Validation of the gravity model in predicting the global spread of influenza

High-resolution epidemiological landscape from ~290,000 SARS-CoV-2 genomes from Denmark

Vast amounts of pathogen genomic, demographic and spatial data are transforming our understanding of SARS-CoV-2 emergence and spread. We examined the drivers of molecular evolution and spread of 291,791 SARS-CoV-2 genomes from Denmark in 2021. With a sequencing rate consistently exceeding 60%, and up to 80% of PCR-positive samples between March and November, the viral genome set is broadly whole-epidemic representative. We identify a consistent rise in viral diversity over time, with notable spikes upon the importation of novel variants (e.g., Delta and Omicron). By linking genomic data with rich individual-level demographic data from national registers, we find that individuals aged  < 15 and  > 75 years had a lower contribution to molecular change (i.e., branch lengths) compared to other age groups, but similar molecular evolutionary rates, suggesting a lower likelihood of introducing novel variants. Similarly, we find greater molecular change among vaccinated individuals, suggestive of immune evasion. We also observe evidence of transmission in rural areas to follow predictable diffusion processes. Conversely, urban areas are expectedly more complex due to their high mobility, emphasising the role of population structure in driving virus spread. Our analyses highlight the added value of integrating genomic data with detailed demographic and spatial information, particularly in the absence of structured infection surveys.

Spatial Interaction Analysis of Infectious Disease Import and Export between Regions

Human travel plays a crucial role in the spread of infectious disease between regions. Travel of infected individuals from one region to another can transport a virus to places that were previously unaffected or may accelerate the spread of disease in places where the disease is not yet well established. We develop and apply models and metrics to analyze the role of inter-regional travel relative to the spread of disease, drawing from data on COVID-19 in the United States. To better understand how transportation affects disease transmission, we established a multi-regional time-varying compartmental disease model with spatial interaction. The compartmental model was integrated with statistical estimates of travel between regions. From the integrated model, we derived a transmission import index to assess the risk of COVID-19 transmission between states. Based on the index, we determined states with high risk for disease spreading to other states at the scale of months, and we analyzed how the index changed over time during 2020. Our model provides a tool for policymakers to evaluate the influence of travel between regions on disease transmission in support of strategies for epidemic control.

Mobility constraints in segregation models

Since the development of the original Schelling model of urban segregation, several enhancements have been proposed, but none have considered the impact of mobility constraints on model dynamics. Recent studies have shown that human mobility follows specific patterns, such as a preference for short distances and dense locations. This paper proposes a segregation model incorporating mobility constraints to make agents select their location based on distance and location relevance. Our findings indicate that the mobility-constrained model produces lower segregation levels but takes longer to converge than the original Schelling model. We identified a few persistently unhappy agents from the minority group who cause this prolonged convergence time and lower segregation level as they move around the grid centre. Our study presents a more realistic representation of how agents move in urban areas and provides a novel and insightful approach to analyzing the impact of mobility constraints on segregation models. We highlight the significance of incorporating mobility constraints when policymakers design interventions to address urban segregation.

A spatial interaction incorporated betweenness centrality measure

Betweenness centrality (BC) is widely used to identify critical nodes in a network by exploring the ability of all nodes to act as intermediaries for information exchange. However, one of its assumptions, i.e., the contributions of all shortest paths are equal, is inconsistent with variations in spatial interactions along these paths and has been questioned when applied to spatial networks. Hence, this paper proposes a spatial interaction incorporated betweenness centrality (SIBC) for spatial networks. SIBC weights the shortest path between each node pair according to the intensity of spatial interaction between them, emphasizing the combination of a network structure and spatial interactions. To test the rationality and validity of SIBC in identifying critical nodes and edges, two specific forms of SIBC are applied to the Shenzhen street network and China’s intercity network. The results demonstrate that SIBC is more significant than BC when we also focus on the network functionality rather than only on the network structure. Moreover, the good performance of SIBC in robustness analysis illustrates its application value in improving network efficiency. This study highlights the meaning of introducing spatial configuration into empirical models of complex networks.

A Deep Gravity model for mobility flows generation

The movements of individuals within and among cities influence critical aspects of our society, such as well-being, the spreading of epidemics, and the quality of the environment. When information about mobility flows is not available for a particular region of interest, we must rely on mathematical models to generate them. In this work, we propose Deep Gravity, an effective model to generate flow probabilities that exploits many features (e.g., land use, road network, transport, food, health facilities) extracted from voluntary geographic data, and uses deep neural networks to discover non-linear relationships between those features and mobility flows. Our experiments, conducted on mobility flows in England, Italy, and New York State, show that Deep Gravity achieves a significant increase in performance, especially in densely populated regions of interest, with respect to the classic gravity model and models that do not use deep neural networks or geographic data. Deep Gravity has good generalization capability, generating realistic flows also for geographic areas for which there is no data availability for training. Finally, we show how flows generated by Deep Gravity may be explained in terms of the geographic features and highlight crucial differences among the three considered countries interpreting the model's prediction with explainable AI techniques.

Trip duration drives shift in travel network structure with implications for the predictability of spatial disease spread

Human travel is one of the primary drivers of infectious disease spread. Models of travel are often used that assume the amount of travel to a specific destination decreases as cost of travel increases with higher travel volumes to more populated destinations. Trip duration, the length of time spent in a destination, can also impact travel patterns. We investigated the spatial patterns of travel conditioned on trip duration and find distinct differences between short and long duration trips. In short-trip duration travel networks, trips are skewed towards urban destinations, compared with long-trip duration networks where travel is more evenly spread among locations. Using gravity models to inform connectivity patterns in simulations of disease transmission, we show that pathogens with shorter generation times exhibit initial patterns of spatial propagation that are more predictable among urban locations. Further, pathogens with a longer generation time have more diffusive patterns of spatial spread reflecting more unpredictable disease dynamics.

During an epidemic of an infectious pathogen, cases of disease can be imported to new locations when people travel. The amount of time that an infected person spends in a destination (trip duration) determines how likely they are to infect others while travelling. In this study, we analyzed travel data and found specific spatial patterns in trip duration, where short-duration trips are more common between urban destinations and long-duration trips are evenly spread out among locations. To show how this spatial pattern impacts the spread of infectious diseases, we used data-driven models and simulations to show that pathogens with shorter generation times have patterns of spatial spread that are more predictable among urban locations. However, pathogens with longer generation times tend to spread along the long-duration travel networks that are more evenly distributed among locations giving them more unpredictable disease dynamics.

Agent-based analysis of contagion events according to sourcing locations

The first human infected with the Covid-19 virus was traced to a seafood market in Wuhan, China. Research shows that there are comparable types of viruses found in different and mutually distant areas. This raises several questions: what if the virus originated in another location? How will future waves of epidemics behave if they originate from different locations with a smaller/larger population than Wuhan? To explore these questions, we implement an agent-based model within fractal cities. Cities radiate gravitational social attraction based on their Zipfian population. The probability and predictability of contagion events are analyzed by examining fractal dimensions and lacunarity. Results show that weak gravitational forces of small locations help dissipate infections across country quicker if the pathogen had originated from that location. Gravitational forces of large cities help contain infections within them if they are the starting locations for the pathogen. Greater connectedness and symmetry allow for a more predictable epidemic outcome since there are no obstructions to spreading. To test our hypothesis, we implement datasets from two countries, Sierra Leone and Liberia, and two diseases, Ebola and Covid-19, and obtain the same results.

Assessing the interplay between travel patterns and SARS-CoV-2 outbreak in realistic urban setting

BACKGROUND

The dense social contact networks and high mobility in congested urban areas facilitate the rapid transmission of infectious diseases. Typical mechanistic epidemiological models are either based on uniform mixing with ad-hoc contact processes or need real-time or archived population mobility data to simulate the social networks. However, the rapid and global transmission of the novel coronavirus (SARS-CoV-2) has led to unprecedented lockdowns at global and regional scales, leaving the archived datasets to limited use.

FINDINGS

While it is often hypothesized that population density is a significant driver in disease propagation, the disparate disease trajectories and infection rates exhibited by the different cities with comparable densities require a high-resolution description of the disease and its drivers. In this study, we explore the impact of creation of containment zones on travel patterns within the city. Further, we use a dynamical network-based infectious disease model to understand the key drivers of disease spread at sub-kilometer scales demonstrated in the city of Ahmedabad, India, which has been classified as a SARS-CoV-2 hotspot. We find that in addition to the contact network and population density, road connectivity patterns and ease of transit are strongly correlated with the rate of transmission of the disease. Given the limited access to real-time traffic data during lockdowns, we generate road connectivity networks using open-source imageries and travel patterns from open-source surveys and government reports. Within the proposed framework, we then analyze the relative merits of social distancing, enforced lockdowns, and enhanced testing and quarantining mitigating the disease spread.

SCOPE

Our results suggest that the declaration of micro-containment zones within the city with high road network density combined with enhanced testing can help in containing the outbreaks until clinical interventions become available.

Sub-district level correlation between tuberculosis notifications and socio-demographic factors in Dhaka City corporation, Bangladesh

We developed a novel method to align two data sources (TB notifications and the Demographic Health Survey, DHS) captured at different geographic scales. We used this method to identify sociodemographic indicators – specifically population density – that were ecologically correlated with elevated TB notification rates across wards (~100 000 people) in Dhaka, Bangladesh. We found population density was the variable most closely correlated with ward-level TB notification rates (Spearman's rank correlation 0.45). Our approach can be useful, as publicly available data (e.g. DHS data) could help identify factors that are ecologically associated with disease burden when more granular data (e.g. ward-level TB notifications) are not available. Use of this approach might help in designing spatially targeted interventions for TB and other diseases in settings of weak existing data on disease burden at the subdistrict level.

A parsimonious approach for spatial transmission and heterogeneity in the COVID-19 propagation

Raw data on the number of deaths at a country level generally indicate a spatially variable distribution of COVID-19 incidence. An important issue is whether this pattern is a consequence of environmental heterogeneities, such as the climatic conditions, during the course of the outbreak. Another fundamental issue is to understand the spatial spreading of COVID-19. To address these questions, we consider four candidate epidemiological models with varying complexity in terms of initial conditions, contact rates and non-local transmissions, and we fit them to French mortality data with a mixed probabilistic-ODE approach. Using statistical criteria, we select the model with non-local transmission corresponding to a diffusion on the graph of counties that depends on the geographic proximity, with time-dependent contact rate and spatially constant parameters. This suggests that in a geographically middle size centralized country such as France, once the epidemic is established, the effect of global processes such as restriction policies and sanitary measures overwhelms the effect of local factors. Additionally, this approach reveals the latent epidemiological dynamics including the local level of immunity, and allows us to evaluate the role of non-local interactions on the future spread of the disease.

INVESTIGATING THE ROLE OF WITHIN- AND BETWEEN-PATCH MOVEMENT IN A DYNAMIC MODEL OF DISEASE SPREAD

The impact of human mobility on the spreading of disease in a metapopulation is emphasized on interconnecting between patches, whereas the current volume of movement within the local population is usually neglected. Here, the role of internal commuters is taken into account by two means, a local transmission rate and the volume of internal commuters. Dynamic model of human mobility in the metapopulation with gravity coupling is presented. In conjunction with the disease spreading, the impact on invasion threshold and epidemic final size are analyzed. For two-patch model, we show that under fixing parameters in gravity model, the existence of invasion threshold depends on the difference of local transmission rates and the proportion of internal commuters between two patches. For a fully connected network with an identical transmission rate, the difference in patch final sizes is driven by patch distribution of internal commuters. By neglecting the effect of spatial variation in a simple core–satellite model, we show that the heterogeneity of internal commuters and gravity coupling induce a complex pattern of threshold, which depend mostly on the exponent in gravity model, and are responsible for the differences among local epidemic sizes.

Data Flow Analysis and Visualization for Spatiotemporal Statistical Data without Trajectory Information

Geographic visualization research has focused on a variety of techniques to represent and explore spatiotemporal data. The goal of those techniques is to enable users to explore events and interactions over space and time in order to facilitate the discovery of patterns, anomalies and relationships within the data. However, it is difficult to extract and visualize data flow patterns over time for non-directional statistical data without trajectory information. In this work, we develop a novel flow analysis technique to extract, represent, and analyze flow maps of non-directional spatiotemporal data unaccompanied by trajectory information. We estimate a continuous distribution of these events over space and time, and extract flow fields for spatial and temporal changes utilizing a gravity model. Then, we visualize the spatiotemporal patterns in the data by employing flow visualization techniques. The user is presented with temporal trends of geo-referenced discrete events on a map. As such, overall spatiotemporal data flow patterns help users analyze geo-referenced temporal events, such as disease outbreaks, crime patterns, etc. To validate our model, we discard the trajectory information in an origin-destination dataset and apply our technique to the data and compare the derived trajectories and the original. Finally, we present spatiotemporal trend analysis for statistical datasets including twitter data, maritime search and rescue events, and syndromic surveillance.

Spatio-temporal patterns of proportions of influenza B cases

We studied the spatio-temporal patterns of the proportions of influenza B cases out of all typed cases, with data from 139 countries and regions downloaded from the FluNet compiled by the World Health Organization, from January 2006 to October 2015. We restricted our analysis to 34 countries that reported more than 2,000 confirmations for each of types A and B over the study period. Globally, we found that Pearson’s correlation is greater than 0.6 between effective distance from Mexico and the proportions of influenza B cases among the countries during the post-pandemic era (i.e. Week 1, 2010 to Week 40, 2015). Locally, in the United States, the proportions of influenza B cases in the pre-pandemic period (2003–2008) negatively correlated with that in the post-pandemic era (2010–2015) at the regional level. Our study limitations are the country-level variations in both surveillance methods and testing policies. The proportions of influenza B cases displayed wide variations over the study period. Our findings suggest that the 2009 influenza pandemic has an evident impact on the relative burden of the two influenza types. Future studies should examine whether there are other additional factors. This study has potential implications in prioritizing public health control measures.

Mathematical and computational approaches to epidemic modeling: a comprehensive review

Mathematical and computational approaches are important tools for understanding epidemic spread patterns and evaluating policies of disease control. In recent years, epidemiology has become increasingly integrated with mathematics, sociology, management science, complexity science, and computer science. The cross of multiple disciplines has caused rapid development of mathematical and computational approaches to epidemic modeling. In this article, we carry out a comprehensive review of epidemic models to provide an insight into the literature of epidemic modeling and simulation. We introduce major epidemic models in three directions, including mathematical models, complex network models, and agent-based models. We discuss the principles, applications, advantages, and limitations of these models. Meanwhile, we also propose some future research directions in epidemic modeling.

Was mandatory quarantine necessary in China for controlling the 2009 H1N1 pandemic?

The Chinese government enforced mandatory quarantine for 60 days (from 10 May to 8 July 2009) as a preventative strategy to control the spread of the 2009 H1N1 pandemic. Such a prevention strategy was stricter than other non-pharmaceutical interventions that were carried out in many other countries. We evaluated the effectiveness of the mandatory quarantine and provide suggestions for interventions against possible future influenza pandemics. We selected one city, Beijing, as the analysis target. We reviewed the epidemiologic dynamics of the 2009 H1N1 pandemic and the implementation of quarantine measures in Beijing. The infectious population was simulated under two scenarios (quarantined and not quarantined) using a deterministic Susceptible-Exposed-Infectious-Recovered (SEIR) model. The basic reproduction number R0 was adjusted to match the epidemic wave in Beijing. We found that mandatory quarantine served to postpone the spread of the 2009 H1N1 pandemic in Beijing by one and a half months. If mandatory quarantine was not enforced in Beijing, the infectious population could have reached 1,553 by 21 October, i.e., 5.6 times higher than the observed number. When the cost of quarantine is taken into account, mandatory quarantine was not an economically effective intervention approach against the 2009 H1N1 pandemic. We suggest adopting mitigation methods for an influenza pandemic with low mortality and morbidity.

Using the gravity model to estimate the spatial spread of vector-borne diseases

The gravity models are commonly used spatial interaction models. They have been widely applied in a large set of domains dealing with interactions amongst spatial entities. The spread of vector-borne diseases is also related to the intensity of interaction between spatial entities, namely, the physical habitat of pathogens’ vectors and/or hosts, and urban areas, thus humans. This study implements the concept behind gravity models in the spatial spread of two vector-borne diseases, nephropathia epidemica and Lyme borreliosis, based on current knowledge on the transmission mechanism of these diseases. Two sources of information on vegetated systems were tested: the CORINE land cover map and MODIS NDVI. The size of vegetated areas near urban centers and a local indicator of occupation-related exposure were found significant predictors of disease risk. Both the land cover map and the space-borne dataset were suited yet not equivalent input sources to locate and measure vegetated areas of importance for disease spread. The overall results point at the compatibility of the gravity model concept and the spatial spread of vector-borne diseases.

Reconstruction of the evolutionary dynamics of the A(H1N1)pdm09 influenza virus in Italy during the pandemic and post-pandemic phases

The aim of this study was to reconstruct the evolutionary dynamics of the A(H1N1)pdm09 influenza virus in Italy during two epidemic seasons (2009/2010 and 2010/2011) in the light of the forces driving the evolution of the virus. Nearly six thousands respiratory specimens were collected from patients with influenza-like illness within the framework of the Italian Influenza Surveillance Network, and the A(H1N1)pdm09 hemagglutinin (HA) gene was amplified and directly sequenced from 227 of these. Phylodynamic and phylogeographical analyses were made using a Bayesian Markov Chain Monte Carlo method, and codon-specific positive selection acting on the HA coding sequence was evaluated. The global and local phylogenetic analyses showed that all of the Italian sequences sampled in the post-pandemic (2010/2011) season grouped into at least four highly significant Italian clades, whereas those of the pandemic season (2009/2010) were interspersed with isolates from other countries at the tree root. The time of the most recent common ancestor of the strains circulating in the pandemic season in Italy was estimated to be between the spring and summer of 2009, whereas the Italian clades of the post-pandemic season originated in the spring of 2010 and showed radiation in the summer/autumn of the same year; this was confirmed by a Bayesian skyline plot showing the biphasic growth of the effective number of infections. The local phylogeography analysis showed that the first season of infection originated in Northern Italian localities with high density populations, whereas the second involved less densely populated localities, in line with a gravity-like model of geographical dispersion. Two HA sites, codons 97 and 222, were under positive selection. In conclusion, the A(H1N1)pdm09 virus was introduced into Italy in the spring of 2009 by means of multiple importations. This was followed by repeated founder effects in the post-pandemic period that originated specific Italian clades.