The impact of contact structure on infectious disease control: influenza and antiviral agents

Repetition in social contacts: implications in modelling the transmission of respiratory infectious diseases in pre-pandemic and pandemic settings

The spread of viral respiratory infections is intricately linked to human interactions, and this relationship can be characterized and modelled using social contact data. However, many analyses tend to overlook the recurrent nature of these contacts. To bridge this gap, we undertake the task of describing individuals' contact patterns over time by characterizing the interactions made with distinct individuals during a week. Moreover, we gauge the implications of this temporal reconstruction on disease transmission by juxtaposing it with the assumption of random mixing over time. This involves the development of an age-structured individual-based model, using social contact data from a pre-pandemic scenario (the POLYMOD study) and a pandemic setting (the Belgian CoMix study), respectively. We found that accounting for the frequency of contacts impacts the number of new, distinct, contacts, revealing a lower total count than a naive approach, where contact repetition is neglected. As a consequence, failing to account for the repetition of contacts can result in an underestimation of the transmission probability given a contact, potentially leading to inaccurate conclusions when using mathematical models for disease control. We, therefore, underscore the necessity of acknowledging contact repetition when formulating effective public health strategies.

Modeling workplace contact networks: The effects of organizational structure, architecture, and reporting errors on epidemic predictions

Face-to-face social contacts are potentially important transmission routes for acute respiratory infections, and understanding the contact network can improve our ability to predict, contain, and control epidemics. Although workplaces are important settings for infectious disease transmission, few studies have collected workplace contact data and estimated workplace contact networks. We use contact diaries, architectural distance measures, and institutional structures to estimate social contact networks within a Swiss research institute. Some contact reports were inconsistent, indicating reporting errors. We adjust for this with a latent variable model, jointly estimating the true (unobserved) network of contacts and duration-specific reporting probabilities. We find that contact probability decreases with distance, and that research group membership, role, and shared projects are strongly predictive of contact patterns. Estimated reporting probabilities were low only for 0-5 min contacts. Adjusting for reporting error changed the estimate of the duration distribution, but did not change the estimates of covariate effects and had little effect on epidemic predictions. Our epidemic simulation study indicates that inclusion of network structure based on architectural and organizational structure data can improve the accuracy of epidemic forecasting models.

Comparison of contact patterns relevant for transmission of respiratory pathogens in Thailand and The Netherlands using respondent-driven sampling

Understanding infection dynamics of respiratory diseases requires the identification and quantification of behavioural, social and environmental factors that permit the transmission of these infections between humans. Little empirical information is available about contact patterns within real-world social networks, let alone on differences in these contact networks between populations that differ considerably on a socio-cultural level. Here we compared contact network data that were collected in The Netherlands and Thailand using a similar online respondent-driven method. By asking participants to recruit contact persons we studied network links relevant for the transmission of respiratory infections. We studied correlations between recruiter and recruited contacts to investigate mixing patterns in the observed social network components. In both countries, mixing patterns were assortative by demographic variables and random by total numbers of contacts. However, in Thailand participants reported overall more contacts which resulted in higher effective contact rates. Our findings provide new insights on numbers of contacts and mixing patterns in two different populations. These data could be used to improve parameterisation of mathematical models used to design control strategies. Although the spread of infections through populations depends on more factors, found similarities suggest that spread may be similar in The Netherlands and Thailand.

Addressing population heterogeneity and distribution in epidemics models using a cellular automata approach

BACKGROUND

The spread of an infectious disease is determined by biological and social factors. Models based on cellular automata are adequate to describe such natural systems consisting of a massive collection of simple interacting objects. They characterize the time evolution of the global system as the emergent behaviour resulting from the interaction of the objects, whose behaviour is defined through a set of simple rules that encode the individual behaviour and the transmission dynamic.

METHODS

An epidemic is characterized trough an individual-based-model built upon cellular automata. In the proposed model, each individual of the population is represented by a cell of the automata. This way of modeling an epidemic situation allows to individually define the characteristic of each individual, establish different scenarios and implement control strategies.

RESULTS

A cellular automata model to study the time evolution of a heterogeneous populations through the various stages of disease was proposed, allowing the inclusion of individual heterogeneity, geographical characteristics and social factors that determine the dynamic of the desease. Different assumptions made to built the classical model were evaluated, leading to following results: i) for low contact rate (like in quarantine process or low density population areas) the number of infective individuals is lower than other areas where the contact rate is higher, and ii) for different initial spacial distributions of infected individuals different epidemic dynamics are obtained due to its influence on the transition rate and the reproductive ratio of disease.

CONCLUSIONS

The contact rate and spatial distributions have a central role in the spread of a disease. For low density populations the spread is very low and the number of infected individuals is lower than in highly populated areas. The spacial distribution of the population and the disease focus as well as the geographical characteristic of the area play a central role in the dynamics of the desease.

ESTIMATING WITHIN-SCHOOL CONTACT NETWORKS TO UNDERSTAND INFLUENZA TRANSMISSION

Many epidemic models approximate social contact behavior by assuming random mixing within mixing groups (e.g., homes, schools, and workplaces). The effect of more realistic social network structure on estimates of epidemic parameters is an open area of exploration. We develop a detailed statistical model to estimate the social contact network within a high school using friendship network data and a survey of contact behavior. Our contact network model includes classroom structure, longer durations of contacts to friends than non-friends and more frequent contacts with friends, based on reports in the contact survey. We performed simulation studies to explore which network structures are relevant to influenza transmission. These studies yield two key findings. First, we found that the friendship network structure important to the transmission process can be adequately represented by a dyad-independent exponential random graph model (ERGM). This means that individual-level sampled data is sufficient to characterize the entire friendship network. Second, we found that contact behavior was adequately represented by a static rather than dynamic contact network. We then compare a targeted antiviral prophylaxis intervention strategy and a grade closure intervention strategy under random mixing and network-based mixing. We find that random mixing overestimates the effect of targeted antiviral prophylaxis on the probability of an epidemic when the probability of transmission in 10 minutes of contact is less than 0.004 and underestimates it when this transmission probability is greater than 0.004. We found the same pattern for the final size of an epidemic, with a threshold transmission probability of 0.005. We also find random mixing overestimates the effect of a grade closure intervention on the probability of an epidemic and final size for all transmission probabilities. Our findings have implications for policy recommendations based on models assuming random mixing, and can inform further development of network-based models.

Influence of contact definitions in assessment of the relative importance of social settings in disease transmission risk

Background

Realistic models of disease transmission incorporating complex population heterogeneities require input from quantitative population mixing studies. We use contact diaries to assess the relative importance of social settings in respiratory pathogen spread using three measures of person contact hours (PCH) as proxies for transmission risk with an aim to inform bipartite network models of respiratory pathogen transmission.

Methods and Findings

Our survey examines the contact behaviour for a convenience sample of 65 adults, with each encounter classified as occurring in a work, retail, home, social, travel or “other” setting. The diary design allows for extraction of PCH-interaction (cumulative time in face-face conversational or touch interaction with contacts) – analogous to the contact measure used in several existing surveys – as well as PCH-setting (product of time spent in setting and number of people present) and PCH-reach (product of time spent in setting and number of people in close proximity). Heterogeneities in day-dependent distribution of risk across settings are analysed using partitioning and cluster analyses and compared between days and contact measures. Although home is typically the highest-risk setting when PCH measures isolate two-way interactions, its relative importance compared to social and work settings may reduce when adopting a more inclusive contact measure that considers the number and duration of potential exposure events.

Conclusions

Heterogeneities in location-dependent contact behaviour as measured by contact diary studies depend on the adopted contact definition. We find that contact measures isolating face-face conversational or touch interactions suggest that contact in the home dominates, whereas more inclusive contact measures indicate that home and work settings may be of higher importance. In the absence of definitive knowledge of the contact required to facilitate transmission of various respiratory pathogens, it is important for surveys to consider alternative contact measures.

Influence on disease spread dynamics of herd characteristics in a structured livestock industry

Studies of between-herd contacts may provide important insight to disease transmission dynamics. By comparing the result from models with different levels of detail in the description of animal movement, we studied how factors influence the final epidemic size as well as the dynamic behaviour of an outbreak. We investigated the effect of contact heterogeneity of pig herds in Sweden due to herd size, between-herd distance and production type. Our comparative study suggests that the production-type structure is the most influential factor. Hence, our results imply that production type is the most important factor to obtain valid data for and include when modelling and analysing this system. The study also revealed that all included factors reduce the final epidemic size and also have yet more diverse effects on initial rate of disease spread. This implies that a large set of factors ought to be included to assess relevant predictions when modelling disease spread between herds. Furthermore, our results show that a more detailed model changes predictions regarding the variability in the outbreak dynamics and conclude that this is an important factor to consider in risk assessment.

Epidemic spreading in networks with nonrandom long-range interactions

An "infection," understood here in a very broad sense, can be propagated through the network of social contacts among individuals. These social contacts include both "close" contacts and "casual" encounters among individuals in transport, leisure, shopping, etc. Knowing the first through the study of the social networks is not a difficult task, but having a clear picture of the network of casual contacts is a very hard problem in a society of increasing mobility. Here we assume, on the basis of several pieces of empirical evidence, that the casual contacts between two individuals are a function of their social distance in the network of close contacts. Then, we assume that we know the network of close contacts and infer the casual encounters by means of nonrandom long-range (LR) interactions determined by the social proximity of the two individuals. This approach is then implemented in a susceptible-infected-susceptible (SIS) model accounting for the spread of infections in complex networks. A parameter called "conductance" controls the feasibility of those casual encounters. In a zero conductance network only contagion through close contacts is allowed. As the conductance increases the probability of having casual encounters also increases. We show here that as the conductance parameter increases, the rate of propagation increases dramatically and the infection is less likely to die out. This increment is particularly marked in networks with scale-free degree distributions, where infections easily become epidemics. Our model provides a general framework for studying epidemic spreading in networks with arbitrary topology with and without casual contacts accounted for by means of LR interactions.

Collecting close-contact social mixing data with contact diaries: reporting errors and biases

The analysis of contact networks plays a major role to understanding the dynamics of disease spread. Empirical contact data is often collected using contact diaries. Such studies rely on self-reported perceptions of contacts, and arrangements for validation are usually not made. Our study was based on a complete network study design that allowed for the analysis of reporting accuracy in contact diary studies. We collected contact data of the employees of three research groups over a period of 1 work week. We found that more than one third of all reported contacts were only reported by one out of the two involved contact partners. Non-reporting is most frequent in cases of short, non-intense contact. We estimated that the probability of forgetting a contact of ≤5 min duration is greater than 50%. Furthermore, the number of forgotten contacts appears to be proportional to the total number of contacts.

Social contact patterns in Vietnam and implications for the control of infectious diseases

Background

The spread of infectious diseases from person to person is determined by the frequency and nature of contacts between infected and susceptible members of the population. Although there is a long history of using mathematical models to understand these transmission dynamics, there are still remarkably little empirical data on contact behaviors with which to parameterize these models. Even starker is the almost complete absence of data from developing countries. We sought to address this knowledge gap by conducting a household based social contact diary in rural Vietnam.

Methods and Findings

A diary based survey of social contact patterns was conducted in a household-structured community cohort in North Vietnam in 2007. We used generalized estimating equations to model the number of contacts while taking into account the household sampling design, and used weighting to balance the household size and age distribution towards the Vietnamese population. We recorded 6675 contacts from 865 participants in 264 different households and found that mixing patterns were assortative by age but were more homogenous than observed in a recent European study. We also observed that physical contacts were more concentrated in the home setting in Vietnam than in Europe but the overall level of physical contact was lower. A model of individual versus household vaccination strategies revealed no difference between strategies in the impact on R₀.

Conclusions and Significance

This work is the first to estimate contact patterns relevant to the spread of infections transmitted from person to person by non-sexual routes in a developing country setting. The results show interesting similarities and differences from European data and demonstrate the importance of context specific data.

Models of epidemics: when contact repetition and clustering should be included

BACKGROUND

The spread of infectious disease is determined by biological factors, e.g. the duration of the infectious period, and social factors, e.g. the arrangement of potentially contagious contacts. Repetitiveness and clustering of contacts are known to be relevant factors influencing the transmission of droplet or contact transmitted diseases. However, we do not yet completely know under what conditions repetitiveness and clustering should be included for realistically modelling disease spread.

METHODS

We compare two different types of individual-based models: One assumes random mixing without repetition of contacts, whereas the other assumes that the same contacts repeat day-by-day. The latter exists in two variants, with and without clustering. We systematically test and compare how the total size of an outbreak differs between these model types depending on the key parameters transmission probability, number of contacts per day, duration of the infectious period, different levels of clustering and varying proportions of repetitive contacts.

RESULTS

The simulation runs under different parameter constellations provide the following results: The difference between both model types is highest for low numbers of contacts per day and low transmission probabilities. The number of contacts and the transmission probability have a higher influence on this difference than the duration of the infectious period. Even when only minor parts of the daily contacts are repetitive and clustered can there be relevant differences compared to a purely random mixing model.

CONCLUSION

We show that random mixing models provide acceptable estimates of the total outbreak size if the number of contacts per day is high or if the per-contact transmission probability is high, as seen in typical childhood diseases such as measles. In the case of very short infectious periods, for instance, as in Norovirus, models assuming repeating contacts will also behave similarly as random mixing models. If the number of daily contacts or the transmission probability is low, as assumed for MRSA or Ebola, particular consideration should be given to the actual structure of potentially contagious contacts when designing the model.

A review of network analysis terminology and its application to foot-and-mouth disease modelling and policy development

Livestock movements are important in spreading infectious diseases and many countries have developed regulations that require farmers to report livestock movements to authorities. This has led to the availability of large amounts of data for analysis and inclusion in computer simulation models developed to support policy formulation. Social network analysis has become increasingly popular to study and characterize the networks resulting from the movement of livestock from farm-to-farm and through other types of livestock operations. Network analysis is a powerful tool that allows one to study the relationships created among these operations, providing information on the role that they play in acquiring and spreading infectious diseases, information that is not readily available from more traditional livestock movement studies. Recent advances in the study of real-world complex networks are now being applied to veterinary epidemiology and infectious disease modelling and control. A review of the principles of network analysis and of the relevance of various complex network theories to infectious disease modelling and control is presented in this paper.

Household structure and infectious disease transmission

One of the central tenets of modern infectious disease epidemiology is that an understanding of heterogeneities, both in host demography and transmission, allows control to be efficiently optimized. Due to the strong interactions present, households are one of the most important heterogeneities to consider, both in terms of predicting epidemic severity and as a target for intervention. We consider these effects in the context of pandemic influenza in Great Britain, and find that there is significant local (ward-level) variation in the basic reproductive ratio, with some regions predicted to suffer 50% faster growth rate of infection than the mean. Childhood vaccination was shown to be highly effective at controlling an epidemic, generally outperforming random vaccination and substantially reducing the variation between regions; only nine out of over 10 000 wards did not obey this rule and these can be identified as demographically atypical regions. Since these benefits of childhood vaccination are a product of correlations between household size and number of dependent children in the household, our results are qualitatively robust for a variety of disease scenarios.

Quantifying the transmission potential of pandemic influenza

This article reviews quantitative methods to estimate the basic reproduction number of pandemic influenza, a key threshold quantity to help determine the intensity of interventions required to control the disease. Although it is difficult to assess the transmission potential of a probable future pandemic, historical epidemiologic data is readily available from previous pandemics, and as a reference quantity for future pandemic planning, mathematical and statistical analyses of historical data are crucial. In particular, because many historical records tend to document only the temporal distribution of cases or deaths (i.e. epidemic curve), our review focuses on methods to maximize the utility of time-evolution data and to clarify the detailed mechanisms of the spread of influenza.

First, we highlight structured epidemic models and their parameter estimation method which can quantify the detailed disease dynamics including those we cannot observe directly. Duration-structured epidemic systems are subsequently presented, offering firm understanding of the definition of the basic and effective reproduction numbers. When the initial growth phase of an epidemic is investigated, the distribution of the generation time is key statistical information to appropriately estimate the transmission potential using the intrinsic growth rate. Applications of stochastic processes are also highlighted to estimate the transmission potential using similar data. Critically important characteristics of influenza data are subsequently summarized, followed by our conclusions to suggest potential future methodological improvements.

The influenza pandemic preparedness planning tool InfluSim

Background

Planning public health responses against pandemic influenza relies on predictive models by which the impact of different intervention strategies can be evaluated. Research has to date rather focused on producing predictions for certain localities or under specific conditions, than on designing a publicly available planning tool which can be applied by public health administrations. Here, we provide such a tool which is reproducible by an explicitly formulated structure and designed to operate with an optimal combination of the competing requirements of precision, realism and generality.

Results

InfluSim is a deterministic compartment model based on a system of over 1,000 differential equations which extend the classic SEIR model by clinical and demographic parameters relevant for pandemic preparedness planning. It allows for producing time courses and cumulative numbers of influenza cases, outpatient visits, applied antiviral treatment doses, hospitalizations, deaths and work days lost due to sickness, all of which may be associated with economic aspects. The software is programmed in Java, operates platform independent and can be executed on regular desktop computers.

Conclusion

InfluSim is an online available software which efficiently assists public health planners in designing optimal interventions against pandemic influenza. It can reproduce the infection dynamics of pandemic influenza like complex computer simulations while offering at the same time reproducibility, higher computational performance and better operability.