Heterogeneity In Contact Patterns Research Articles

Age-differentiated incentives for adaptive behavior during epidemics produce oscillatory and chaotic dynamics.

Heterogeneity in contact patterns, mortality rates, and transmissibility among and between different age classes can have significant effects on epidemic outcomes. Adaptive behavior in response to the spread of an infectious pathogen may give rise to complex epidemiological dynamics. Here we model an infectious disease in which adaptive behavior incentives, and mortality rates, can vary between two and three age classes. The model indicates that age-dependent variability in infection aversion can produce more complex epidemic dynamics at lower levels of pathogen transmissibility and that those at less risk of infection can still drive complexity in the dynamics of those at higher risk of infection. Policymakers should consider the interdependence of such heterogeneous groups when making decisions.

Heterogeneity is a key factor describing the initial outbreak of COVID-19

Assessing the transmission potential of emerging infectious diseases, such as COVID-19, is crucial for implementing prompt and effective intervention policies. The basic reproduction number is widely used to measure the severity of the early stages of disease outbreaks. The basic reproduction number of standard ordinary differential equation models is computed for homogeneous contact patterns; however, realistic contact patterns are far from homogeneous, specifically during the early stages of disease transmission. Heterogeneity of contact patterns can lead to superspreading events that show a significantly high level of heterogeneity in generating secondary infections. This is primarily due to the large variance in the contact patterns of complex human behaviours. Hence, in this work, we investigate the impacts of heterogeneity in contact patterns on the basic reproduction number by developing two distinct model frameworks: 1) an SEIR-Erlang ordinary differential equation model and 2) an SEIR stochastic agent-based model. Furthermore, we estimated the transmission probability of both models in the context of COVID-19 in South Korea. Our results highlighted the importance of heterogeneity in contact patterns and indicated that there should be more information than one quantity (the basic reproduction number as the mean quantity), such as a degree-specific basic reproduction number in the distributional sense when the contact pattern is highly heterogeneous.

Context-specific emergence and growth of the SARS-CoV-2 Delta variant

The SARS-CoV-2 Delta (Pango lineage B.1.617.2) variant of concern spread globally, causing resurgences of COVID-19 worldwide1,2. The emergence of the Delta variant in the UK occurred on the background of a heterogeneous landscape of immunity and relaxation of non-pharmaceutical interventions. Here we analyse 52,992 SARS-CoV-2 genomes from England together with 93,649 genomes from the rest of the world to reconstruct the emergence of Delta and quantify its introduction to and regional dissemination across England in the context of changing travel and social restrictions. Using analysis of human movement, contact tracing and virus genomic data, we find that the geographic focus of the expansion of Delta shifted from India to a more global pattern in early May 2021. In England, Delta lineages were introduced more than 1,000 times and spread nationally as non-pharmaceutical interventions were relaxed. We find that hotel quarantine for travellers reduced onward transmission from importations; however, the transmission chains that later dominated the Delta wave in England were seeded before travel restrictions were introduced. Increasing inter-regional travel within England drove the nationwide dissemination of Delta, with some cities receiving more than 2,000 observable lineage introductions from elsewhere. Subsequently, increased levels of local population mixing—and not the number of importations—were associated with the faster relative spread of Delta. The invasion dynamics of Delta depended on spatial heterogeneity in contact patterns, and our findings will inform optimal spatial interventions to reduce the transmission of current and future variants of concern, such as Omicron (Pango lineage B.1.1.529).

Predicting the diversity of early epidemic spread on networks

The interplay of biological, social, structural and random factors makes disease forecasting extraordinarily complex. The course of an epidemic exhibits average growth dynamics determined by features of the pathogen and the population, yet also features significant variability reflecting the stochastic nature of disease spread. In this work, we reframe a stochastic branching process analysis in terms of probability generating functions and compare it to continuous time epidemic simulations on networks. In doing so, we predict the diversity of emerging epidemic courses on both homogeneous and heterogeneous networks. We show how the challenge of inferring the early course of an epidemic falls on the randomness of disease spread more so than on the heterogeneity of contact patterns. We provide an analysis which helps quantify, in real time, the probability that an epidemic goes supercritical or conversely, dies stochastically. These probabilities are often assumed to be one and zero, respectively, if the basic reproduction number, or R0, is greater than 1, ignoring the heterogeneity and randomness inherent to disease spread. This framework can give more insight into early epidemic spread by weighting standard deterministic models with likelihood to inform pandemic preparedness with probabilistic forecasts.

Infectious disease dynamics in metapopulations with heterogeneous transmission and recurrent mobility

Human mobility, contact patterns, and their interplay are key aspects of our social behavior that shape the spread of infectious diseases across different regions. In the light of new evidence and data sets about these two elements, epidemic models should be refined to incorporate both the heterogeneity of human contacts and the complexity of mobility patterns. Here, we propose a theoretical framework that allows accommodating these two aspects in the form of a set of Markovian equations. We validate these equations with extensive mechanistic simulations and derive analytically the epidemic threshold. The expression of this critical value allows us to evaluate its dependence on the specific demographic distribution, the structure of mobility flows, and the heterogeneity of contact patterns, thus shedding light on the microscopic mechanisms responsible for the epidemic detriment driven by recurrent mobility patterns reported in the literature.

Multilayer and Multiplex Networks: An Introduction to Their Use in Veterinary Epidemiology

Contact network analysis has become a vital tool for conceptualizing the spread of pathogens in animal populations and is particularly useful for understanding the implications of heterogeneity in contact patterns for transmission. However, the transmission of most pathogens cannot be simplified to a single mode of transmission and, thus, a single definition of contact. In addition, host-pathogen interactions occur in a community context, with many pathogens infecting multiple host species and most hosts being infected by multiple pathogens. Multilayer networks provide a formal framework for researching host-pathogen systems in which multiple types of transmission-relevant interactions, defined as network layers, can be analyzed jointly. Here, we provide an overview of multilayer network analysis and review applications of this novel method to epidemiological research questions. We then demonstrate the use of this technique to analyze heterogeneity in direct and indirect contact patterns amongst swine farms in the United States. When contact among nodes can be defined in multiple ways, a multilayer approach can advance our ability to use networks in epidemiological research by providing an improved approach for defining epidemiologically relevant groups of interacting nodes and changing the way we identify epidemiologically important individuals such as superspreaders.

Epidemic dynamics on complex networks with general infection rate and immune strategies

This paper mainly aims to study the influence of individuals' different heterogeneous contact patterns on the spread of the disease. For this purpose, an SIS epidemic model with a general form of heterogeneous infection rate is investigated on complex heterogeneous networks. A qualitative analysis of this model reveals that, depending on the epidemic threshold \begin{document}$R_0$ \end{document} , either the disease-free equilibrium or the endemic equilibrium is globally asymptotically stable. Interestingly, no matter what functional form the heterogeneous infection rate is, whether the disease will disappear or not is completely determined by the value of \begin{document}$R_0$ \end{document} , but the heterogeneous infection rate has close relation with the epidemic threshold \begin{document}$R_0$ \end{document} . Especially, the heterogeneous infection rate can directly affect the final number of infected nodes when the disease is endemic. The obtained results improve and generalize some known results. Finally, based on the heterogeneity of contact patterns, the effects of different immunization schemes are discussed and compared. Meanwhile, we explore the relation between the immunization rate and the recovery rate, which are the two important parameters that can be improved. To illustrate our theoretical results, the corresponding numerical simulations are also included.

Seasonality and pathogen transmission in pastoral cattle contact networks.

Capturing heterogeneity in contact patterns in animal populations is essential for understanding the spread of infectious diseases. In contrast to other regions of the world in which livestock movement networks are integral to pathogen prevention and control policies, contact networks are understudied in pastoral regions of Africa due to the challenge of measuring contact among mobile herds of cattle whose movements are driven by access to resources. Furthermore, the extent to which seasonal changes in the distribution of water and resources impacts the structure of contact networks in cattle is uncertain. Contact networks may be more conducive to pathogen spread in the dry season due to congregation at limited water sources. Alternatively, less abundant forage may result in decreased pathogen transmission due to competitive avoidance among herds, as measured by reduced contact rates. Here, we use GPS technology to concurrently track 49 free-roaming cattle herds within a semi-arid region of Kenya, and use these data to characterize seasonal contact networks and model the spread of a highly infectious pathogen. This work provides the first empirical data on the local contact network structure of mobile herds based on quantifiable contact events. The contact network demonstrated high levels of interconnectivity. An increase in contacts near to water resources in the dry season resulted in networks with both higher contact rates and higher potential for pathogen spread than in the wet season. Simulated disease outbreaks were also larger in the dry season. Results support the hypothesis that limited water resources enhance connectivity and transmission within contact networks, as opposed to reducing connectivity as a result of competitive avoidance. These results cast light on the impact of seasonal heterogeneity in resource availability on predicting pathogen transmission dynamics, which has implications for other free-ranging wild and domestic populations.

Contact heterogeneity, rather than transmission efficiency, limits the emergence and spread of canine influenza virus.

Host-range shifts in influenza virus are a major risk factor for pandemics. A key question in the study of emerging zoonoses is how the evolution of transmission efficiency interacts with heterogeneity in contact patterns in the new host species, as this interplay influences disease dynamics and prospects for control. Here we use a synergistic mixture of models and data to tease apart the evolutionary and demographic processes controlling a host-range shift in equine H3N8-derived canine influenza virus (CIV). CIV has experienced 15 years of continuous transfer among dogs in the United States, but maintains a patchy distribution, characterized by sporadic short-lived outbreaks coupled with endemic hotspots in large animal shelters. We show that CIV has a high reproductive potential in these facilities (mean R0 = 3.9) and that these hotspots act as refugia from the sparsely connected majority of the dog population. Intriguingly, CIV has evolved a transmission efficiency that closely matches the minimum required to persist in these refugia, leaving it poised on the extinction/invasion threshold of the host contact network. Corresponding phylogenetic analyses show strong geographic clustering in three US regions, and that the effective reproductive number of the virus (Re) in the general dog population is close to 1.0. Our results highlight the critical role of host contact structure in CIV dynamics, and show how host contact networks could shape the evolution of pathogen transmission efficiency. Importantly, efficient control measures could eradicate the virus, in turn minimizing the risk of future sustained transmission among companion dogs that could represent a potential new axis to the human-animal interface for influenza.

Epidemic fronts in complex networks with metapopulation structure

Infection dynamics have been studied extensively on complex networks, yielding insight into the effects of heterogeneity in contact patterns on disease spread. Somewhat separately, metapopulations have provided a paradigm for modeling systems with spatially extended and "patchy" organization. In this paper we expand on the use of multitype networks for combining these paradigms, such that simple contagion models can include complexity in the agent interactions and multiscale structure. Using a generalization of the Miller-Volz mean-field approximation for susceptible-infected-recovered (SIR) dynamics on multitype networks, we study the special case of epidemic fronts propagating on a one-dimensional lattice of interconnected networks-representing a simple chain of coupled population centers-as a necessary first step in understanding how macroscale disease spread depends on microscale topology. Applying the formalism of front propagation into unstable states, we derive the effective transport coefficients of the linear spreading: asymptotic speed, characteristic wavelength, and diffusion coefficient for the leading edge of the pulled fronts, and analyze their dependence on the underlying graph structure. We also derive the epidemic threshold for the system and study the front profile for various network configurations.

Patterns of direct and indirect contact between cattle and badgers naturally infected with tuberculosis

Tuberculosis (TB) due to infection with Mycobacterium bovis is transmitted between cattle and badgers (Meles meles) in the UK and Ireland but it is unclear where or when transmission occurs. We investigated direct and indirect interactions between badgers and cattle using automated proximity loggers on animals and at badger latrines located on pasture, in an area of south-west England with a high-density badger population. Direct contacts (interactions within 1.4 m) between badgers and cattle at pasture were very rare (four out of >500000 recorded animal-to-animal contacts) despite ample opportunity for interactions to occur. Indirect interactions (visits to badger latrines by badgers and cattle) were two orders of magnitude more frequent than direct contacts: 400 visits by badgers and 1700 visits by cattle were recorded. This suggests that indirect contacts might be more important than direct contacts in terms of disease transmission at pasture. The TB infection status of individual badgers (ascribed with 93% accuracy using three diagnostic tests) did not affect the frequency or duration of their visits to latrines located on pasture grazed by cattle. Nevertheless, there was wide variation in contact behaviour between individuals, which highlights the importance of understanding heterogeneity in contact patterns when developing strategies to control disease spread in wildlife and livestock.

Behavioural trait assortment in a social network: patterns and implications

The social fine structure of a population plays a central role in ecological and evolutionary processes. Whilst many studies have investigated how morphological traits such as size affect social structure of populations, comparatively little is known about the influence of behaviours such as boldness and shyness. Using information on social interactions in a wild population of Trinidadian guppies (Poecilia reticulata), we construct a social network. For each individual in the network, we quantify its behavioural phenotype using two measures of boldness, predator inspection tendency, a repeatable and reliably measured behaviour well studied in the context of co-operation, and shoaling tendency. We observe striking heterogeneity in contact patterns, with strong ties being positively assorted and weak ties negatively assorted by our measured behavioural traits. Moreover, shy fish had more network connections than bold fish and these were on average stronger. In other words, social fine structure is strongly influenced by behavioural trait. We assert that such structure will have implications for the outcome of selection on behavioural traits and we speculate that the observed positive assortment may act as an amplifier of selection contributing to the maintenance of co-operation during predator inspection.

Susceptible-infected-recovered epidemics in populations with heterogeneous contact rates

Heterogeneity of contact patterns is recognized as an important feature for realistic modeling of many epidemics. During an outbreak, the frequency of contacts can vary a great deal from person to person and period to period. Contact heterogeneity has been shown to have a large impact on epidemic thresholds and the final size of epidemics. We develop and apply a model which incorporates an arbitrary distribution of contact rates. The model consists of a low-dimensional system of ordinary differential equations which incorporates arbitrary heterogeneity by making use of generating functions of the contact rate distribution. We show further how this model can be applied to the study of simple intervention strategies, such as quarantine of public venues with probability proportional to size. The dynamic model allows us to investigate the effects of gradually implementing such strategies in response to an ongoing epidemic, and we investigate these strategies using data on the contact patterns within a large US city.

Simulations of the HIV Epidemic in Sub-Saharan Africa: Sexual Transmission Versus Transmission Through Unsafe Medical Injections

Heterosexual transmission has long been considered the predominant route of transmission of HIV-1 in sub-Saharan Africa. However, some have argued that unsafe medical injections account for the majority of transmission in this region. The goal of this study was to compare the HIV-1 epidemics associated with different transmission routes. An age-structured deterministic compartmental model of HIV-1 transmission through both sexual contact and unsafe injections was developed and simulations of sexual transmission and iatrogenic transmission were compared with observed prevalence. Iatrogenic transmission probabilities and numbers of unsafe injections required to generate observed prevalence are unfeasibly high. Simulations of sexually transmitted HIV-1 generate observed prevalence using transmission probabilities and average partner change rates that are within plausible bounds. Heterosexual transmission seems a more likely route of transmission in the region. However, heterogeneity in contact patterns is of key importance. Further information on groups who are likely to receive more injections is required.

Estimability and interpretation of vaccine efficacy using frailty mixing models.

The authors consider estimability and interpretation of vaccine efficacy based on time to event data, allowing that some of the population might have a very low probability of acquiring disease, and the rest have partial, possibly continuously distributed, susceptibility. The efficacy parameters of interest in the frailty mixing model include the fraction highly unlikely to acquire the infection or disease due to the vaccine, the degree of partial protection in those still susceptible, and the average protection or summary measure of efficacy under heterogeneity. The efficacy estimates can still be usefully interpreted when the heterogeneity results from heterogeneity in contact patterns, contact rates, or infectiousness of the contacts, as long as these are equal in the vaccinated and unvaccinated groups. A likelihood-based method allows estimation of the efficacy parameters of interest from grouped time to event data. Simulated vaccine studies assuming different levels and distributions of efficacy demonstrate that ignoring heterogeneity in susceptibility or exposure to infection generally results in underestimation of vaccine efficacy as well as incorrect interpretation of the estimates. The approach is also applicable to other covariates affecting susceptibility or exposure to infection in infectious diseases. Exploitation of the dependent happening structure of infectious diseases to obtain a shape for the baseline hazard may help identifiability. The authors recommend fitting several models to time to event data in vaccine studies.