, provided the maximum degree is not of the order of the population size.

The effect of clumped population structure on the variability of spreading dynamics

Processes that spread through local contact, including outbreaks of infectious diseases, are inherently noisy, and are frequently observed to be far noisier than predicted by standard stochastic models that assume homogeneous mixing. One way to reproduce the observed levels of noise is to introduce significant individual-level heterogeneity with respect to infection processes, such that some individuals are expected to generate more secondary cases than others. Here we consider a population where individuals can be naturally aggregated into clumps (subpopulations) with stronger interaction within clumps than between them. This clumped structure induces significant increases in the noisiness of a spreading process, such as the transmission of infection, despite complete homogeneity at the individual level. Given the ubiquity of such clumped aggregations (such as homes, schools and workplaces for humans or farms for livestock) we suggest this as a plausible explanation for noisiness of many epidemic time series.

Synchronization of stochastic oscillators in biochemical systems

We investigate the synchronization of stochastic oscillations in biochemical models by calculating the complex coherence function within the linear noise approximation. The method is illustrated on a simple example and then applied to study the synchronization of chemical concentrations in social amoeba. The degree to which variation of rate constants in different cells and the volume of the cells affects synchronization of the oscillations is explored and the phase lag calculated. In all cases the analytical results are shown to be in good agreement with those obtained through numerical simulations.