本研究将疫苗接种建模为网络上的进化博弈，结合 SIR 模型分析网络拓扑与相对成本对进化稳定接种水平的影响，发现网络异质性显著改变接种动态。
摘要：
疫苗接种是预防疾病的重要工具。疫苗接种对人群中的每个成员通常是自愿的，疫苗接种决策受个体风险感知和人群内部接触结构的影响。在本研究中，我们将疫苗接种 uptake 建模为一个进化博弈，其中个体权衡来自疫苗接种和感染的感知发病率风险。我们使用一个基于网络结构的 SIR 模型来纳入流行病学动态，使我们能够确定任何给定网络拓扑的进化稳定疫苗接种水平。我们的分析表明，疫苗接种覆盖率因网络结构以及疫苗接种的相对成本（疫苗发病率风险与感染发病率风险之比）而异。随着该成本增加，疫苗接种 uptake 普遍下降，当成本高时，导致非接种者策略占主导。我们发现，当该成本低时，具有低至中度度变异性的网络具有相对较低的进化稳定疫苗接种水平，因为在这样的人群中，需要较低的疫苗接种水平即可达到与具有高度变异性的更异质网络相当的疾病流行水平，因此后者在较低的相对成本下显示出更高的疫苗接种水平。然而，对于异质网络，随着成本上升，疫苗接种水平下降得更快，最终降至低于更同质网络的水平。我们的发现与先前关于结构化人群疫苗接种阈值的研究一致，并突显了网络异质性如何影响疫苗接种动态。
英文摘要：
Vaccinations are an important tool in the prevention of disease. Vaccinations are generally voluntary for each member of a population and vaccination decisions are influenced by individual risk perceptions and contact structures within populations. In this study, we model vaccination uptake as an evolutionary game where individuals weigh perceived morbidity risks from both vaccination and infection. We incorporate epidemiological dynamics using an SIR model structured on networks, allowing us to determine the evolutionarily stable vaccination level for any given network topology. Our analysis shows that vaccination coverage varies across networks depending on their structure and the relative cost of vaccination (the ratio of vaccine morbidity risk to infection morbidity risk). As this cost increases, vaccination uptake decreases universally, leading to a dominant non-vaccinator strategy when the cost is high. We find that networks with low to moderate degree variability have a relatively low evolutionarily stable vaccination level when this cost is low, as in such populations lower vaccination levels are necessary to achieve equivalent levels of disease prevalence to more heterogeneous networks with high degree variability, which thus show higher vaccination levels at lower relative costs. However, for heterogeneous networks, vaccination levels decline faster as costs rise, eventually falling below the level for the more homogeneous networks. Our findings align with previous studies on vaccination thresholds in structured populations and highlight how network heterogeneity influences vaccination dynamics.
We propose a model describing the synergetic feedback between word-of-mouth (WoM) and epidemic dynamics controlled by voluntary vaccination. We combine a game-theoretic model for the spread of WoM and a compartmental model describing $SIR$ disease dynamics in the presence of a program of voluntary vaccination. We evaluate and compare two scenarios, depending on what WoM disseminates: (1) vaccine advertising, which may occur whether or not an epidemic is ongoing and (2) epidemic status, notably disease prevalence. Understanding the synergy between the two strategies could be particularly import…
Voluntary vaccination is effective to prevent infectious diseases from spreading. Both vaccination behavior and cognition of the vaccination risk play important roles in individual vaccination decision making. However, it is not clear how the co-evolution of the two shapes the population-wide vaccination behavior. We establish a coupled dynamics of epidemic, vaccination behavior and perceived vaccination risk with three different time scales. We assume that the increase of vaccination level inhibits the rise of perceived vaccination risk, and the increase of perceived vaccination risk inhibits…
Preventing infectious disease like flu from spreading to large communities is one of the most important issues for humans. One effective strategy is voluntary vaccination, however, there is always the temptation for people refusing to be vaccinated because once herd immunity is achieved, infection risk is greatly reduced. In this paper, we study the effect of social impact on the vaccination behavior resulting in preventing infectious disease in networks. The evolutionary simulation results show that the social impact has both positive and negative effects on the vaccination behavior. Especial…
Opposition to vaccination has long been a non-negligible public health phenomenon resulted from people's varied perceptions toward vaccination (e.g., vaccine-phobia). This paper investigates the voluntary vaccination behavior of a heterogeneous population during an epidemic outbreak, where each individual makes its own vaccination decision to minimize its expected disutility from both vaccine-phobia and the risk of infection. Such a problem is known as a vaccination game, as people's vaccination decisions not only affect their own disutilities but those of all others through probabilistic dise…
The impact of information dissemination on epidemic control is essentially subject to individual behaviors. Unlike information-driven behaviors, vaccination is determined by many cost-related factors, whose correlation with the information dissemination should be better understood. To this end, we propose an evolutionary vaccination game model in multiplex networks by integrating an information-epidemic spreading process into the vaccination dynamics, and explore how information dissemination influences vaccination. The spreading process is described by a two-layer coupled susceptible-alert-in…
Vaccination is crucial for the control of epidemics. Yet it is a social dilemma since non-vaccinators can benefit from the herd immunity created by the vaccinators. Thus the optimum vaccination level is not reached via voluntary vaccination at times. Intensive studies incorporate social networks to study vaccination behavior, and it is shown that vaccination can be promoted on some networks. The underlying network, however, is often assumed to be static, neglecting the dynamical nature of social networks. We investigate the vaccination behavior on dynamical social networks using both simulatio…
Since the recent introduction of several viable vaccines for SARS-CoV-2, vaccination uptake has become the key factor that will determine our success in containing the COVID-19 pandemic. We argue that game theory and social network models should be used to guide decisions pertaining to vaccination programmes for the best possible results. In the months following the introduction of vaccines, their availability and the human resources needed to run the vaccination programmes have been scarce in many countries. Vaccine hesitancy is also being encountered from some sections of the general public.…
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 ou…
The resurgence of measles is largely attributed to the decline in vaccine adoption and the increase in mobility. Although the vaccine for measles is readily available and highly successful, its current adoption is not adequate to prevent epidemics. Vaccine adoption is directly affected by individual vaccination decisions, and has a complex interplay with the spatial spread of disease shaped by an underlying mobility (travelling) network. In this paper, we model the travelling connectivity as a scale-free network, and investigate dependencies between the network's assortativity and the resultan…
The vaccination game is a social dilemma that refers to the conundrum individuals face (to get immunized or not) when the population is exposed to an infectious disease. The model has recently gained much traction due to the COVID-19 pandemic since the public perception of vaccines plays a significant role in disease dynamics. This paper studies the vaccination game in the thermodynamic limit with an analytical method derived from the 1D Ising model called Nash equilibrium mapping. The individual dilemma regarding Vaccination comes from an internal conflict wherein one tries to balance the per…
We present a series of SIR-network models, extended with a game-theoretic treatment of imitation dynamics which result from regular population mobility across residential and work areas and the ensuing interactions. Each considered SIR-network model captures a class of vaccination behaviours influenced by epidemic characteristics, interaction topology, and imitation dynamics. Our focus is the eventual vaccination coverage, produced under voluntary vaccination schemes, in response to these varying factors. Using the next generation matrix method, we analytically derive and compare expressions f…
Vaccination is an effective way to prevent and control the occurrence and epidemic of infectious diseases. However, many factors influence whether the residents decide to get vaccinated or not, such as the efficacy and side effects while individuals hope to obtain immunity through vaccination. In this paper, the public attitude toward vaccination is investigated, especially how it is influenced by the public estimation of vaccines efficacy and reliance on their neighbors' vaccination behavior. We find that improving people's trust in the vaccination greatly benefits increasing the vaccination …
This paper is concerned with the analysis of vaccination strategies in a stochastic SIR (susceptible $\to$ infected $\to$ removed) model for the spread of an epidemic amongst a population of individuals with a random network of social contacts that is also partitioned into households. Under various vaccine action models, we consider both household-based vaccination schemes, in which the way in which individuals are chosen for vaccination depends on the size of the households in which they reside, and acquaintance vaccination, which targets individuals of high degree in the social network. For …
In this work we analyze the evolution of voluntary vaccination in networked populations by entangling the spreading dynamics of an influenza-like disease with an evolutionary framework taking place at the end of each influenza season so that individuals take or not the vaccine upon their previous experience. Our framework thus put in competition two well-known dynamical properties of scale-free networks: the fast propagation of diseases and the promotion of cooperative behaviors. Our results show that when vaccine is perfect scale-free networks enhance the vaccination behavior with respect to …
The slogan "nobody is safe until everybody is safe" is a dictum to raise awareness that in an interconnected world, pandemics such as COVID-19, require a global approach. Motivated by the ongoing COVID-19 pandemic, we model here the spread of a virus in interconnected communities and explore different vaccination scenarios, assuming that the efficacy of the vaccination wanes over time. We start with susceptible populations and consider a susceptible-vaccinated-infected-recovered model with unvaccinated ("Bronze"), moderately vaccinated ("Silver") and very well vaccinated ("Gold") communities, …
The effectiveness of vaccination highly depends on the choice of individuals to vaccinate, even if the same number of individuals are vaccinated. Vaccinating individuals with high centrality measures such as betweenness centrality (BC) and eigenvector centrality (EC) are effective in containing epidemics. However, in many real-world cases, each individual has distinct epidemic characteristics such as contagion, recovery, fatality rate, efficacy, and probability of severe reaction to a vaccine. Moreover, the relative effectiveness of vaccination strategies depends on the number of available vac…
The risk for severe illness and mortality from COVID-19 significantly increases with age. As a result, age-stratified modeling for COVID-19 dynamics is the key to study how to reduce hospitalizations and mortality from COVID-19. By taking advantage of network theory, we develop an age-stratified epidemic model for COVID-19 in complex contact networks. Specifically, we present an extension of standard SEIR (susceptible-exposed-infectious-removed) compartmental model, called age-stratified SEAHIR (susceptible-exposedasymptomatic-hospitalized-infectious-removed) model, to capture the spread of CO…
Infectious diseases are still a major global burden for modern society causing 13 million deaths annually. One way to reduce the morbidity and mortality rates from infectious diseases is through preventative or targeted vaccinations. Current vaccination strategies, however, rely on the highly specific individual contact information that is difficult and costly to obtain, in order to identify influential spreading individuals. Current approaches also focus only on direct contacts between individuals for spreading, and disregard indirect transmission where a pathogen can spread between one infec…
We develop a model of infection spread that takes into account the existence of a vulnerable group as well as the variability of the social relations of individuals. We develop a compartmentalized power-law model, with power-law connections between the vulnerable and the general population, considering these connections as well as the connections among the vulnerable as parameters that we vary in our tests. We use the model to study a number of vaccination strategies under two hypotheses: first, we assume a limited availability of vaccine but an infinite vaccination capacity, so that all the a…
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 diseas…
Considering the global pandemic of coronavirus disease 2019 (COVID-19), around the world several vaccines are being developed. Till now, these vaccines are the most effective way to reduce the high burden on the global health infrastructure. However, the public acceptance towards vaccination is a crucial and pressing problem for health authorities. This study has been designed to determine the parameters affecting the decisions of common individuals towards COVID-19 vaccine. In our study, using the platforms of compartmental model and network simulation, we categorize people and observe their …
Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barabási-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effect…
We use mobile device data to construct empirical interpersonal physical contact networks in the city of Portland, Oregon, both before and after social distancing measures were enacted during the COVID-19 pandemic. These networks reveal how social distancing measures and the public's reaction to the incipient pandemic affected the connectivity patterns within the city. We find that as the pandemic developed there was a substantial decrease in the number of individuals with many contacts. We further study the impact of these different network topologies on the spread of COVID-19 by simulating an…
Network-based interventions against epidemic spread are most powerful when the full network structure is known. However, in practice, resource constraints require decisions to be made based on partial network information. We investigated how the accuracy of network data available at individual and village levels affected network-based vaccination effectiveness. We simulated a Susceptible-Infected-Recovered process on empirical social networks from 75 villages. First, we used regression to predict the percentage of individuals ever infected based on village-level network. Second, we simulated v…
In this work we propose and investigate a new strategy of vaccination, which we call "dynamic vaccination". In our model, susceptible people become aware that one or more of their contacts are infected, and thereby get vaccinated with probability $ω$, before having physical contact with any infected patient. Then, the non-vaccinated individuals will be infected with probability $β$. We apply the strategy to the SIR epidemic model in a multiplex network composed by two networks, where a fraction $q$ of the nodes acts in both networks. We map this model of dynamic vaccination into bond percolati…
Often, vaccination programs are carried out based on self-interest rather than being mandatory. Owing to the perceptions about risks associated with vaccines and the `herd immunity' effect, it may provide suboptimal vaccination coverage for the population as a whole. In this case, some subsidy policies may be offered by the government to promote vaccination coverage. But, not all subsidy policies are effective in controlling the transmission of infectious diseases. We address the question of which subsidy policy is best, and how to appropriately distribute the limited subsidies to maximize vac…
We study the effect of vaccination on robustness of networks against propagating attacks that obey the susceptible-infected-removed model.By extending the generating function formalism developed by Newman (2005), we analytically determine the robustness of networks that depends on the vaccination parameters. We consider the random defense where nodes are vaccinated randomly and the degree-based defense where hubs are preferentially vaccinated. We show that when vaccines are inefficient, the random graph is more robust against propagating attacks than the scale-free network. When vaccines are r…
Vaccination strategy is crucial in fighting against the COVID-19 pandemic. Since the supply is limited, contact network-based interventions can be most powerful to set an optimal strategy by identifying high-risk individuals or communities. However, due to the high dimension, only partial and noisy network information can be available in practice, especially for dynamical systems where the contact networks are highly time-variant. Furthermore, numerous mutations of SARS-CoV-2 impact considerably the current infectious probability, requiring real-time network updating algorithms. In this study,…
We study the impact of vaccination on the risk of epidemics spreading through structured networks using the cavity method of statistical physics. We relax the assumption that vaccination prevents all transmission of a disease used in previous studies, such that vaccinated nodes have a small probability of transmission. To do so we extend the cavity method to study networks where nodes have heterogeneous transmissibility. We find that vaccination with partial transmission still provides herd immunity and show how the herd immunity threshold depends upon the assortativity between nodes of differ…
Coronavirus disease (COVID-19), which was caused by SARS-CoV-2, has become a global public health concern. A great proportion of the world needs to be vaccinated in order to stop the rapid spread of the disease. In addition to prioritising vulnerable sections of the population to receive the vaccine, an ideal degree-based vaccination strategy uses fine-grained contact networks to prioritise vaccine recipients. This strategy is costly and impractical due to the enormous amount of specific contact information needed. It also does not capture indirect famine or aerosol-based transmission. We rece…
Miss-information is usually adjusted to fit distinct narratives and can propagate rapidly through communities of interest, which work as echo chambers, cause reinforcement and foster confirmation bias. False beliefs, once adopted, are rarely corrected. Amidst the COVID-19 crisis, pandemic-deniers and people who oppose wearing face masks or quarantines have already been a substantial aspect of the development of the pandemic. With a potential vaccine for COVID-19, different anti-vaccine narratives will be created and, likely, adopted by large population groups, with critical consequences. Here,…
In the face of serious infectious diseases, governments endeavour to implement containment measures such as public vaccination at a macroscopic level. Meanwhile, individuals tend to protect themselves by avoiding contacts with infections at a microscopic level. However, a comprehensive understanding of how such combined strategy influences epidemic dynamics is still lacking. We study a susceptible-infected-susceptible epidemic model with imperfect vaccination on dynamic contact networks, where the macroscopic intervention is represented by random vaccination of the population and the microscop…
Vaccination and outbreak monitoring are essential tools for preventing and minimizing outbreaks of infectious diseases. Targeted strategies, where the individuals most important for monitoring or preventing outbreaks are selected for intervention, offer a possibility to significantly improve these measures. Although targeted strategies carry a strong potential, identifying optimal target groups remains a challenge. Here we consider the problem of identifying target groups based on digital communication networks (telecommunication, online social media) in order to predict and contain an infecti…
We propose a multi-layer network model for the spread of COVID-19 that accounts for interactions within the family, between schoolmates, and casual contacts in the population. We utilize the proposed model-calibrated on epidemiological and demographic data-to investigate current questions concerning the implementation of non-pharmaceutical interventions (NPIs) during the vaccination campaign. Specifically, we consider scenarios in which the most fragile population has already received the vaccine, and we focus our analysis on the role of schools as drivers of the contagions and on the implemen…
Empirical data on contacts between individuals in social contexts play an important role in providing information for models describing human behavior and how epidemics spread in populations. Here, we analyze data on face-to-face contacts collected in an office building. The statistical properties of contacts are similar to other social situations, but important differences are observed in the contact network structure. In particular, the contact network is strongly shaped by the organization of the offices in departments, which has consequences in the design of accurate agent-based models of …
Network-based epidemic models have been extensively employed to understand the spread of infectious diseases, but have generally overlooked the fact that most realistic networks are dynamical rather than static. In this paper, we study a susceptible-infected-susceptible epidemic model with vaccination in a dynamical contact network of moving individuals, where we regard mobile individuals as random walkers that are allowed to perform long-range jumps. Different from previous studies of epidemics in a random walk network with a constant interaction radius, we consider the scenario where the ind…
We consider the problem of controlling the propagation of an epidemic outbreak in an arbitrary contact network by distributing vaccination resources throughout the network. We analyze a networked version of the Susceptible-Infected-Susceptible (SIS) epidemic model when individuals in the network present different levels of susceptibility to the epidemic. In this context, controlling the spread of an epidemic outbreak can be written as a spectral condition involving the eigenvalues of a matrix that depends on the network structure and the parameters of the model. We study the problem of finding…
The success of a vaccination program is crucially dependent on its adoption by a critical fraction of the population, as the resulting herd immunity prevents future outbreaks of an epidemic. However, the effectiveness of a campaign can engender its own undoing if individuals choose to not get vaccinated in the belief that they are protected by herd immunity. Although this may appear to be an optimal decision, based on a rational appraisal of cost and benefits to the individual, it exposes the population to subsequent outbreaks. We investigate if voluntary vaccination can emerge in a an integra…
Returning universities to full on-campus operations while the COVID-19 pandemic is ongoing has been a controversial discussion in many countries. The risk of large outbreaks in dense course settings is contrasted by the benefits of in-person teaching. Transmission risk depends on a range of parameters, such as vaccination coverage and efficacy, number of contacts and adoption of non-pharmaceutical intervention measures (NPIs). Due to the generalised academic freedom in Europe, many universities are asked to autonomously decide on and implement intervention measures and regulate on-campus opera…
We study the changes of opinions about vaccination together with the evolution of a disease. In our model we consider a multiplex network consisting of two layers. One of the layers corresponds to a social network where people share their opinions and influence others opinions. The social model that rules the dynamic is the M-model, which takes into account two different processes that occurs in a society: persuasion and compromise. This two processes are related through a parameter $r$, $r<1$ describes a moderate and committed society, for $r>1$ the society tends to have extremist opinions, w…
Recent Covid-19 pandemic has demonstrated the need of efficient epidemic outbreak management. We study the optimal control problem of minimizing the fraction of infected population by applying vaccination and treatment control strategies, while at the same time minimizing the cost of implementing them. We model the epidemic using the degree based Susceptible-Infected-Recovered (SIR) compartmental model. We study the impact of varying network topologies on the optimal epidemic management strategies and present results for the Erdos-Renyi, scale free, and real world networks. For efficient compu…
Vaccination rates are decreasing in many areas of the world, and outbreaks of preventable diseases tend to follow in areas with particular low rates. Much research has been devoted to improving our understanding of the motivations behind vaccination decisions and the effects of various types of information offered to skeptics, no large-scale study of the structure of online vaccination discourse have been conducted. Here, we offer an approach to quantitatively study the vaccine discourse in an online system, exemplified by Twitter. We use train a deep neural network to predict tweet vaccine se…
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include Internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, citation networks, etc. The research of complex networks has attracted many scientists' attention. Physicists have shown that these networks exhibit some surprising characters, such as high clustering coefficient, small diameter, and the absence of the thresholds of percolation. Scientists in mathematical epidemiology discovered that the threshold of infectious disease disappears on contact n…
