Epidemic Percolation Networks, Epidemic Outcomes, and Interventions

Epidemic percolation networks (EPNs) are directed random networks that can be used to analyze stochastic “Susceptible-Infectious-Removed” (SIR) and “Susceptible-Exposed-Infectious-Removed” (SEIR) epidemic models, unifying and generalizing previous uses of networks and branching processes to analyze mass-action and network-based S(E)IR models. This paper explains the fundamental concepts underlying the definition and use of EPNs, using them to build intuition about the final outcomes of epidemics. We then show how EPNs provide a novel and useful perspective on the design of vaccination strategies

Effects of epidemic threshold definition on disease spread statistics

We study the statistical properties of the SIR epidemics in heterogeneous networks, when an epidemic is defined as only those SIR propagations that reach or exceed a minimum size s_c. Using percolation theory to calculate the average fractional size of an epidemic, we find that the strength of the spanning link percolation cluster $P_{\infty}$ is an upper bound to . For small values of s_c, $P_{\infty}$ is no longer a good approximation, and the average fractional size has to be computed directly. The value of s_c for which $P_{\infty}$ is a good approximation is found to depend on the transmissibility T of the SIR. We also study Q, the probability that an SIR propagation reaches the epidemic mass s_c, and find that it is well characterized by percolation theory. We apply our results to real networks (DIMES and Tracerouter) to measure the consequences of the choice s_c on predictions of average outcome sizes of computer failure epidemics.Comment: 12 pages, 8 figure

Commentary on the use of the reproduction number R during the COVID-19 pandemic

Since the beginning of the COVID-19 pandemic, the reproduction number R has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, R is defined as the average number of secondary infections caused by one primary infected individual. R seems convenient, because the epidemic is expanding if R>1 and contracting if R<1. The magnitude of R indicates by how much transmission needs to be reduced to control the epidemic. Using R in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of R but many, and the precise definition of R affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined R, there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate R vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when R is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of R, and the data and methods used to estimate it, can make R a more useful metric for future management of the epidemic

Mean-field models for non-Markovian epidemics on networks

This paper introduces a novel extension of the edge-based compartmental model to epidemics where the transmission and recovery processes are driven by general independent probability distributions. Edge-based compartmental modelling is just one of many different approaches used to model the spread of an infectious disease on a network; the major result of this paper is the rigorous proof that the edge-based compartmental model and the message passing models are equivalent for general independent transmission and recovery processes. This implies that the new model is exact on the ensemble of configuration model networks of infinite size. For the case of Markovian transmission themessage passing model is re-parametrised into a pairwise-like model which is then used to derive many well-known pairwise models for regular networks, or when the infectious period is exponentially distributed or is of a fixed length

Effects of Heterogeneous and Clustered Contact Patterns on Infectious Disease Dynamics

The spread of infectious diseases fundamentally depends on the pattern of contacts between individuals. Although studies of contact networks have shown that heterogeneity in the number of contacts and the duration of contacts can have far-reaching epidemiological consequences, models often assume that contacts are chosen at random and thereby ignore the sociological, temporal and/or spatial clustering of contacts. Here we investigate the simultaneous effects of heterogeneous and clustered contact patterns on epidemic dynamics. To model population structure, we generalize the configuration model which has a tunable degree distribution (number of contacts per node) and level of clustering (number of three cliques). To model epidemic dynamics for this class of random graph, we derive a tractable, low-dimensional system of ordinary differential equations that accounts for the effects of network structure on the course of the epidemic. We find that the interaction between clustering and the degree distribution is complex. Clustering always slows an epidemic, but simultaneously increasing clustering and the variance of the degree distribution can increase final epidemic size. We also show that bond percolation-based approximations can be highly biased if one incorrectly assumes that infectious periods are homogeneous, and the magnitude of this bias increases with the amount of clustering in the network. We apply this approach to model the high clustering of contacts within households, using contact parameters estimated from survey data of social interactions, and we identify conditions under which network models that do not account for household structure will be biased

Erratic Flu Vaccination Emerges from Short-Sighted Behavior in Contact Networks

The effectiveness of seasonal influenza vaccination programs depends on individual-level compliance. Perceptions about risks associated with infection and vaccination can strongly influence vaccination decisions and thus the ultimate course of an epidemic. Here we investigate the interplay between contact patterns, influenza-related behavior, and disease dynamics by incorporating game theory into network models. When individuals make decisions based on past epidemics, we find that individuals with many contacts vaccinate, whereas individuals with few contacts do not. However, the threshold number of contacts above which to vaccinate is highly dependent on the overall network structure of the population and has the potential to oscillate more wildly than has been observed empirically. When we increase the number of prior seasons that individuals recall when making vaccination decisions, behavior and thus disease dynamics become less variable. For some networks, we also find that higher flu transmission rates may, counterintuitively, lead to lower (vaccine-mediated) disease prevalence. Our work demonstrates that rich and complex dynamics can result from the interaction between infectious diseases, human contact patterns, and behavior

Environmental Predictors of Seasonal Influenza Epidemics across Temperate and Tropical Climates

Human influenza infections exhibit a strong seasonal cycle in temperate regions. Recent laboratory and epidemiological evidence suggests that low specific humidity conditions facilitate the airborne survival and transmission of the influenza virus in temperate regions, resulting in annual winter epidemics. However, this relationship is unlikely to account for the epidemiology of influenza in tropical and subtropical regions where epidemics often occur during the rainy season or transmit year-round without a well-defined season. We assessed the role of specific humidity and other local climatic variables on influenza virus seasonality by modeling epidemiological and climatic information from 78 study sites sampled globally. We substantiated that there are two types of environmental conditions associated with seasonal influenza epidemics: “cold-dry” and “humid-rainy”. For sites where monthly average specific humidity or temperature decreases below thresholds of approximately 11–12 g/kg and 18–21°C during the year, influenza activity peaks during the cold-dry season (i.e., winter) when specific humidity and temperature are at minimal levels. For sites where specific humidity and temperature do not decrease below these thresholds, seasonal influenza activity is more likely to peak in months when average precipitation totals are maximal and greater than 150 mm per month. These findings provide a simple climate-based model rooted in empirical data that accounts for the diversity of seasonal influenza patterns observed across temperate, subtropical and tropical climates

A systematic review to identify areas of enhancements of pandemic simulation models for operational use at provincial and local levels

<p>Abstract</p> <p>Background</p> <p>In recent years, computer simulation models have supported development of pandemic influenza preparedness policies. However, U.S. policymakers have raised several <it>concerns </it>about the practical use of these models. In this review paper, we examine the extent to which the current literature already addresses these <it>concerns </it>and identify means of enhancing the current models for higher operational use.</p> <p>Methods</p> <p>We surveyed PubMed and other sources for published research literature on simulation models for influenza pandemic preparedness. We identified 23 models published between 1990 and 2010 that consider single-region (e.g., country, province, city) outbreaks and multi-pronged mitigation strategies. We developed a plan for examination of the literature based on the concerns raised by the policymakers.</p> <p>Results</p> <p>While examining the concerns about the adequacy and validity of data, we found that though the epidemiological data supporting the models appears to be adequate, it should be validated through as many updates as possible during an outbreak. Demographical data must improve its interfaces for access, retrieval, and translation into model parameters. Regarding the concern about credibility and validity of modeling assumptions, we found that the models often simplify reality to reduce computational burden. Such simplifications may be permissible if they do not interfere with the performance assessment of the mitigation strategies. We also agreed with the concern that social behavior is inadequately represented in pandemic influenza models. Our review showed that the models consider only a few social-behavioral aspects including contact rates, withdrawal from work or school due to symptoms appearance or to care for sick relatives, and compliance to social distancing, vaccination, and antiviral prophylaxis. The concern about the degree of accessibility of the models is palpable, since we found three models that are currently accessible by the public while other models are seeking public accessibility. Policymakers would prefer models scalable to any population size that can be downloadable and operable in personal computers. But scaling models to larger populations would often require computational needs that cannot be handled with personal computers and laptops. As a limitation, we state that some existing models could not be included in our review due to their limited available documentation discussing the choice of relevant parameter values.</p> <p>Conclusions</p> <p>To adequately address the concerns of the policymakers, we need continuing model enhancements in critical areas including: updating of epidemiological data during a pandemic, smooth handling of large demographical databases, incorporation of a broader spectrum of social-behavioral aspects, updating information for contact patterns, adaptation of recent methodologies for collecting human mobility data, and improvement of computational efficiency and accessibility.</p

A mechanistic spatio-temporal framework for modelling individual-to-individual transmission—With an application to the 2014-2015 West Africa Ebola outbreak

In recent years there has been growing availability of individual-level spatio-temporal disease data, particularly due to the use of modern communicating devices with GPS tracking functionality. These detailed data have been proven useful for inferring disease transmission to a more refined level than previously. However, there remains a lack of statistically sound frameworks to model the underlying transmission dynamic in a mechanistic manner. Such a development is particularly crucial for enabling a general epidemic predictive framework at the individual level. In this paper we propose a new statistical framework for mechanistically modelling individual-to-individual disease transmission in a landscape with heterogeneous population density. Our methodology is first tested using simulated datasets, validating our inferential machinery. The methodology is subsequently applied to data that describes a regional Ebola outbreak in Western Africa (2014-2015). Our results show that the methods are able to obtain estimates of key epidemiological parameters that are broadly consistent with the literature, while revealing a significantly shorter distance of transmission. More importantly, in contrast to existing approaches, we are able to perform a more general model prediction that takes into account the susceptible population. Finally, our results show that, given reasonable scenarios, the framework can be an effective surrogate for susceptible-explicit individual models which are often computationally challenging

Quantifying Type-Specific Reproduction Numbers for Nosocomial Pathogens: Evidence for Heightened Transmission of an Asian Sequence Type 239 MRSA Clone

An important determinant of a pathogen's success is the rate at which it is transmitted from infected to susceptible hosts. Although there are anecdotal reports that methicillin-resistant Staphylococcus aureus (MRSA) clones vary in their transmissibility in hospital settings, attempts to quantify such variation are lacking for common subtypes, as are methods for addressing this question using routinely-collected MRSA screening data in endemic settings. Here we present a method to quantify the time-varying transmissibility of different subtypes of common bacterial nosocomial pathogens using routine surveillance data. The method adapts approaches for estimating reproduction numbers based on the probabilistic reconstruction of epidemic trees, but uses relative hazards rather than serial intervals to assign probabilities to different sources for observed transmission events. The method is applied to data collected as part of a retrospective observational study of a concurrent MRSA outbreak in the United Kingdom with dominant endemic MRSA clones (ST22 and ST36) and an Asian ST239 MRSA strain (ST239-TW) in two linked adult intensive care units, and compared with an approach based on a fully parametric transmission model. The results provide support for the hypothesis that the clones responded differently to an infection control measure based on the use of topical antiseptics, which was more effective at reducing transmission of endemic clones. They also suggest that in one of the two ICUs patients colonized or infected with the ST239-TW MRSA clone had consistently higher risks of transmitting MRSA to patients free of MRSA. These findings represent some of the first quantitative evidence of enhanced transmissibility of a pandemic MRSA lineage, and highlight the potential value of tailoring hospital infection control measures to specific pathogen subtypes