Dueling biological and social contagions

Paradoxes in the coevolution of contagions and institutions

Epidemic models study the spread of undesired agents through populations, be it infectious diseases through a country, misinformation in social media or pests infesting a region. In combating these epidemics, we rely neither on global top-down interventions, nor solely on individual adaptations. Instead, interventions commonly come from local institutions such as public health departments, moderation teams on social media platforms or other forms of group governance. Classic models, which are often individual or agent-based, are ill-suited to capture local adaptations. We leverage developments of institutional dynamics based on cultural group selection to study how groups attempt local control of an epidemic by taking inspiration from the successes and failures of other groups. Incorporating institutional changes into epidemic dynamics reveals paradoxes: a higher transmission rate can result in smaller outbreaks as does decreasing the speed of institutional adaptation. When groups perceive a contagion as more worrisome, they can invest in improved policies and, if they maintain these policies long enough to have impact, lead to a reduction in endemicity. By looking at the interplay between the speed of institutions and the transmission rate of the contagions, we find rich coevolutionary dynamics that reflect the complexity of known biological and social contagions.

Enhancing Mass Vaccination Programs with Queueing Theory and Spatial Optimization

Background

Mass vaccination is a cornerstone of public health emergency preparedness and response. However, injudicious placement of vaccination sites can lead to the formation of long waiting lines or queues, which discourages individuals from waiting to be vaccinated and may thus jeopardize the achievement of public health targets. Queueing theory offers a framework for modeling queue formation at vaccination sites and its effect on vaccine uptake.

Methods

We developed an algorithm that integrates queueing theory within a spatial optimization framework to optimize the placement of mass vaccination sites. The algorithm was built and tested using data from a mass canine rabies vaccination campaign in Arequipa, Peru. We compared expected vaccination coverage and losses from queueing (i.e., attrition) for sites optimized with our queue-conscious algorithm to those obtained from a queue-naive version of the same algorithm.

Results

Sites placed by the queue-conscious algorithm resulted in 9-19% less attrition and 1-2% higher vaccination coverage compared to sites placed by the queue-naïve algorithm. Compared to the queue-naïve algorithm, the queue-conscious algorithm favored placing more sites in densely populated areas to offset high arrival volumes, thereby reducing losses due to excessive queueing. These results were not sensitive to misspecification of queueing parameters or relaxation of the constant arrival rate assumption.

Conclusion

One should consider losses from queueing to optimally place mass vaccination sites, even when empirically derived queueing parameters are not available. Due to the negative impacts of excessive wait times on participant satisfaction, reducing queueing attrition is also expected to yield downstream benefits and improve vaccination coverage in subsequent mass vaccination campaigns.

A behaviour and disease transmission model: incorporating the Health Belief Model for human behaviour into a simple transmission model

The health and economic impacts of infectious diseases such as COVID-19 affect all levels of a community from the individual to the governing bodies. However, the spread of an infectious disease is intricately linked to the behaviour of the people within a community since crowd behaviour affects individual human behaviour, while human behaviour affects infection spread, and infection spread affects human behaviour. Capturing these feedback loops of behaviour and infection is a well-known challenge in infectious disease modelling. Here, we investigate the interface of behavioural science theory and infectious disease modelling to explore behaviour and disease (BaD) transmission models. Specifically, we incorporate a visible protective behaviour into the susceptible-infectious-recovered-susceptible (SIRS) transmission model using the socio-psychological Health Belief Model to motivate behavioural uptake and abandonment. We characterize the mathematical thresholds for BaD emergence in the BaD SIRS model and the feasible steady states. We also explore, under different infectious disease scenarios, the effects of a fully protective behaviour on long-term disease prevalence in a community, and describe how BaD modelling can investigate non-pharmaceutical interventions that target-specific components of the Health Belief Model. This transdisciplinary BaD modelling approach may reduce the health and economic impacts of future epidemics.

Catch the tweet to fight the flu: Using Twitter to promote flu shots on a college campus

Objective: Over the 2018-2019 flu season we conducted a randomized controlled trial examining the efficacy of a Twitter campaign on vaccination rates. Concurrently we investigated potential interactions between digital social network structure and vaccination status. Participants: Undergratuates at a large midwestern public university were randomly assigned to an intervention (n = 353) or control (n = 349) group. Methods: Vaccination data were collected via monthly surveys. Participant Twitter data were collected through the public-facing Twitter API. Intervention impact was assessed with logistic regression. Standard network science tools examined vaccination coverage over online social networks. Results: The campaign had no effect on vaccination outcome. Receiving a flu shot the prior year had a positive impact on participant vaccination. Evidence of an interaction between digital social network structure and vaccination status was detected. Conclusions: Social media campaigns may not be sufficient for increasing vaccination rates. There may be potential for social media campaigns that leverage network structure.

The impact of threshold decision mechanisms of collective behavior on disease spread

Humans are a hyper-social species, which greatly impacts the spread of infectious diseases. How do social dynamics impact epidemiology and what are the implications for public health policy? Here, we develop a model of disease transmission that incorporates social dynamics and a behavior that reduces the spread of disease, a voluntary nonpharmaceutical intervention (NPI). We use a "tipping-point" dynamic, previously used in the sociological literature, where individuals adopt a behavior given a sufficient prevalence of the behavior in the population. The thresholds at which individuals adopt the NPI behavior are modulated by the perceived risk of infection, i.e., the disease prevalence and transmission rate, costs to adopt the NPI behavior, and the behavior of others. Social conformity creates a type of "stickiness" whereby individuals are resistant to changing their behavior due to the population's inertia. In this model, we observe a nonmonotonicity in the attack rate as a function of various biological and social parameters such as the transmission rate, efficacy of the NPI, costs of the NPI, weight of social consequences of shirking the social norm, and the degree of heterogeneity in the population. We also observe that the attack rate can be highly sensitive to these parameters due to abrupt shifts in the collective behavior of the population. These results highlight the complex interplay between the dynamics of epidemics and norm-driven collective behaviors.

From Isles of Königsberg to Islets of Langerhans: Examining the Function of the Endocrine Pancreas Through Network Science

Islets of Langerhans are multicellular microorgans located in the pancreas that play a central role in whole-body energy homeostasis. Through secretion of insulin and other hormones they regulate postprandial storage and interprandial usage of energy-rich nutrients. In these clusters of hormone-secreting endocrine cells, intricate cell-cell communication is essential for proper function. Electrical coupling between the insulin-secreting beta cells through gap junctions composed of connexin36 is particularly important, as it provides the required, most important, basis for coordinated responses of the beta cell population. The increasing evidence that gap-junctional communication and its modulation are vital to well-regulated secretion of insulin has stimulated immense interest in how subpopulations of heterogeneous beta cells are functionally arranged throughout the islets and how they mediate intercellular signals. In the last decade, several novel techniques have been proposed to assess cooperation between cells in islets, including the prosperous combination of multicellular imaging and network science. In the present contribution, we review recent advances related to the application of complex network approaches to uncover the functional connectivity patterns among cells within the islets. We first provide an accessible introduction to the basic principles of network theory, enumerating the measures characterizing the intercellular interactions and quantifying the functional integration and segregation of a multicellular system. Then we describe methodological approaches to construct functional beta cell networks, point out possible pitfalls, and specify the functional implications of beta cell network examinations. We continue by highlighting the recent findings obtained through advanced multicellular imaging techniques supported by network-based analyses, giving special emphasis to the current developments in both mouse and human islets, as well as outlining challenges offered by the multilayer network formalism in exploring the collective activity of islet cell populations. Finally, we emphasize that the combination of these imaging techniques and network-based analyses does not only represent an innovative concept that can be used to describe and interpret the physiology of islets, but also provides fertile ground for delineating normal from pathological function and for quantifying the changes in islet communication networks associated with the development of diabetes mellitus.

Double transition in kinetic exchange opinion models with activation dynamics

In this work, we study a model of opinion dynamics considering activation/deactivation of agents. In other words, individuals are not static and can become inactive and drop out from the discussion. A probability [Formula: see text] governs the deactivation dynamics, whereas social interactions are ruled by kinetic exchanges, considering competitive positive/negative interactions. Inactive agents can become active due to interactions with active agents. Our analytical and numerical results show the existence of two distinct non-equilibrium phase transitions, with the occurrence of three phases, namely ordered (ferromagnetic-like), disordered (paramagnetic-like) and absorbing phases. The absorbing phase represents a collective state where all agents are inactive, i.e. they do not participate in the dynamics, inducing a frozen state. We determine the critical value [Formula: see text] above which the system is in the absorbing phase independently of the other parameters. We also verify a distinct critical behaviour for the transitions among different phases. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

Highly coordinated nationwide massive travel restrictions are central to effective mitigation and control of COVID-19 outbreaks in China

COVID-19, the disease caused by the novel coronavirus 2019, has caused grave woes across the globe since it was first reported in the epicentre of Wuhan, Hubei, China, in December 2019. The spread of COVID-19 in China has been successfully curtailed by massive travel restrictions that rendered more than 900 million people housebound for more than two months since the lockdown of Wuhan, and elsewhere, on 23 January 2020. Here, we assess the impact of China's massive lockdowns and travel restrictions reflected by the changes in mobility patterns across and within provinces, before and during the lockdown period. We calibrate movement flow between provinces with an epidemiological compartment model to quantify the effectiveness of lockdowns and reductions in disease transmission. Our analysis demonstrates that the onset and phase of local community transmission in other provinces depends on the cumulative population outflow received from the epicentre Hubei. Moreover, we show that synchronous lockdowns and consequent reduced mobility lag a certain time to elicit an actual impact on suppressing the spread. Such highly coordinated nationwide lockdowns, applied via a top-down approach along with high levels of compliance from the bottom up, are central to mitigating and controlling early-stage outbreaks and averting a massive health crisis.

Highly coordinated nationwide massive travel restrictions are central to effective mitigation and control of COVID-19 outbreaks in China

The COVID-19, the disease caused by the novel coronavirus 2019 (SARS-CoV-2), has caused graving woes across the globe since first reported in the epicenter Wuhan, Hubei, China, December 2019. The spread of COVID-19 in China has been successfully curtailed by massive travel restrictions that put more than 900 million people housebound for more than two months since the lockdown of Wuhan on 23 January 2020 when other provinces in China followed suit. Here, we assess the impact of China's massive lockdowns and travel restrictions reflected by the changes in mobility patterns before and during the lockdown period. We quantify the synchrony of mobility patterns across provinces and within provinces. Using these mobility data, we calibrate movement flow between provinces in combination with an epidemiological compartment model to quantify the effectiveness of lockdowns and reductions in disease transmission. Our analysis demonstrates that the onset and phase of local community transmission in other provinces depends on the cumulative population outflow received from the epicenter Hubei. As such, infections can propagate further into other interconnected places both near and far, thereby necessitating synchronous lockdowns. Moreover, our data-driven modeling analysis shows that lockdowns and consequently reduced mobility lag a certain time to elicit an actual impact on slowing down the spreading and ultimately putting the epidemic under check. In spite of the vastly heterogeneous demographics and epidemiological characteristics across China, mobility data shows that massive travel restrictions have been applied consistently via a top-down approach along with high levels of compliance from the bottom up.

Antivax movement and epidemic spreading in the era of social networks: Nonmonotonic effects, bistability, and network segregation

In this work, we address a multicoupled dynamics on complex networks with tunable structural segregation. Specifically, we work on a networked epidemic spreading under a vaccination campaign with agents in favor and against the vaccine. Our results show that such coupled dynamics exhibits a myriad of phenomena such as nonequilibrium transitions accompanied by bistability. Besides we observe the emergence of an intermediate optimal segregation level where the community structure enhances negative opinions over vaccination but counterintuitively hinders-rather than favoring-the global disease spreading. Thus our results hint vaccination campaigns should avoid policies that end up segregating excessively antivaccine groups so that they effectively work as echo chambers in which individuals look to confirmation without jeopardizing the safety of the whole population.

Vaccination intentions generate racial disparities in the societal persistence of COVID-19

We combined survey, mobility, and infections data in greater Boston, MA to simulate the effects of racial disparities in the inclination to become vaccinated on continued infection rates and the attainment of herd immunity. The simulation projected marked inequities, with communities of color experiencing infection rates 3 times higher than predominantly White communities and reaching herd immunity 45 days later on average. Persuasion of individuals uncertain about vaccination was crucial to preventing the worst inequities but could only narrow them so far because 1/5th of Black and Latinx individuals said that they would never vaccinate. The results point to a need for well-crafted, compassionate messaging that reaches out to those most resistant to the vaccine.

Triple contagion: a two-fears epidemic model

We present a differential equations model in which contagious disease transmission is affected by contagious fear of the disease and contagious fear of the control, in this case vaccine. The three contagions are coupled. The two fears evolve and interact in ways that shape distancing behaviour, vaccine uptake, and their relaxation. These behavioural dynamics in turn can amplify or suppress disease transmission, which feeds back to affect behaviour. The model reveals several coupled contagion mechanisms for multiple epidemic waves. Methodologically, the paper advances infectious disease modelling by including human behavioural adaptation, drawing on the neuroscience of fear learning, extinction and transmission.

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.

Coupled dynamics of behaviour and disease contagion among antagonistic groups

Disease transmission and behaviour change are both fundamentally social phenomena. Behaviour change can have profound consequences for disease transmission, and epidemic conditions can favour the more rapid adoption of behavioural innovations. We analyse a simple model of coupled behaviour change and infection in a structured population characterised by homophily and outgroup aversion. Outgroup aversion slows the rate of adoption and can lead to lower rates of adoption in the later-adopting group or even behavioural divergence between groups when outgroup aversion exceeds positive ingroup influence. When disease dynamics are coupled to the behaviour-adoption model, a wide variety of outcomes are possible. Homophily can either increase or decrease the final size of the epidemic depending on its relative strength in the two groups and on R0 for the infection. For example, if the first group is homophilous and the second is not, the second group will have a larger epidemic. Homophily and outgroup aversion can also produce dynamics suggestive of a 'second wave' in the first group that follows the peak of the epidemic in the second group. Our simple model reveals dynamics that are suggestive of the processes currently observed under pandemic conditions in culturally and/or politically polarised populations such as the USA.

Endogenous social distancing and its underappreciated impact on the epidemic curve

Social distancing is an effective strategy to mitigate the impact of infectious diseases. If sick or healthy, or both, predominantly socially distance, the epidemic curve flattens. Contact reductions may occur for different reasons during a pandemic including health-related mobility loss (severity of symptoms), duty of care for a member of a high-risk group, and forced quarantine. Other decisions to reduce contacts are of a more voluntary nature. In particular, sick people reduce contacts consciously to avoid infecting others, and healthy individuals reduce contacts in order to stay healthy. We use game theory to formalize the interaction of voluntary social distancing in a partially infected population. This improves the behavioral micro-foundations of epidemiological models, and predicts differential social distancing rates dependent on health status. The model's key predictions in terms of comparative statics are derived, which concern changes and interactions between social distancing behaviors of sick and healthy. We fit the relevant parameters for endogenous social distancing to an epidemiological model with evidence from influenza waves to provide a benchmark for an epidemic curve with endogenous social distancing. Our results suggest that spreading similar in peak and case numbers to what partial immobilization of the population produces, yet quicker to pass, could occur endogenously. Going forward, eventual social distancing orders and lockdown policies should be benchmarked against more realistic epidemic models that take endogenous social distancing into account, rather than be driven by static, and therefore unrealistic, estimates for social mixing that intrinsically overestimate spreading.

Community-Level Sports Group Participation and Health Behaviors Among Older Non-Participants in a Sports Group: A Multilevel Cross-Sectional Study

This study validates the relationship between community-level sports group participation and the frequency of leaving the house and transtheoretical model stages of behavior change for exercise among older individuals who did not participate in a sports group. We used cross-sectional data from the 2016 Japan Gerontological Evaluation Study. The proportion of sports group participants at the community level was calculated using the data from 157,233 older individuals living in 1000 communities. We conducted a multilevel regression analysis to examine the relationship between the proportion of sports group participants and the frequency of leaving the house (1 day/week or less) and the transtheoretical model stages of behavior change for exercise. A statistically significant relationship was observed between a high prevalence of sports group participation and lower risk of homeboundness (odds ratio: 0.94) and high transtheoretical model stages (partial regression coefficient: 0.06) as estimated by 10 percentage points of participation proportion. Older individuals, even those not participating in a sports group, living in a community with a high prevalence of sports group participation are less likely to be homebound; they are highly interested and have numerous opportunities to engage in exercise.

Oscillatory dynamics in the dilemma of social distancing

Social distancing as one of the main non-pharmaceutical interventions can help slow down the spread of diseases, like in the COVID-19 pandemic. Effective social distancing, unless enforced as drastic lockdowns and mandatory cordon sanitaire, requires consistent strict collective adherence. However, it remains unknown what the determinants for the resultant compliance of social distancing and their impact on disease mitigation are. Here, we incorporate into the epidemiological process with an evolutionary game theory model that governs the evolution of social distancing behaviour. In our model, we assume an individual acts in their best interest and their decisions are driven by adaptive social learning of the real-time risk of infection in comparison with the cost of social distancing. We find interesting oscillatory dynamics of social distancing accompanied with waves of infection. Moreover, the oscillatory dynamics are dampened with a non-trivial dependence on model parameters governing decision-makings and gradually cease when the cumulative infections exceed the herd immunity. Compared to the scenario without social distancing, we quantify the degree to which social distancing mitigates the epidemic and its dependence on individuals’ responsiveness and rationality in their behaviour changes. Our work offers new insights into leveraging human behaviour in support of pandemic response.

Best response dynamics improve sustainability and equity outcomes in common-pool resources problems, compared to imitation dynamics

Shared resource extraction among profit-seeking individuals involves a tension between individual benefit and the collective well-being represented by the persistence of the resource. Many game theoretic models explore this scenario, but these models tend to assume either best response dynamics (where individuals instantly switch to better paying strategies) or imitation dynamics (where individuals copy successful strategies from neighbours), and do not systematically compare predictions under the two assumptions. Here we propose an iterated game on a social network with payoff functions that depend on the state of the resource. Agents harvest the resource, and the strategy composition of the population evolves until an equilibrium is reached. The system is then repeatedly perturbed and allowed to re-equilibrate. We compare model predictions under best response and imitation dynamics. Compared to imitation dynamics, best response dynamics increase sustainability of the system, the persistence of cooperation while decreasing inequality and debt corresponding to the Gini index in the agents' cumulative payoffs. Additionally, for best response dynamics, the number of strategy switches before equilibrium fits a power-law distribution under a subset of the parameter space, suggesting the system is in a state of self-organized criticality. We find little variation in most mean results over different network topologies; however, there is significant variation in the distributions of the raw data, equality of payoff, clustering of like strategies and power-law fit. We suggest the primary mechanisms driving the difference in sustainability between the two strategy update rules to be the clustering of like strategies as well as the time delay imposed by an imitation processes. Given the strikingly different outcomes for best response versus imitation dynamics for common-pool resource systems, our results suggest that modellers should choose strategy update rules that best represent decision-making in their study systems.

Collective communication and behaviour in response to uncertain 'Danger' in network experiments

In emergencies, social coordination is especially challenging. People connected with each other may respond better or worse to an uncertain danger than isolated individuals. We performed experiments involving a novel scenario simulating an unpredictable situation faced by a group in which 2480 subjects in 108 groups had to both communicate information and decide whether to ‘evacuate’. We manipulated the permissible sorts of interpersonal communication and varied group topology and size. Compared to groups of isolated individuals, we find that communication networks suppress necessary evacuations because of the spontaneous and diffuse emergence of false reassurance; yet, communication networks also restrain unnecessary evacuations in situations without disasters. At the individual level, subjects have thresholds for responding to social information that are sensitive to the negativity, but not the actual accuracy, of the signals being transmitted. Social networks can function poorly as pathways for inconvenient truths that people would rather ignore.

Fuel shortages during hurricanes: Epidemiological modeling and optimal control

Hurricanes are powerful agents of destruction with significant socioeconomic impacts. A persistent problem due to the large-scale evacuations during hurricanes in the southeastern United States is the fuel shortages during the evacuation. Computational models can aid in emergency preparedness and help mitigate the impacts of hurricanes. In this paper, we model the hurricane fuel shortages using the SIR epidemic model. We utilize the crowd-sourced data corresponding to Hurricane Irma and Florence to parametrize the model. An estimation technique based on Unscented Kalman filter (UKF) is employed to evaluate the SIR dynamic parameters. Finally, an optimal control approach for refueling based on a vaccination analogue is presented to effectively reduce the fuel shortages under a resource constraint. We find the basic reproduction number corresponding to fuel shortages in Miami during Hurricane Irma to be 3.98. Using the control model we estimated the level of intervention needed to mitigate the fuel-shortage epidemic. For example, our results indicate that for Naples- Fort Myers affected by Hurricane Irma, a per capita refueling rate of 0.1 for 2.2 days would have reduced the peak fuel shortage from 55% to 48% and a refueling rate of 0.75 for half a day before landfall would have reduced to 37%.

Macroscopic patterns of interacting contagions are indistinguishable from social reinforcement

From fake news to innovative technologies, many contagions spread as complex contagions via a process of social reinforcement, where multiple exposures are distinct from prolonged exposure to a single source.1 Contrarily, biological agents such as Ebola or measles are typically thought to spread as simple contagions.2 Here, we demonstrate that these different spreading mechanisms can have indistinguishable population-level dynamics once multiple contagions interact. In the social context, our results highlight the challenge of identifying and quantifying spreading mechanisms, such as social reinforcement,3 in a world where an innumerable amount of ideas, memes and behaviors interact. In the biological context, this parallel allows the use of complex contagions to effectively quantify the non-trivial interactions of infectious diseases.

Local risk perception enhances epidemic control

As infectious disease outbreaks emerge, public health agencies often enact vaccination and social distancing measures to slow transmission. Their success depends on not only strategies and resources, but also public adherence. Individual willingness to take precautions may be influenced by global factors, such as news media, or local factors, such as infected family members or friends. Here, we compare three modes of epidemiological decision-making in the midst of a growing outbreak using network-based mathematical models that capture plausible heterogeneity in human contact patterns. Individuals decide whether to adopt a recommended intervention based on overall disease prevalence, the proportion of social contacts infected, or the number of social contacts infected. While all strategies can substantially mitigate transmission, vaccinating (or self isolating) based on the number of infected acquaintances is expected to prevent the most infections while requiring the fewest intervention resources. Unlike the other strategies, it has a substantial herd effect, providing indirect protection to a large fraction of the population.

The impact of rare but severe vaccine adverse events on behaviour-disease dynamics: a network model

The propagation of rumours about rare but severe adverse vaccination or infection events through social networks can strongly impact vaccination uptake. Here we model a coupled behaviour-disease system where individual risk perception regarding vaccines and infection are shaped by their personal experiences and the experiences of others. Information about vaccines and infection either propagates through the network or becomes available through globally available sources. Dynamics are studied on a range of network types. Individuals choose to vaccinate according to their personal perception of risk and information about infection prevalence. We study events ranging from common and mild, to severe and rare. We find that vaccine and infection adverse events have asymmetric impacts. Vaccine (but not infection) adverse events may significantly prolong the tail of an outbreak. Similarly, introducing a small risk of a vaccine adverse event may cause a steep decline in vaccine coverage, especially on scale-free networks. Global dissemination of information about infection prevalence boosts vaccine coverage more than local dissemination. Taken together, these findings highlight the dangers associated with vaccine rumour propagation through scale-free networks such as those exhibited by online social media, as well as the benefits of disseminating public health information through mass media.

Imperfect vaccine and hysteresis

Addressing vaccine compliance problems is of particular relevance and significance to public health. Despite resurgence of vaccine-preventable diseases and public awareness of vaccine importance, why is it so challenging to boost population vaccination coverage to desired levels especially in the wake of declining vaccine uptake? To understand this puzzling phenomenon, here we study how social imitation dynamics of vaccination can be impacted by the presence of imperfect vaccine, which only confers partial protection against the disease. Besides weighing the perceived cost of vaccination with the risk of infection, the effectiveness of vaccination is also an important factor driving vaccination decisions. We discover that there can exist multiple stable vaccination equilibria if vaccine efficacy is below a certain threshold. Furthermore, our bifurcation analysis reveals the occurrence of hysteresis loops of vaccination rate with respect to changes in the perceived vaccination cost as well as in the vaccination effectiveness. Moreover, we find that hysteresis is more likely to arise in spatial populations than in well-mixed populations, even for parameter choices that do not allow for bifurcation in the latter. Our work shows that hysteresis can appear as an unprecedented roadblock for the recovery of vaccination uptake, thereby helping explain the persistence of vaccine compliance problem.

The Radiation-Transmission-Reception (RTR) model of propagation: Implications for the effectiveness of network interventions

Propagating phenomena in networks have received significant amount of attention within various domains, ranging from contagion in epidemiology, to diffusion of innovations and social influence on behavior and communication. Often these studies attempt to model propagation processes in networks to create interventions that steer propagation dynamics towards desired or away from undesired outcomes. Traditionally, studies have used relatively simple models of the propagation mechanism. In most propagation models this mechanism is described as a monolithic process and a single parameter for the infection rate. Such a description of the propagation mechanism is a severe simplification of mechanisms described in various theoretical exchange theories and phenomena found in real world settings, and largely fails to capture the nuances present in such descriptions. Recent work has suggested that such a simplification may not be sufficient to explain observed propagation dynamics, as nuances of the mechanism of propagation can have a severe impact on its dynamics. This suggests a better understanding of the role of the propagation mechanism is desired. In this paper we put forward a novel framework and model for propagation, the RTR framework. This framework, based on communication theory, decomposes the propagation mechanism into three sub-processes; Radiation, Transmission and Reception (RTR). We show that the RTR framework provides a more detailed way for specifying and conceptually thinking about the process of propagation, aligns better with existing real world interventions, and allows for gaining new insights into effective intervention strategies. By decomposing the propagation mechanism, we show that the specifications of this mechanism can have significant impact on the effectiveness of network interventions. We show that for the same composite single-parameter specification, different decompositions in Radiation, Transmission and Reception yield very different effectiveness estimates for the same network intervention, from 30% less effective to 70% more effective. We find that the appropriate choice for intervention depends strongly on the decomposition of the propagation mechanism. Our findings highlight that a correct decomposition of the mechanism is a prerequisite for developing effective network intervention strategies, and that the use of monolithic models, which oversimplify the mechanism, can be problematic of supporting decisions related to network interventions. In contrast, by allowing more detailed specification of the propagation mechanism and enabling this mechanism to be linked to existing interventions, the RTR framework provides a valuable tool for those designing interventions and implementing interventions strategies.

Complex contagion leads to complex dynamics in models coupling behaviour and disease

Models coupling behaviour and disease as two unique but interacting contagions have existed since the mid 2000s. In these coupled contagion models, behaviour is typically treated as a 'simple contagion'. However, the means of behaviour spread may in fact be more complex. We develop a family of disease-behaviour coupled contagion compartmental models in order to examine the effect of behavioural contagion type on disease-behaviour dynamics. Coupled contagion models treating behaviour as a simple contagion and a complex contagion are investigated, showing that behavioural contagion type can have a significant impact on dynamics. We find that a simple contagion behaviour leads to simple dynamics, while a complex contagion behaviour supports complex dynamics with the possibility of bistability and periodic orbits.

Exposure, hazard, and survival analysis of diffusion on social networks

Sociologists, economists, epidemiologists, and others recognize the importance of social networks in the diffusion of ideas and behaviors through human societies. To measure the flow of information on real-world networks, researchers often conduct comprehensive sociometric mapping of social links between individuals and then follow the spread of an "innovation" from reports of adoption or change in behavior over time. The innovation is introduced to a small number of individuals who may also be encouraged to spread it to their network contacts. In conjunction with the known social network, the pattern of adoptions gives researchers insight into the spread of the innovation in the population and factors associated with successful diffusion. Researchers have used widely varying statistical tools to estimate these quantities, and there is disagreement about how to analyze diffusion on fully observed networks. Here, we describe a framework for measuring features of diffusion processes on social networks using the epidemiological concepts of exposure and competing risks. Given a realization of a diffusion process on a fully observed network, we show that classical survival regression models can be adapted to estimate the rate of diffusion, and actor/edge attributes associated with successful transmission or adoption, while accounting for the topology of the social network. We illustrate these tools by applying them to a randomized network intervention trial conducted in Honduras to estimate the rate of adoption of 2 health-related interventions-multivitamins and chlorine bleach for water purification-and determine factors associated with successful social transmission.

Fast and accurate detection of spread source in large complex networks

Spread over complex networks is a ubiquitous process with increasingly wide applications. Locating spread sources is often important, e.g. finding the patient one in epidemics, or source of rumor spreading in social network. Pinto, Thiran and Vetterli introduced an algorithm (PTVA) to solve the important case of this problem in which a limited set of nodes act as observers and report times at which the spread reached them. PTVA uses all observers to find a solution. Here we propose a new approach in which observers with low quality information (i.e. with large spread encounter times) are ignored and potential sources are selected based on the likelihood gradient from high quality observers. The original complexity of PTVA is O(N α ), where α ∈ (3,4) depends on the network topology and number of observers (N denotes the number of nodes in the network). Our Gradient Maximum Likelihood Algorithm (GMLA) reduces this complexity to O (N2log (N)). Extensive numerical tests performed on synthetic networks and real Gnutella network with limitation that id's of spreaders are unknown to observers demonstrate that for scale-free networks with such limitation GMLA yields higher quality localization results than PTVA does.