Enhanced vaccine control of epidemics in adaptive networks

Subject Modeling-Based Analysis of the Evolution and Intervention Strategies of Major Emerging Infectious Disease Events

Objective

Due to the popularity of the Internet and the extensive use of new media, after the occurrence of infectious diseases, the spread of social media information greatly affects the group's opinion and cognition and even the health behaviors they take, thus affecting the spread of infectious diseases. Therefore, this paper studies the event evolution from multiple dimensions.

Methods

To address this gap, we developed a three-layer model framework of major infectious disease event evolution based on subject modeling. This framework integrates three key factors-health transmission, perspective interaction, and risk perception-to analyze group perspective evolution, behavioral change, and virus transmission processes. The model's effectiveness was evaluated through simulation and sensitivity analysis. In addition, we conducted an empirical analysis by constructing a social media health transmission effect index system to identify the critical factors affecting health transmission.

Results

Simulation results reveal that among the three factors, health transmission has the most significant impact on the evolution of group perspectives during infectious disease events. Moreover, the dynamics of public viewpoint evolution influence individual decisions regarding the adoption of non-pharmacological interventions, which are shown to effectively reduce both the transmission rate of the virus and the peak number of infections.

Conclusion

The findings of this study enhance our understanding of the complex mechanisms and evolutionary pathways in infectious disease events. By integrating multiple dimensions of event evolution, the proposed model offers valuable insights for the design of effective countermeasures and strategies in emergency management and response to infectious disease outbreaks.

Dynamical vaccination behavior with risk perception and vaccination rewards

Vaccination is the most effective way to control the epidemic spreading. However, the probability of people getting vaccinated changes with the epidemic situation due to personal psychology. Facing various risks, some people are reluctant to vaccinate and even prefer herd immunity. To encourage people to get vaccinated, many countries set up reward mechanisms. In this paper, we propose a disease transmission model combining vaccination behaviors based on the SIR (Susceptible-Infected-Recovered) model and introduce three vaccination mechanisms. We analyze the impact of the infection rate and the recovery rate on the total cost and the epidemic prevalence. Numerical simulations fit with our intuitive feelings. Then, we study the impact of vaccination rewards on the total social cost. We find that when vaccination rewards offset vaccination costs, both the total cost and the epidemic prevalence reach the lowest levels. Finally, this paper suggests that encouraging people to get vaccinated at the beginning of an epidemic has the best effect.

Self-adapting infectious dynamics on random networks

Self-adaptive dynamics occurs in many fields of research, such as socio-economics, neuroscience, or biophysics. We consider a self-adaptive modeling approach, where adaptation takes place within a set of strategies based on the history of the state of the system. This leads to piecewise deterministic Markovian dynamics coupled to a non-Markovian adaptive mechanism. We apply this framework to basic epidemic models (SIS, SIR) on random networks. We consider a co-evolutionary dynamical network where node-states change through the epidemics and network topology changes through the creation and deletion of edges. For a simple threshold base application of lockdown measures, we observe large regions in parameter space with oscillatory behavior, thereby exhibiting one of the most reduced mechanisms leading to oscillations. For the SIS epidemic model, we derive analytic expressions for the oscillation period from a pairwise closed model, which is validated with numerical simulations for random uniform networks. Furthermore, the basic reproduction number fluctuates around one indicating a connection to self-organized criticality.

Spatial dynamics of synergistic coinfection in rock-paper-scissors models

We investigate the spatial dynamics of two-disease epidemics reaching a three-species cyclic model. Regardless of their species, all individuals are susceptible to being infected with two different pathogens, which spread through person-to-person contact. We consider that the simultaneous presence of multiple infections leads to a synergistic amplification in the probability of host mortality due to complications arising from any of the co-occurring diseases. Employing stochastic simulations, we explore the ramifications of this synergistic coinfection on spatial configurations that emerge from stochastic initial conditions. Under conditions of pronounced synergistic coinfection, we identify the emergence of zones inhabited solely by hosts affected by a singular pathogen. At the boundaries of spatial domains dominated by a single disease, interfaces of coinfected hosts appear. The dynamics of these interfaces are shaped by curvature-driven processes and display a scaling behavior reflective of the topological attributes of the underlying two-dimensional space. As the lethality linked to coinfection diminishes, the evolution of the interface network's spatial dynamics is influenced by fluctuations stemming from waves of coinfection that infiltrate territories predominantly occupied by a single disease. Our analysis extends to quantifying the implications of synergistic coinfection at both the individual and population levels Our outcomes show that organisms' infection risk is maximized if the coinfection increases the death due to disease by 30% and minimized as the network dynamics reach the scaling regime, with species populations being maximum. Our conclusions may help ecologists understand the dynamics of epidemics and their impact on the stability of ecosystems.

Stochastic dynamics of an SIS epidemic on networks

We derive a stochastic SIS pairwise model by considering the change of the variables of this system caused by an event. Based on approximations, we construct a low-dimensional deterministic system that can be used to describe the epidemic spread on a regular network. The mathematical treatment of the model yields explicit expressions for the variances of each variable at equilibrium. Then a comparison between the stochastic pairwise model and the stochastic mean-field SIS model is performed to indicate the effect of network structure. We find that the variances of the prevalence of infection for these two models are almost equal when the number of neighbors of every individual is large. Furthermore, approximations for the quasi-stationary distribution of the number of infected individuals and the expected time to extinction starting in quasi-stationary are derived. We analyze the approximations for the critical number of neighbors and the persistence threshold based on the stochastic model. The approximate performance is then examined by numerical and stochastic simulations. Moreover, during the early development phase, the temporal variance of the infection is also obtained. The simulations show that our analytical results are asymptotically accurate and reasonable.

A review and agenda for integrated disease models including social and behavioural factors

Social and behavioural factors are critical to the emergence, spread and containment of human disease, and are key determinants of the course, duration and outcomes of disease outbreaks. Recent epidemics of Ebola in West Africa and coronavirus disease 2019 (COVID-19) globally have reinforced the importance of developing infectious disease models that better integrate social and behavioural dynamics and theories. Meanwhile, the growth in capacity, coordination and prioritization of social science research and of risk communication and community engagement (RCCE) practice within the current pandemic response provides an opportunity for collaboration among epidemiological modellers, social scientists and RCCE practitioners towards a mutually beneficial research and practice agenda. Here, we provide a review of the current modelling methodologies and describe the challenges and opportunities for integrating them with social science research and RCCE practice. Finally, we set out an agenda for advancing transdisciplinary collaboration for integrated disease modelling and for more robust policy and practice for reducing disease transmission.

A multi-stage stochastic programming approach to epidemic resource allocation with equity considerations

Existing compartmental models in epidemiology are limited in terms of optimizing the resource allocation to control an epidemic outbreak under disease growth uncertainty. In this study, we address this core limitation by presenting a multi-stage stochastic programming compartmental model, which integrates the uncertain disease progression and resource allocation to control an infectious disease outbreak. The proposed multi-stage stochastic program involves various disease growth scenarios and optimizes the distribution of treatment centers and resources while minimizing the total expected number of new infections and funerals. We define two new equity metrics, namely infection and capacity equity, and explicitly consider equity for allocating treatment funds and facilities over multiple time stages. We also study the multi-stage value of the stochastic solution (VSS), which demonstrates the superiority of the proposed stochastic programming model over its deterministic counterpart. We apply the proposed formulation to control the Ebola Virus Disease (EVD) in Guinea, Sierra Leone, and Liberia of West Africa to determine the optimal and fair resource-allocation strategies. Our model balances the proportion of infections over all regions, even without including the infection equity or prevalence equity constraints. Model results also show that allocating treatment resources proportional to population is sub-optimal, and enforcing such a resource allocation policy might adversely impact the total number of infections and deaths, and thus resulting in a high cost that we have to pay for the fairness. Our multi-stage stochastic epidemic-logistics model is practical and can be adapted to control other infectious diseases in meta-populations and dynamically evolving situations.

State-based targeted vaccination

Vaccination has become one of the most prominent measures for preventing the spread of infectious diseases in modern times. However, mass vaccination of the population may not always be possible due to high costs, severe side effects, or shortage. Therefore, identifying individuals with a high potential of spreading the disease and targeted vaccination of these individuals is of high importance. While various strategies for identifying such individuals have been proposed in the network epidemiology literature, the vast majority of them rely solely on the network topology. In contrast, in this paper, we propose a novel targeted vaccination strategy that considers both the static network topology and the dynamic states of the network nodes over time. This allows our strategy to find the individuals with the highest potential to spread the disease at any given point in time. Extensive evaluation that we conducted over various real-world network topologies, network sizes, vaccination budgets, and parameters of the contagion model, demonstrates that the proposed strategy considerably outperforms existing state-of-the-art targeted vaccination strategies in reducing the spread of the disease. In particular, the proposed vaccination strategy further reduces the number of infected nodes by 23-99%, compared to a vaccination strategy based on Betweenness Centrality.

Asymmetry in interdependence makes a multilayer system more robust against cascading failures

Multilayer networked systems are ubiquitous in nature and engineering, and the robustness of these systems against failures is of great interest. A main line of theoretical pursuit has been percolation-induced cascading failures, where interdependence between network layers is conveniently and tacitly assumed to be symmetric. In the real world, interdependent interactions are generally asymmetric. To uncover and quantify the impact of asymmetry in interdependence on network robustness, we focus on percolation dynamics in double-layer systems and implement the following failure mechanism: Once a node in a network layer fails, the damage it can cause depends not only on its position in the layer but also on the position of its counterpart neighbor in the other layer. We find that the characteristics of the percolation transition depend on the degree of asymmetry, where the striking phenomenon of a switch in the nature of the phase transition from first to second order arises. We derive a theory to calculate the percolation transition points in both network layers, as well as the transition switching point, with strong numerical support from synthetic and empirical networks. Not only does our work shed light on the factors that determine the robustness of multilayer networks against cascading failures, but it also provides a scenario by which the system can be designed or controlled to reach a desirable level of resilience.

Integrating social behaviour, demography and disease dynamics in network models: applications to disease management in declining wildlife populations

The emergence and spread of infections can contribute to the decline and extinction of populations, particularly in conjunction with anthropogenic environmental change. The importance of heterogeneity in processes of transmission, resistance and tolerance is increasingly well understood in theory, but empirical studies that consider both the demographic and behavioural implications of infection are scarce. Non-random mixing of host individuals can impact the demographic thresholds that determine the amplification or attenuation of disease prevalence. Risk assessment and management of disease in threatened wildlife populations must therefore consider not just host density, but also the social structure of host populations. Here we integrate the most recent developments in epidemiological research from a demographic and social network perspective, and synthesize the latest developments in social network modelling for wildlife disease, to explore their applications to disease management in populations in decline and at risk of extinction. We use simulated examples to support our key points and reveal how disease-management strategies can and should exploit both behavioural and demographic information to prevent or control the spread of disease. Our synthesis highlights the importance of considering the combined impacts of demographic and behavioural processes in epidemics to successful disease management in a conservation context. This article is part of the theme issue 'Linking behaviour to dynamics of populations and communities: application of novel approaches in behavioural ecology to conservation'.

Effect of time varying transmission rates on the coupled dynamics of epidemic and awareness over a multiplex network

A non-linear stochastic model is presented to study the effect of time variation of transmission rates on the co-evolution of epidemics and its corresponding awareness over a two layered multiplex network. In the model, the infection transmission rate of a given node in the epidemic layer depends upon its awareness probability in the awareness layer. Similarly, the infection information transmission rate of a node in the awareness layer depends upon its infection probability in the epidemic layer. The spread of disease resulting from physical contacts is described in terms of a Susceptible Infected Susceptible process over the epidemic layer and the spread of information about the disease outbreak is described in terms of an Unaware Aware Unaware process over the virtual interaction mediated awareness layer. The time variation of the transmission rates and the resulting co-evolution of these mutually competing processes are studied in terms of a network topology dependent parameter ( α ). Using a second order linear theory, it is shown that in the continuous time limit, the co-evolution of these processes can be described in terms of damped and driven harmonic oscillator equations. From the results of a Monte-Carlo simulation, it is shown that for a suitable choice of the parameter ( α ) , the two processes can either exhibit sustained oscillatory or damped dynamics. The damped dynamics corresponds to the endemic state. Furthermore, for the case of an endemic state, it is shown that the inclusion of the awareness layer significantly lowers the disease transmission rate and reduces the size of the epidemic. The infection probability of the nodes in the endemic state is found to have a dependence on both the transmission rates and on their absolute degrees in each of the network layers and on the relative differences between their degrees in the respective layers.

New perspectives for the prediction and statistical quantification of extreme events in high-dimensional dynamical systems

We discuss extreme events as random occurrences of strongly transient dynamics that lead to nonlinear energy transfers within a chaotic attractor. These transient events are the result of finite-time instabilities and therefore are inherently connected with both statistical and dynamical properties of the system. We consider two classes of problems related to extreme events and nonlinear energy transfers, namely (i) the derivation of precursors for the short-term prediction of extreme events, and (ii) the efficient sampling of random realizations for the fastest convergence of the probability density function in the tail region. We summarize recent methods on these problems that rely on the simultaneous consideration of the statistical and dynamical characteristics of the system. This is achieved by combining available data, in the form of second-order statistics, with dynamical equations that provide information for the transient events that lead to extreme responses. We present these methods through two high-dimensional, prototype systems that exhibit strongly chaotic dynamics and extreme responses due to transient instabilities, the Kolmogorov flow and unidirectional nonlinear water waves.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies

While deterministic metapopulation models for the spread of epidemics between populations have been well-studied in the literature, variability in disease transmission rates and interaction rates between individual agents or populations suggests the need to consider stochastic fluctuations in model parameters in order to more fully represent realistic epidemics. In the present paper, we have extended a stochastic SIS epidemic model - which introduces stochastic perturbations in the form of white noise to the force of infection (the rate of disease transmission from classes of infected to susceptible populations) - to spatial networks, thereby obtaining a stochastic epidemic metapopulation model. We solved the stochastic model numerically and found that white noise terms do not drastically change the overall long-term dynamics of the system (for sufficiently small variance of the noise) relative to the dynamics of a corresponding deterministic system. The primary difference between the stochastic and deterministic metapopulation models is that for large time, solutions tend to quasi-stationary distributions in the stochastic setting, rather than to constant steady states in the deterministic setting. We then considered different approaches to controlling the spread of a stochastic SIS epidemic over spatial networks, comparing results for a spectrum of controls utilizing local to global information about the state of the epidemic. Variation in white noise was shown to be able to counteract the treatment rate (treated curing rate) of the epidemic, requiring greater treatment rates on the part of the control and suggesting that in real-life epidemics one should be mindful of such random variations in order for a treatment to be effective. Additionally, we point out some problems using white noise perturbations as a model, but show that a truncated noise process gives qualitatively comparable behaviors without these issues.

Cost-efficient vaccination protocols for network epidemiology

We investigate methods to vaccinate contact networks—i.e. removing nodes in such a way that disease spreading is hindered as much as possible—with respect to their cost-efficiency. Any real implementation of such protocols would come with costs related both to the vaccination itself, and gathering of information about the network. Disregarding this, we argue, would lead to erroneous evaluation of vaccination protocols. We use the susceptible-infected-recovered model—the generic model for diseases making patients immune upon recovery—as our disease-spreading scenario, and analyze outbreaks on both empirical and model networks. For different relative costs, different protocols dominate. For high vaccination costs and low costs of gathering information, the so-called acquaintance vaccination is the most cost efficient. For other parameter values, protocols designed for query-efficient identification of the network’s largest degrees are most efficient.

Finding methods to identify important spreaders—and consequently protocols to identify individuals to vaccinate in targeted vaccination campaigns—is one of the most important topics of network theory. Earlier studies typically make some assumption about what information is available about the contact network that the disease spreads over. Then they try to optimize an objective function—either the average outbreak size in disease simulations, or (simpler) the size of the largest connected component. For public-health practitioners, gathering the network information cannot be detached from the decision process—their cost function includes the costs for both the vaccination itself and mapping of the network. This is the first paper to evaluate the cost efficiency of vaccination protocols—a problem that is much more relevant and not so much more complicated, than the oversimplified objective functions optimized in previous studies. We find a “no-free lunch” situation, where different protocols proposed in the past are most efficient at different cost scenarios. However, some methods are never cost efficient due to the amount of information they need. What protocol that is the best depends on network structure in a non-trivial way. We use both analytical and simulation techniques to reach these conclusions.

Optimizing sentinel surveillance in temporal network epidemiology

To help health policy makers gain response time to mitigate infectious disease threats, it is essential to have an efficient epidemic surveillance. One common method of disease surveillance is to carefully select nodes (sentinels, or sensors) in the network to report outbreaks. One would like to choose sentinels so that they discover the outbreak as early as possible. The optimal choice of sentinels depends on the network structure. Studies have addressed this problem for static networks, but this is a first step study to explore designing surveillance systems for early detection on temporal networks. This paper is based on the idea that vaccination strategies can serve as a method to identify sentinels. The vaccination problem is a related question that is much more  well studied for temporal networks. To assess the ability to detect epidemic outbreaks early, we calculate the time difference (lead time) between the surveillance set and whole population in reaching 1% prevalence. We find that the optimal selection of sentinels depends on both the network's temporal structures and the infection probability of the disease. We find that, for a mild infectious disease (low infection probability) on a temporal network in relation to potential disease spreading (the Prostitution network), the strategy of selecting latest contacts of random individuals provide the most amount of lead time. And for a more uniform, synthetic network with community structure the strategy of selecting frequent contacts of random individuals provide the most amount of lead time.

Dynamics of epidemic diseases on a growing adaptive network

The study of epidemics on static networks has revealed important effects on disease prevalence of network topological features such as the variance of the degree distribution, i.e. the distribution of the number of neighbors of nodes, and the maximum degree. Here, we analyze an adaptive network where the degree distribution is not independent of epidemics but is shaped through disease-induced dynamics and mortality in a complex interplay. We study the dynamics of a network that grows according to a preferential attachment rule, while nodes are simultaneously removed from the network due to disease-induced mortality. We investigate the prevalence of the disease using individual-based simulations and a heterogeneous node approximation. Our results suggest that in this system in the thermodynamic limit no epidemic thresholds exist, while the interplay between network growth and epidemic spreading leads to exponential networks for any finite rate of infectiousness when the disease persists.

Control of epidemics via social partnership adjustment

Epidemic control is of great importance for human society. Adjusting interacting partners is an effective individualized control strategy. Intuitively, it is done either by shortening the interaction time between susceptible and infected individuals or by increasing the opportunities for contact between susceptible individuals. Here, we provide a comparative study on these two control strategies by establishing an epidemic model with nonuniform stochastic interactions. It seems that the two strategies should be similar, since shortening the interaction time between susceptible and infected individuals somehow increases the chances for contact between susceptible individuals. However, analytical results indicate that the effectiveness of the former strategy sensitively depends on the infectious intensity and the combinations of different interaction rates, whereas the latter one is quite robust and efficient. Simulations are shown to verify our analytical predictions. Our work may shed light on the strategic choice of disease control.

Toward a Realistic Modeling of Epidemic Spreading with Activity Driven Networks

Models of epidemic spreading are widely used to predict the evolution of an outbreak, test specific intervention scenarios, and steer interventions in the field. Compartmental models are the most common class of models. They are very effective for qualitative analysis, but they rely on simplifying assumptions, such as homogeneous mixing and time scale separation. On the other end of the spectrum, detailed agent-based models, based on realistic mobility pattern models, provide extremely accurate predictions. However, these models require significant computing power and are not suitable for analytical treatment. Our research aims at bridging the gap between these two approaches, toward time-varying network models that are sufficiently accurate to make predictions for real-world applications, while being computationally affordable and amenable to analytical treatment. We leverage the novel paradigm of activity driven networks (ADNs), a particular type of time-varying network that accounts for inherent inhomogeinities within a population. Starting from the basic incarnation of ADNs, we expand on the framework to include behavioral factors triggered by health status and spreading awareness. The enriched paradigm is then utilized to model the 2014–2015 Ebola Virus Disease (EVD) spreading in Liberia, and perform a what-if analysis on the timely application of sanitary interventions in the field. Finally, we propose a new formulation, which is amenable to analytical treatment, beyond the mere computation of the epidemic threshold.

Behavioural change models for infectious disease transmission: a systematic review (2010-2015)

We review behavioural change models (BCMs) for infectious disease transmission in humans. Following the Cochrane collaboration guidelines and the PRISMA statement, our systematic search and selection yielded 178 papers covering the period 2010-2015. We observe an increasing trend in published BCMs, frequently coupled to (re)emergence events, and propose a categorization by distinguishing how information translates into preventive actions. Behaviour is usually captured by introducing information as a dynamic parameter (76/178) or by introducing an economic objective function, either with (26/178) or without (37/178) imitation. Approaches using information thresholds (29/178) and exogenous behaviour formation (16/178) are also popular. We further classify according to disease, prevention measure, transmission model (with 81/178 population, 6/178 metapopulation and 91/178 individual-level models) and the way prevention impacts transmission. We highlight the minority (15%) of studies that use any real-life data for parametrization or validation and note that BCMs increasingly use social media data and generally incorporate multiple sources of information (16/178), multiple types of information (17/178) or both (9/178). We conclude that individual-level models are increasingly used and useful to model behaviour changes. Despite recent advancements, we remain concerned that most models are purely theoretical and lack representative data and a validation process.

The impact of vaccine success and awareness on epidemic dynamics

The role of vaccine success is introduced into an epidemic spreading model consisting of three states: susceptible, infectious, and vaccinated. Moreover, the effect of three types, namely, contact, local, and global, of infection awareness and immunization awareness is also taken into consideration. The model generalizes those considered in Pastor-Satorras and Vespignani [Phys. Rev. E 63, 066117 (2001)], Pastor-Satorras and Vespignani [Phys. Rev. E 65, 036104 (2002)], Moreno et al. [Eur. Phys. J. B 26, 521-529 (2002)], Wu et al. [Chaos 22, 013101 (2012)], and Wu et al. [Chaos 24, 023108 (2014)]. Our main results contain the following. First, the epidemic threshold is explicitly obtained. In particular, we show that, for any initial conditions, the epidemic eventually dies out regardless of what other factors are whenever some type of immunization awareness is considered, and vaccination has a perfect success. Moreover, the threshold is independent of the global type of awareness. Second, we compare the effect of contact and local types of awareness on the epidemic thresholds between heterogeneous networks and homogeneous networks. Specifically, we find that the epidemic threshold for the homogeneous network can be lower than that of the heterogeneous network in an intermediate regime for intensity of contact infection awareness while it is higher otherwise. In summary, our results highlight the important and crucial roles of both vaccine success and contact infection awareness on epidemic dynamics.

Network inoculation: Heteroclinics and phase transitions in an epidemic model

In epidemiological modelling, dynamics on networks, and, in particular, adaptive and heterogeneous networks have recently received much interest. Here, we present a detailed analysis of a previously proposed model that combines heterogeneity in the individuals with adaptive rewiring of the network structure in response to a disease. We show that in this model, qualitative changes in the dynamics occur in two phase transitions. In a macroscopic description, one of these corresponds to a local bifurcation, whereas the other one corresponds to a non-local heteroclinic bifurcation. This model thus provides a rare example of a system where a phase transition is caused by a non-local bifurcation, while both micro- and macro-level dynamics are accessible to mathematical analysis. The bifurcation points mark the onset of a behaviour that we call network inoculation. In the respective parameter region, exposure of the system to a pathogen will lead to an outbreak that collapses but leaves the network in a configuration where the disease cannot reinvade, despite every agent returning to the susceptible class. We argue that this behaviour and the associated phase transitions can be expected to occur in a wide class of models of sufficient complexity.

The impacts of simultaneous disease intervention decisions on epidemic outcomes

Mathematical models of the interplay between disease dynamics and human behavioural dynamics can improve our understanding of how diseases spread when individuals adapt their behaviour in response to an epidemic. Accounting for behavioural mechanisms that determine uptake of infectious disease interventions such as vaccination and non-pharmaceutical interventions (NPIs) can significantly alter predicted health outcomes in a population. However, most previous approaches that model interactions between human behaviour and disease dynamics have modelled behaviour of these two interventions separately. Here, we develop and analyze an agent based network model to gain insights into how behaviour toward both interventions interact adaptively with disease dynamics (and therefore, indirectly, with one another) during the course of a single epidemic where an SIRV infection spreads through a contact network. In the model, individuals decide to become vaccinated and/or practice NPIs based on perceived infection prevalence (locally or globally) and on what other individuals in the network are doing. We find that introducing adaptive NPI behaviour lowers vaccine uptake on account of behavioural feedbacks, and also decreases epidemic final size. When transmission rates are low, NPIs alone are as effective in reducing epidemic final size as NPIs and vaccination combined. Also, NPIs can compensate for delays in vaccine availability by hindering early disease spread, decreasing epidemic size significantly compared to the case where NPI behaviour does not adapt to mitigate early surges in infection prevalence. We also find that including adaptive NPI behaviour strongly mitigates the vaccine behavioural feedbacks that would otherwise result in higher vaccine uptake at lower vaccine efficacy as predicted by most previous models, and the same feedbacks cause epidemic final size to remain approximately constant across a broad range of values for vaccine efficacy. Finally, when individuals use local information about others' behaviour and infection prevalence, instead of population-level information, infection is controlled more efficiently through ring vaccination, and this is reflected in the time evolution of pair correlations on the network. This model shows that accounting for both adaptive NPI behaviour and adaptive vaccinating behaviour regarding social effects and infection prevalence can result in qualitatively different predictions than if only one type of adaptive behaviour is modelled.

A network model for Ebola spreading

The availability of accurate models for the spreading of infectious diseases has opened a new era in management and containment of epidemics. Models are extensively used to plan for and execute vaccination campaigns, to evaluate the risk of international spreadings and the feasibility of travel bans, and to inform prophylaxis campaigns. Even when no specific therapeutical protocol is available, as for the Ebola Virus Disease (EVD), models of epidemic spreading can provide useful insight to steer interventions in the field and to forecast the trend of the epidemic. Here, we propose a novel mathematical model to describe EVD spreading based on activity driven networks (ADNs). Our approach overcomes the simplifying assumption of homogeneous mixing, which is central to most of the mathematically tractable models of EVD spreading. In our ADN-based model, each individual is not bound to contact every other, and its network of contacts varies in time as a function of an activity potential. Our model contemplates the possibility of non-ideal and time-varying intervention policies, which are critical to accurately describe EVD spreading in afflicted countries. The model is calibrated from field data of the 2014 April-to-December spreading in Liberia. We use the model as a predictive tool, to emulate the dynamics of EVD in Liberia and offer a one-year projection, until December 2015. Our predictions agree with the current vision expressed by professionals in the field, who consider EVD in Liberia at its final stage. The model is also used to perform a what-if analysis to assess the efficacy of timely intervention policies. In particular, we show that an earlier application of the same intervention policy would have greatly reduced the number of EVD cases, the duration of the outbreak, and the infrastructures needed for the implementation of the intervention.

Coupled disease-behavior dynamics on complex networks: A review

It is increasingly recognized that a key component of successful infection control efforts is understanding the complex, two-way interaction between disease dynamics and human behavioral and social dynamics. Human behavior such as contact precautions and social distancing clearly influence disease prevalence, but disease prevalence can in turn alter human behavior, forming a coupled, nonlinear system. Moreover, in many cases, the spatial structure of the population cannot be ignored, such that social and behavioral processes and/or transmission of infection must be represented with complex networks. Research on studying coupled disease-behavior dynamics in complex networks in particular is growing rapidly, and frequently makes use of analysis methods and concepts from statistical physics. Here, we review some of the growing literature in this area. We contrast network-based approaches to homogeneous-mixing approaches, point out how their predictions differ, and describe the rich and often surprising behavior of disease-behavior dynamics on complex networks, and compare them to processes in statistical physics. We discuss how these models can capture the dynamics that characterize many real-world scenarios, thereby suggesting ways that policy makers can better design effective prevention strategies. We also describe the growing sources of digital data that are facilitating research in this area. Finally, we suggest pitfalls which might be faced by researchers in the field, and we suggest several ways in which the field could move forward in the coming years.

Trust-Enhanced Cloud Service Selection Model Based on QoS Analysis

Cloud computing technology plays a very important role in many areas, such as in the construction and development of the smart city. Meanwhile, numerous cloud services appear on the cloud-based platform. Therefore how to how to select trustworthy cloud services remains a significant problem in such platforms, and extensively investigated owing to the ever-growing needs of users. However, trust relationship in social network has not been taken into account in existing methods of cloud service selection and recommendation. In this paper, we propose a cloud service selection model based on the trust-enhanced similarity. Firstly, the direct, indirect, and hybrid trust degrees are measured based on the interaction frequencies among users. Secondly, we estimate the overall similarity by combining the experience usability measured based on Jaccard's Coefficient and the numerical distance computed by Pearson Correlation Coefficient. Then through using the trust degree to modify the basic similarity, we obtain a trust-enhanced similarity. Finally, we utilize the trust-enhanced similarity to find similar trusted neighbors and predict the missing QoS values as the basis of cloud service selection and recommendation. The experimental results show that our approach is able to obtain optimal results via adjusting parameters and exhibits high effectiveness. The cloud services ranking by our model also have better QoS properties than other methods in the comparison experiments.

Can rewiring strategy control the epidemic spreading?

Relation existed in the social contact network can affect individuals' behaviors greatly. Considering the diversity of relation intimacy among network nodes, an epidemic propagation model is proposed by incorporating the link-breaking threshold, which is normally neglected in the rewiring strategy. The impact of rewiring strategy on the epidemic spreading in the weighted adaptive network is explored. The results show that the rewiring strategy cannot always control the epidemic prevalence, especially when the link-breaking threshold is low. Meanwhile, as well as strong links, weak links also play a significant role on epidemic spreading.

Mathematical and computational approaches to epidemic modeling: a comprehensive review

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

Large epidemic thresholds emerge in heterogeneous networks of heterogeneous nodes

One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts. In particular, in networks of identical nodes it has been shown that network heterogeneity, i.e. a broad degree distribution, can lower the epidemic threshold at which epidemics can invade the system. Network heterogeneity can thus allow diseases with lower transmission probabilities to persist and spread. However, it has been pointed out that networks in which the properties of nodes are intrinsically heterogeneous can be very resilient to disease spreading. Heterogeneity in structure can enhance or diminish the resilience of networks with heterogeneous nodes, depending on the correlations between the topological and intrinsic properties. Here, we consider a plausible scenario where people have intrinsic differences in susceptibility and adapt their social network structure to the presence of the disease. We show that the resilience of networks with heterogeneous connectivity can surpass those of networks with homogeneous connectivity. For epidemiology, this implies that network heterogeneity should not be studied in isolation, it is instead the heterogeneity of infection risk that determines the likelihood of outbreaks.

Disease Interventions Can Interfere with One Another through Disease-Behaviour Interactions

Theoretical models of disease dynamics on networks can aid our understanding of how infectious diseases spread through a population. Models that incorporate decision-making mechanisms can furthermore capture how behaviour-driven aspects of transmission such as vaccination choices and the use of non-pharmaceutical interventions (NPIs) interact with disease dynamics. However, these two interventions are usually modelled separately. Here, we construct a simulation model of influenza transmission through a contact network, where individuals can choose whether to become vaccinated and/or practice NPIs. These decisions are based on previous experience with the disease, the current state of infection amongst one's contacts, and the personal and social impacts of the choices they make. We find that the interventions interfere with one another: because of negative feedback between intervention uptake and infection prevalence, it is difficult to simultaneously increase uptake of all interventions by changing utilities or perceived risks. However, on account of vaccine efficacy being higher than NPI efficacy, measures to expand NPI practice have only a small net impact on influenza incidence due to strongly mitigating feedback from vaccinating behaviour, whereas expanding vaccine uptake causes a significant net reduction in influenza incidence, despite the reduction of NPI practice in response. As a result, measures that support expansion of only vaccination (such as reducing vaccine cost), or measures that simultaneously support vaccination and NPIs (such as emphasizing harms of influenza infection, or satisfaction from preventing infection in others through both interventions) can significantly reduce influenza incidence, whereas measures that only support expansion of NPI practice (such as making hand sanitizers more available) have little net impact on influenza incidence. (However, measures that improve NPI efficacy may fare better.) We conclude that the impact of interference on programs relying on multiple interventions should be more carefully studied, for both influenza and other infectious diseases.

The impact of vaccine failure rate on epidemic dynamics in responsive networks

An SIS model based on the microscopic Markov-chain approximation is considered in this paper. It is assumed that the individual vaccination behavior depends on the contact awareness, local and global information of an epidemic. To better simulate the real situation, the vaccine failure rate is also taken into consideration. Our main conclusions are given in the following. First, we show that if the vaccine failure rate α is zero, then the epidemic eventually dies out regardless of what the network structure is or how large the effective spreading rate and the immunization response rates of an epidemic are. Second, we show that for any positive α, there exists a positive epidemic threshold depending on an adjusted network structure, which is only determined by the structure of the original network, the positive vaccine failure rate and the immunization response rate for contact awareness. Moreover, the epidemic threshold increases with respect to the strength of the immunization response rate for contact awareness. Finally, if the vaccine failure rate and the immunization response rate for contact awareness are positive, then there exists a critical vaccine failure rate αc > 0 so that the disease free equilibrium (DFE) is stable (resp., unstable) if α < αc (resp., α > αc). Numerical simulations to see the effectiveness of our theoretical results are also provided.

Predicting epidemic risk from past temporal contact data

Understanding how epidemics spread in a system is a crucial step to prevent and control outbreaks, with broad implications on the system’s functioning, health, and associated costs. This can be achieved by identifying the elements at higher risk of infection and implementing targeted surveillance and control measures. One important ingredient to consider is the pattern of disease-transmission contacts among the elements, however lack of data or delays in providing updated records may hinder its use, especially for time-varying patterns. Here we explore to what extent it is possible to use past temporal data of a system’s pattern of contacts to predict the risk of infection of its elements during an emerging outbreak, in absence of updated data. We focus on two real-world temporal systems; a livestock displacements trade network among animal holdings, and a network of sexual encounters in high-end prostitution. We define the node’s loyalty as a local measure of its tendency to maintain contacts with the same elements over time, and uncover important non-trivial correlations with the node’s epidemic risk. We show that a risk assessment analysis incorporating this knowledge and based on past structural and temporal pattern properties provides accurate predictions for both systems. Its generalizability is tested by introducing a theoretical model for generating synthetic temporal networks. High accuracy of our predictions is recovered across different settings, while the amount of possible predictions is system-specific. The proposed method can provide crucial information for the setup of targeted intervention strategies.

Following the emergence of a transmissible disease epidemic, interventions and resources need to be prioritized to efficiently control its spread. While the knowledge of the pattern of disease-transmission contacts among hosts would be ideal for this task, the continuously changing nature of such pattern makes its use less practical in real public health emergencies (or otherwise highly resource-demanding when possible). We show that in such situations critical knowledge to assess the real-time risk of infection can be extracted from past temporal contact data. An index expressing the conservation of contacts over time is proposed as an effective tool to prioritize interventions, and its efficiency is tested considering real data on livestock movements and on human sexual encounters.

Estimating the epidemic threshold on networks by deterministic connections

For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect than those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.

Dynamical immunization strategy for seasonal epidemics

The topic of finding an effective strategy to halt virus in a complex network is of current interest. We propose an immunization strategy for seasonal epidemics that occur periodically. Based on the local information of the infection status from the previous epidemic season, the selection of vaccinated nodes is optimized gradually. The evolution of vaccinated nodes during iterations demonstrates that the immunization tends to locate in both global hubs and local hubs. We analyze the epidemic prevalence using a heterogeneous mean-field method, and we present numerical simulations of our model. This immunization performs better than some other previously known strategies. Our work highlights an alternative direction in immunization for seasonal epidemics.

Hierarchy and polysynchrony in an adaptive network

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be nontrivial. The structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous: Nodes can be divided in differently synchronized classes but, contrary to cluster synchronization, nodes in the same class need not be connected to each other. These complicated synchrony patterns have been conjectured to play roles in systems biology and circuits. The adaptive system we study describes ways whereby this behavior can evolve from undifferentiated nodes.

Responsive immunization and intervention for infectious diseases in social networks

By using the microscopic Markov-chain approximation approach, we investigate the epidemic spreading and the responsive immunization in social networks. It is assumed that individual vaccination behavior depends on the local information of an epidemic. Our results suggest that the responsive immunization has negligible impact on the epidemic threshold and the critical value of initial epidemic outbreak, but it can effectively inhibit the outbreak of epidemic. We also analyze the influence of the intervention on the disease dynamics, where the vaccination is available only to those individuals whose number of neighbors is greater than a certain value. Simulation analysis implies that the intervention strategy can effectively reduce the vaccine use under the epidemic control.

Behavior of susceptible-vaccinated-infected-recovered epidemics with diversity in the infection rate of individuals

We study a susceptible-vaccinated-infected-recovered (SVIR) epidemic-spreading model with diversity of infection rate of the individuals. By means of analytical arguments as well as extensive computer simulations, we demonstrate that the heterogeneity in infection rate can either impede or accelerate the epidemic spreading, which depends on the amount of vaccinated individuals introduced in the population as well as the contact pattern among the individuals. Remarkably, as long as the individuals with different capability of acquiring the disease interact with unequal frequency, there always exist a cross point for the fraction of vaccinated, below which the diversity of infection rate hinders the epidemic spreading and above which expedites it. The overall results are robust to the SVIR dynamics defined on different population models; the possible applications of the results are discussed.

Impacts of subsidy policies on vaccination decisions in contact networks

To motivate more people to participate in vaccination campaigns, various subsidy policies are often supplied by government and the health sectors. However, these external incentives may also alter the vaccination decisions of the broader public, and hence the choice of incentive needs to be carefully considered. Since human behavior and the networking-constrained interactions among individuals significantly impact the evolution of an epidemic, here we consider the voluntary vaccination on human contact networks. To this end, two categories of typical subsidy policies are considered: (1) under the free subsidy policy, the total amount of subsidy is distributed to a certain fraction of individual and who are vaccinated without personal cost, and (2) under the partial-offset subsidy policy, each vaccinated person is offset by a certain amount of subsidy. A vaccination decision model based on evolutionary game theory is established to study the effects of these different subsidy policies on disease control. Simulations suggest that, because the partial-offset subsidy policy encourages more people to take vaccination, its performance is significantly better than that of the free subsidy policy. However, an interesting phenomenon emerges in the partial-offset scenario: with limited amount of total subsidy, a moderate subsidy rate for each vaccinated individual can guarantee the group-optimal vaccination, leading to the maximal social benefits, while such an optimal phenomenon is not evident for the free subsidy scenario.

Coupled adaptive complex networks

Adaptive networks, which combine topological evolution of the network with dynamics on the network, are ubiquitous across disciplines. Examples include technical distribution networks such as road networks and the internet, natural and biological networks, and social science networks. These networks often interact with or depend upon other networks, resulting in coupled adaptive networks. In this paper we study susceptible-infected-susceptible (SIS) epidemic dynamics on coupled adaptive networks, where susceptible nodes are able to avoid contact with infected nodes by rewiring their intranetwork connections. However, infected nodes can pass the disease through internetwork connections, which do not change with time: The dependencies between the coupled networks remain constant. We develop an analytical formalism for these systems and validate it using extensive numerical simulation. We find that stability is increased by increasing the number of internetwork links, in the sense that the range of parameters over which both endemic and healthy states coexist (both states are reachable depending on the initial conditions) becomes smaller. Finally, we find a new stable state that does not appear in the case of a single adaptive network but only in the case of weakly coupled networks, in which the infection is endemic in one network but neither becomes endemic nor dies out in the other. Instead, it persists only at the nodes that are coupled to nodes in the other network through internetwork links. We speculate on the implications of these findings.

Random walks and search in time-varying networks

The random walk process underlies the description of a large number of real-world phenomena. Here we provide the study of random walk processes in time-varying networks in the regime of time-scale mixing, i.e., when the network connectivity pattern and the random walk process dynamics are unfolding on the same time scale. We consider a model for time-varying networks created from the activity potential of the nodes and derive solutions of the asymptotic behavior of random walks and the mean first passage time in undirected and directed networks. Our findings show striking differences with respect to the well-known results obtained in quenched and annealed networks, emphasizing the effects of dynamical connectivity patterns in the definition of proper strategies for search, retrieval, and diffusion processes in time-varying networks.

Epidemic spreading induced by diversity of agents' mobility

In this paper, we study the impact of the preference of an individual for public transport on the spread of infectious disease, through a quantity known as the public mobility. Our theoretical and numerical results based on a constructed model reveal that if the average public mobility of the agents is fixed, an increase in the diversity of the agents' public mobility reduces the epidemic threshold, beyond which an enhancement in the rate of infection is observed. Our findings provide an approach to improve the resistance of a society against infectious disease, while preserving the utilization rate of the public transportation system.

Activity driven modeling of time varying networks

Network modeling plays a critical role in identifying statistical regularities and structural principles common to many systems. The large majority of recent modeling approaches are connectivity driven. The structural patterns of the network are at the basis of the mechanisms ruling the network formation. Connectivity driven models necessarily provide a time-aggregated representation that may fail to describe the instantaneous and fluctuating dynamics of many networks. We address this challenge by defining the activity potential, a time invariant function characterizing the agents' interactions and constructing an activity driven model capable of encoding the instantaneous time description of the network dynamics. The model provides an explanation of structural features such as the presence of hubs, which simply originate from the heterogeneous activity of agents. Within this framework, highly dynamical networks can be described analytically, allowing a quantitative discussion of the biases induced by the time-aggregated representations in the analysis of dynamical processes.

Exploiting temporal network structures of human interaction to effectively immunize populations

Decreasing the number of people who must be vaccinated to immunize a community against an infectious disease could both save resources and decrease outbreak sizes. A key to reaching such a lower threshold of immunization is to find and vaccinate people who, through their behavior, are more likely than average to become infected and to spread the disease further. Fortunately, the very behavior that makes these people important to vaccinate can help us to localize them. Earlier studies have shown that one can use previous contacts to find people that are central in static contact networks. However, real contact patterns are not static. In this paper, we investigate if there is additional information in the temporal contact structure for vaccination protocols to exploit. We answer this affirmative by proposing two immunization methods that exploit temporal correlations and showing that these methods outperform a benchmark static-network protocol in four empirical contact datasets under various epidemic scenarios. Both methods rely only on obtainable, local information, and can be implemented in practice. For the datasets directly related to contact patterns of potential disease spreading (of sexually-transmitted and nosocomial infections respectively), the most efficient protocol is to sample people at random and vaccinate their latest contacts. The network datasets are temporal, which enables us to make more realistic evaluations than earlier studies—we use only information about the past for the purpose of vaccination, and about the future to simulate disease outbreaks. Using analytically tractable models, we identify two temporal structures that explain how the protocols earn their efficiency in the empirical data. This paper is a first step towards real vaccination protocols that exploit temporal-network structure—future work is needed both to characterize the structure of real contact sequences and to devise immunization methods that exploit these.

Epidemic reemergence in adaptive complex networks

The dynamic nature of a system gives rise to dynamical features of epidemic spreading, such as oscillation and bistability. In this paper, by studying the epidemic spreading in growing networks, in which susceptible nodes may adaptively break the connections with infected ones yet avoid being isolated, we reveal a phenomenon, epidemic reemergence, where the number of infected nodes is incubated at a low level for a long time and then erupts for a short time. The process may repeat several times before the infection finally vanishes. Simulation results show that all three factors, namely the network growth, the connection breaking, and the isolation avoidance, are necessary for epidemic reemergence to happen. We present a simple theoretical analysis to explain the process of reemergence in detail. Our study may offer some useful insights, helping explain the phenomenon of repeated epidemic explosions.

Adaptive Network Dynamics - Modeling and Control of Time-Dependent Social Contacts

Real networks consisting of social contacts do not possess static connections. That is, social connections may be time dependent due to a variety of individual behavioral decisions based on current network connections. Examples of adaptive networks occur in epidemics, where information about infectious individuals may change the rewiring of healthy people, or in the recruitment of individuals to a cause or fad, where rewiring may optimize recruitment of susceptible individuals. In this paper, we will review some of the dynamical properties of adaptive networks, and show how they predict novel phenomena as well as yield insight into new controls. The applications will be control of epidemic outbreaks and terrorist recruitment modeling.

Control of rare events in reaction and population systems by deterministically imposed transitions

We consider control of reaction and population systems by imposing transitions between states with different numbers of particles or individuals. The transitions take place at predetermined instants of time. Even where they are significantly less frequent than spontaneous transitions, they can exponentially strongly modify the rates of rare events, including switching between metastable states or population extinction. We also study optimal control of rare events. Specifically, we are interested in the optimal control of disease extinction for a limited vaccine supply. A comparison is made with control of rare events by modulating the rates of elementary transitions rather than imposing transitions deterministically. It is found that, unexpectedly, for the same mean control parameters, controlling the transitions rates can be more efficient.