Network structure, and vaccination strategy and effort interact to affect the dynamics of influenza epidemics

A comparison of node vaccination strategies to halt SIR epidemic spreading in real-world complex networks

We compared seven node vaccination strategies in twelve real-world complex networks. The node vaccination strategies are modeled as node removal on networks. We performed node vaccination strategies both removing nodes according to the initial network structure, i.e., non-adaptive approach, and performing partial node rank recalculation after node removal, i.e., semi-adaptive approach. To quantify the efficacy of each vaccination strategy, we used three epidemic spread indicators: the size of the largest connected component, the total number of infected at the end of the epidemic, and the maximum number of simultaneously infected individuals. We show that the best vaccination strategies in the non-adaptive and semi-adaptive approaches are different and that the best strategy also depends on the number of available vaccines. Furthermore, a partial recalculation of the node centrality increases the efficacy of the vaccination strategies by up to 80%.

Network assessment and modeling the management of an epidemic on a college campus with testing, contact tracing, and masking

There remains a great challenge to minimize the spread of epidemics, especially in high-density communities such as colleges and universities. This is particularly true on densely populated, residential college campuses. To construct class and residential networks data from a four-year, residential liberal arts college with 5539 students were obtained from SUNY College at Geneseo, a rural, residential, undergraduate institution in western NY, USA. Equal-sized random networks also were created for each day. Different levels of compliance with mask use (none to 100%), mask efficacy (50% to 100%), and testing frequency (daily, or every 2, 3, 7, 14, 28, or 105 days) were assessed. Tests were assumed to be only 90% accurate and positive results were used to isolate individuals. The effectiveness of contact tracing, and the effect of quarantining neighbors of infectious individuals, was tested. The structure of the college course enrollment and residence networks greatly influenced the dynamics of the epidemics, as compared to the random networks. In particular, average path lengths were longer in the college networks compared to random networks. Students in larger majors generally had shorter average path lengths than students in smaller majors. Average transitivity (clustering) was lower on days when students most frequently were in class (MWF). Degree distributions were generally large and right skewed, ranging from 0 to 719. Simulations began by inoculating twenty students (10 exposed and 10 infectious) with SARS-CoV-2 on the first day of the fall semester and ended once the disease was cleared. Transmission probability was calculated based on an R0 = 2.4. Without interventions epidemics resulted in most students becoming infected and lasted into the second semester. On average students in the college networks experienced fewer infections, shorter duration, and lower epidemic peaks when compared to the dynamics on equal-sized random networks. The most important factors in reducing case numbers were the proportion masking and the frequency of testing, followed by contact tracing and mask efficacy. The paper discusses further high-order interactions and other implications of non-pharmaceutical interventions for disease transmission on a residential college campus.

Effectiveness of non-pharmaceutical interventions against local transmission of COVID-19: An individual-based modelling study

The outbreak of the novel coronavirus disease 2019 (COVID-19), caused by the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has caused global transmission, and been spread all over the world. For those regions that are currently free of infected cases, it is an urgent issue to prevent and control the local outbreak of COVID-19 when there are sporadic cases. To evaluate the effects of non-pharmaceutical interventions against local transmission of COVID-19, and to forecast the epidemic dynamics after local outbreak of diseases under different control measures, we developed an individual-based model (IBM) to simulate the transmission dynamics of COVID-19 from a microscopic perspective of individual-to-individual contacts to heterogenous among individuals. Based on the model, we simulated the effects of different levels of non-pharmaceutical interventions in controlling disease transmission after the appearance of sporadic cases. Simulations shown that isolation of infected cases and quarantine of close contacts alone would not eliminate the local transmission of COVID-19, and there is a risk of a second wave epidemics. Quarantine the second-layer close contacts can obviously reduce the size of outbreak. Moreover, to effectively eliminate the daily new infections in a short time, it is necessary to reduce the individual-to-individual contacts. IBM provides a numerical representation for the local transmission of infectious diseases, and extends the compartmental models to include individual heterogeneity and the close contacts network. Our study suggests that combinations of self-isolation, quarantine of close contacts, and social distancing would be necessary to block the local transmission of COVID-19.

A new SEIAR model on small-world networks to assess the intervention measures in the COVID-19 pandemics

A new susceptible-exposed-infected-asymptomatically infected-removed (SEIAR) model is developed to depict the COVID-19 transmission process, considering the latent period and asymptomatically infected. We verify the suppression effect of typical measures, cultivating human awareness, and reducing social contacts. As for cutting off social connections, the feasible measures encompass social distancing policy, isolating infected communities, and isolating hub nodes. Furthermore, it is found that implementing corresponding anti-epidemic measures at different pandemic stages can achieve significant results at a low cost. In the beginning, global lockdown policy is necessary, but isolating infected wards and hub nodes could be more beneficial as the situation eases. The proposed SEIAR model emphasizes the latent period and asymptomatically infected, thus providing theoretical support for subsequent research.

Vaccination strategies against COVID-19 and the diffusion of anti-vaccination views

Misinformation is usually adjusted to fit distinct narratives and propagates rapidly through social networks. False beliefs, once adopted, are rarely corrected. Amidst the COVID-19 crisis, pandemic-deniers and people who oppose wearing face masks or quarantine have already been a substantial aspect of the development of the pandemic. With the vaccine for COVID-19, different anti-vaccine narratives are being created and are probably being adopted by large population groups with critical consequences. Assuming full adherence to vaccine administration, we use a diffusion model to analyse epidemic spreading and the impact of different vaccination strategies, measured with the average years of life lost, in three network topologies (a proximity, a scale-free and a small-world network). Then, using a similar diffusion model, we consider the spread of anti-vaccine views in the network, which are adopted based on a persuasiveness parameter of anti-vaccine views. Results show that even if anti-vaccine narratives have a small persuasiveness, a large part of the population will be rapidly exposed to them. Assuming that all individuals are equally likely to adopt anti-vaccine views after being exposed, more central nodes in the network, which are more exposed to these views, are more likely to adopt them. Comparing years of life lost, anti-vaccine views could have a significant cost not only on those who share them, since the core social benefits of a limited vaccination strategy (reduction of susceptible hosts, network disruptions and slowing the spread of the disease) are substantially shortened.

Immunization strategies in networks with missing data

Network-based intervention strategies can be effective and cost-efficient approaches to curtailing harmful contagions in myriad settings. As studied, these strategies are often impractical to implement, as they typically assume complete knowledge of the network structure, which is unusual in practice. In this paper, we investigate how different immunization strategies perform under realistic conditions-where the strategies are informed by partially-observed network data. Our results suggest that global immunization strategies, like degree immunization, are optimal in most cases; the exception is at very high levels of missing data, where stochastic strategies, like acquaintance immunization, begin to outstrip them in minimizing outbreaks. Stochastic strategies are more robust in some cases due to the different ways in which they can be affected by missing data. In fact, one of our proposed variants of acquaintance immunization leverages a logistically-realistic ongoing survey-intervention process as a form of targeted data-recovery to improve with increasing levels of missing data. These results support the effectiveness of targeted immunization as a general practice. They also highlight the risks of considering networks as idealized mathematical objects: overestimating the accuracy of network data and foregoing the rewards of additional inquiry.

On the impact of epidemic severity on network immunization algorithms

There has been much recent interest in the prevention and mitigation of epidemics spreading through contact networks of host populations. Here, we investigate how the severity of epidemics, measured by its infection rate, influences the efficiency of well-known vaccination strategies. In order to assess the impact of severity, we simulate the SIR model at different infection rates on various real and model immunized networks. An extensive analysis of our simulation results reveals that immunization algorithms, which efficiently reduce the nodes’ average degree, are more effective in the mitigation of weak and slow epidemics, whereas vaccination strategies that fragment networks to small components, are more successful in suppressing severe epidemics.

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Interaction of the immunization algorithms, epidemic trials and network structure is investigated.

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Immunization algorithms are applied to various real and model networks.

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Degree-based immunization algorithms are more efficient in mitigation of weak epidemics.

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Network largest component size is a vital element in spreading of severe epidemics.

Link removal for the control of stochastically evolving epidemics over networks: a comparison of approaches

For many communicable diseases, knowledge of the underlying contact network through which the disease spreads is essential to determining appropriate control measures. When behavior change is the primary intervention for disease prevention, it is important to understand how to best modify network connectivity using the limited resources available to control disease spread. We describe and compare four algorithms for selecting a limited number of links to remove from a network: two "preventive" approaches (edge centrality, R0 minimization), where the decision of which links to remove is made prior to any disease outbreak and depends only on the network structure; and two "reactive" approaches (S-I edge centrality, optimal quarantining), where information about the initial disease states of the nodes is incorporated into the decision of which links to remove. We evaluate the performance of these algorithms in minimizing the total number of infections that occur over the course of an acute outbreak of disease. We consider different network structures, including both static and dynamic Erdös-Rényi random networks with varying levels of connectivity, a real-world network of residential hotels connected through injection drug use, and a network exhibiting community structure. We show that reactive approaches outperform preventive approaches in averting infections. Among reactive approaches, removing links in order of S-I edge centrality is favored when the link removal budget is small, while optimal quarantining performs best when the link removal budget is sufficiently large. The budget threshold above which optimal quarantining outperforms the S-I edge centrality algorithm is a function of both network structure (higher for unstructured Erdös-Rényi random networks compared to networks with community structure or the real-world network) and disease infectiousness (lower for highly infectious diseases). We conduct a value-of-information analysis of knowing which nodes are initially infected by comparing the performance improvement achieved by reactive over preventive strategies. We find that such information is most valuable for moderate budget levels, with increasing value as disease spread becomes more likely (due to either increased connectedness of the network or increased infectiousness of the disease).

Two-stage effects of awareness cascade on epidemic spreading in multiplex networks

Human awareness plays an important role in the spread of infectious diseases and the control of propagation patterns. The dynamic process with human awareness is called awareness cascade, during which individuals exhibit herd-like behavior because they are making decisions based on the actions of other individuals [Borge-Holthoefer et al., J. Complex Networks 1, 3 (2013)]. In this paper, to investigate the epidemic spreading with awareness cascade, we propose a local awareness controlled contagion spreading model on multiplex networks. By theoretical analysis using a microscopic Markov chain approach and numerical simulations, we find the emergence of an abrupt transition of epidemic threshold β(c) with the local awareness ratio α approximating 0.5, which induces two-stage effects on epidemic threshold and the final epidemic size. These findings indicate that the increase of α can accelerate the outbreak of epidemics. Furthermore, a simple 1D lattice model is investigated to illustrate the two-stage-like sharp transition at α(c)≈0.5. The results can give us a better understanding of why some epidemics cannot break out in reality and also provide a potential access to suppressing and controlling the awareness cascading systems.

Hepatitis C transmission and treatment in contact networks of people who inject drugs

Hepatitis C virus (HCV) chronically infects over 180 million people worldwide, with over 350,000 estimated deaths attributed yearly to HCV-related liver diseases. It disproportionally affects people who inject drugs (PWID). Currently there is no preventative vaccine and interventions feature long treatment durations with severe side-effects. Upcoming treatments will improve this situation, making possible large-scale treatment interventions. How these strategies should target HCV-infected PWID remains an important unanswered question. Previous models of HCV have lacked empirically grounded contact models of PWID. Here we report results on HCV transmission and treatment using simulated contact networks generated from an empirically grounded network model using recently developed statistical approaches in social network analysis. Our HCV transmission model is a detailed, stochastic, individual-based model including spontaneously clearing nodes. On transmission we investigate the role of number of contacts and injecting frequency on time to primary infection and the role of spontaneously clearing nodes on incidence rates. On treatment we investigate the effect of nine network-based treatment strategies on chronic prevalence and incidence rates of primary infection and re-infection. Both numbers of contacts and injecting frequency play key roles in reducing time to primary infection. The change from "less-" to "more-frequent" injector is roughly similar to having one additional network contact. Nodes that spontaneously clear their HCV infection have a local effect on infection risk and the total number of such nodes (but not their locations) has a network wide effect on the incidence of both primary and re-infection with HCV. Re-infection plays a large role in the effectiveness of treatment interventions. Strategies that choose PWID and treat all their contacts (analogous to ring vaccination) are most effective in reducing the incidence rates of re-infection and combined infection. A strategy targeting infected PWID with the most contacts (analogous to targeted vaccination) is the least effective.

Towards multiscale modeling of influenza infection

Aided by recent advances in computational power, algorithms, and higher fidelity data, increasingly detailed theoretical models of infection with influenza A virus are being developed. We review single scale models as they describe influenza infection from intracellular to global scales, and, in particular, we consider those models that capture details specific to influenza and can be used to link different scales. We discuss the few multiscale models of influenza infection that have been developed in this emerging field. In addition to discussing modeling approaches, we also survey biological data on influenza infection and transmission that is relevant for constructing influenza infection models. We envision that, in the future, multiscale models that capitalize on technical advances in experimental biology and high performance computing could be used to describe the large spatial scale epidemiology of influenza infection, evolution of the virus, and transmission between hosts more accurately.

Policy resistance undermines superspreader vaccination strategies for influenza

Theoretical models of infection spread on networks predict that targeting vaccination at individuals with a very large number of contacts (superspreaders) can reduce infection incidence by a significant margin. These models generally assume that superspreaders will always agree to be vaccinated. Hence, they cannot capture unintended consequences such as policy resistance, where the behavioral response induced by a new vaccine policy tends to reduce the expected benefits of the policy. Here, we couple a model of influenza transmission on an empirically-based contact network with a psychologically structured model of influenza vaccinating behavior, where individual vaccinating decisions depend on social learning and past experiences of perceived infections, vaccine complications and vaccine failures. We find that policy resistance almost completely undermines the effectiveness of superspreader strategies: the most commonly explored approaches that target a randomly chosen neighbor of an individual, or that preferentially choose neighbors with many contacts, provide at best a 2% relative improvement over their non-targeted counterpart as compared to 12% when behavioral feedbacks are ignored. Increased vaccine coverage in super spreaders is offset by decreased coverage in non-superspreaders, and superspreaders also have a higher rate of perceived vaccine failures on account of being infected more often. Including incentives for vaccination provides modest improvements in outcomes. We conclude that the design of influenza vaccine strategies involving widespread incentive use and/or targeting of superspreaders should account for policy resistance, and mitigate it whenever possible.

Epidemic progression on networks based on disease generation time

We investigate the time evolution of disease spread on a network and present an analytical framework using the concept of disease generation time. Assuming a susceptible-infected-recovered epidemic process, this network-based framework enables us to calculate in detail the number of links (edges) within the network that are capable of producing new infectious nodes (individuals), the number of links that are not transmitting the infection further (non-transmitting links), as well as the number of contacts that individuals have with their neighbours (also known as degree distribution) within each epidemiological class, for each generation period. Using several examples, we demonstrate very good agreement between our analytical calculations and the results of computer simulations.

Optimal link removal for epidemic mitigation: a two-way partitioning approach

The structure of the contact network through which a disease spreads may influence the optimal use of resources for epidemic control. In this work, we explore how to minimize the spread of infection via quarantining with limited resources. In particular, we examine which links should be removed from the contact network, given a constraint on the number of removable links, such that the number of nodes which are no longer at risk for infection is maximized. We show how this problem can be posed as a non-convex quadratically constrained quadratic program (QCQP), and we use this formulation to derive a link removal algorithm. The performance of our QCQP-based algorithm is validated on small Erdős-Renyi and small-world random graphs, and then tested on larger, more realistic networks, including a real-world network of injection drug use. We show that our approach achieves near optimal performance and out-performs other intuitive link removal algorithms, such as removing links in order of edge centrality.

Mitigating effects of vaccination on influenza outbreaks given constraints in stockpile size and daily administration capacity

Background

Influenza viruses are a major cause of morbidity and mortality worldwide. Vaccination remains a powerful tool for preventing or mitigating influenza outbreaks. Yet, vaccine supplies and daily administration capacities are limited, even in developed countries. Understanding how such constraints can alter the mitigating effects of vaccination is a crucial part of influenza preparedness plans. Mathematical models provide tools for government and medical officials to assess the impact of different vaccination strategies and plan accordingly. However, many existing models of vaccination employ several questionable assumptions, including a rate of vaccination proportional to the population at each point in time.

Methods

We present a SIR-like model that explicitly takes into account vaccine supply and the number of vaccines administered per day and places data-informed limits on these parameters. We refer to this as the non-proportional model of vaccination and compare it to the proportional scheme typically found in the literature.

Results

The proportional and non-proportional models behave similarly for a few different vaccination scenarios. However, there are parameter regimes involving the vaccination campaign duration and daily supply limit for which the non-proportional model predicts smaller epidemics that peak later, but may last longer, than those of the proportional model. We also use the non-proportional model to predict the mitigating effects of variably timed vaccination campaigns for different levels of vaccination coverage, using specific constraints on daily administration capacity.

Conclusions

The non-proportional model of vaccination is a theoretical improvement that provides more accurate predictions of the mitigating effects of vaccination on influenza outbreaks than the proportional model. In addition, parameters such as vaccine supply and daily administration limit can be easily adjusted to simulate conditions in developed and developing nations with a wide variety of financial and medical resources. Finally, the model can be used by government and medical officials to create customized pandemic preparedness plans based on the supply and administration constraints of specific communities.

Comparison of three methods for ascertainment of contact information relevant to respiratory pathogen transmission in encounter networks

Background

Mathematical models of infection that consider targeted interventions are exquisitely dependent on the assumed mixing patterns of the population. We report on a pilot study designed to assess three different methods (one retrospective, two prospective) for obtaining contact data relevant to the determination of these mixing patterns.

Methods

65 adults were asked to record their social encounters in each location visited during 6 study days using a novel method whereby a change in physical location of the study participant triggered data entry. Using a cross-over design, all participants recorded encounters on 3 days in a paper diary and 3 days using an electronic recording device (PDA). Participants were randomised to first prospective recording method.

Results

Both methods captured more contacts than a pre-study questionnaire, but ascertainment using the paper diary was superior to the PDA (mean difference: 4.52 (95% CI 0.28, 8.77). Paper diaries were found more acceptable to the participants compared with the PDA. Statistical analysis confirms that our results are broadly consistent with those reported from large-scale European based surveys. An association between household size (trend 0.14, 95% CI (0.06, 0.22), P < 0.001) and composition (presence of child 0.37, 95% CI (0.17, 0.56), P < 0.001) and the total number of reported contacts was observed, highlighting the importance of sampling study populations based on household characteristics as well as age. New contacts were still being recorded on the third study day, but compliance had declined, indicating that the optimal number of sample days represents a trade-off between completeness and quality of data for an individual.

Conclusions

The study's location-based reporting design allows greater scope compared to other methods for examining differences in the characteristics of encounters over a range of environments. Improved parameterisation of dynamic transmission models gained from work of this type will aid in the development of more robust decision support tools to assist health policy makers and planners.

Disease spread in small-size directed networks: epidemic threshold, correlation between links to and from nodes, and clustering

Network epidemiology has mainly focused on large-scale complex networks. It is unclear whether findings of these investigations also apply to networks of small size. This knowledge gap is of relevance for many biological applications, including meta-communities, plant-pollinator interactions and the spread of the oomycete pathogen Phytophthora ramorum in networks of plant nurseries. Moreover, many small-size biological networks are inherently asymmetrical and thus cannot be realistically modelled with undirected networks. We modelled disease spread and establishment in directed networks of 100 and 500 nodes at four levels of connectance in six network structures (local, small-world, random, one-way, uncorrelated, and two-way scale-free networks). The model was based on the probability of infection persistence in a node and of infection transmission between connected nodes. Regardless of the size of the network, the epidemic threshold did not depend on the starting node of infection but was negatively related to the correlation coefficient between in- and out-degree for all structures, unless networks were sparsely connected. In this case clustering played a significant role. For small-size scale-free directed networks to have a lower epidemic threshold than other network structures, there needs to be a positive correlation between number of links to and from nodes. When this correlation is negative (one-way scale-free networks), the epidemic threshold for small-size networks can be higher than in non-scale-free networks. Clustering does not necessarily have an influence on the epidemic threshold if connectance is kept constant. Analyses of the influence of the clustering on the epidemic threshold in directed networks can also be spurious if they do not consider simultaneously the effect of the correlation coefficient between in- and out-degree.

On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

We study the spreading of contagious diseases in a population of constant size using susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R0) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R0 cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations.

Some elementary properties of SIR networks or, can i get sick because you got vaccinated?

We consider epidemics on social networks and address the question of whether administering a safe vaccine to one or more individuals can raise another individual's chances of becoming infected. Surprisingly, this can happen if transmission probabilities vary over time. If transmission probabilities do not vary with time, we show that in the discrete SIR model vaccination cannot cause collateral damage. We phrase this question in terms of monotonicity properties and answer it using bond percolation methods. By passing to a covering graph we are able to extend these results to models with more complicated latent and infective states.