In this work, we study an epidemic model with vaccination coupled with opinion dynamics in a dynamic network. The network structure evolves as agents with differing opinions disconnect from one another and connect with agents that share similar opinions about vaccination. We consider a SIS-like model with an extra vaccinated state. Agents can have continuous opinions and every time an agent disconnects from a neighbor, they connect to a new neighbor. We have observed the emergence of network homophily and, in certain cases, the complete fragmentation of the network. Our Monte Carlo simulations also show first-order phase transitions with metastable states. An increase in the probability of rewiring yields a dual effect, namely: (a) in the short term, it has the potential to intensify the epidemic peak; (b) in the long term, it can diminish the rate of infection. This transient increase in the epidemic peak is attributed to the fragmentation of the network into smaller, disconnected sub-networks. Therefore, our results suggest that rewiring is optimal when it is as high as possible but before the network starts breaking apart.
In this article we develop a highly integrated effective degree approach to modeling epidemic and awareness spreading processes on multiplex networks coupled with awareness-dependent adaptive rewiring. This approach keeps track of the number of nearest neighbors in each state of an individual; consequently, it allows for the integration of changes in local contacts into the multiplex network model. We derive a formula for the threshold condition of contagion outbreak; also, we provide a lower bound for the threshold parameter to indicate the effect of adaptive rewiring. The threshold analysis …
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…
The effects of local and global connectivity on the spread of synergistic susceptible-infected-removed epidemics were studied in lattice models with infinite- and finite-range rewiring (small-world and small-world-like models). Several effects were found numerically and supported analytically within a simple model: (i) rewiring enhanced resilience to epidemics with strong constructive synergy on networks with high local connectivity; (ii) rewiring enhanced spread of epidemics with destructive or weak constructive synergy on networks with arbitrary local connectivity; (iii) rewiring enhanced sp…
A model for epidemic spreading on rewiring networks is introduced and analyzed for the case of scale free steady state networks. It is found that contrary to what one would have naively expected, the rewiring process typically tends to suppress epidemic spreading. In particular it is found that as in static networks, rewiring networks with degree distribution exponent $γ>3$ exhibit a threshold in the infection rate below which epidemics die out in the steady state. However the threshold is higher in the rewiring case. For $2<γ\leq 3$ no such threshold exists, but for small infection rate the s…
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…
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…
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…
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…
While understanding of periodic recurrent waves of Covid-19 epidemics would aid to combat the pandemics, quantitative analysis of data over a two years period from the outbreak, is lacking. The complexity of Covid-19 recurrent waves is related with the concurrent role of i) the containment measures enforced to mitigate the epidemics spreading ii) the rate of viral gene mutations, and iii) the variable immune response of the host implemented by vaccination. This work focuses on the effect of massive vaccination and gene variants on the recurrent waves in a representative case of countries enfor…
This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate $ω$ (and reconnect to non-infectious individuals with probability $α$ or else simply drop the edge if $α=0$), so-called preventive rewiring. The models are denoted SIR-$ω$ and SEIR-$ω$, and we focus attention on the early stages of an outbreak, where we derive expression for the basic reproduction number $R_0$ and the expected degree of the infectious nodes $E(D_I)$ using two different approximation approaches. The first approach appr…
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…
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…
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…
The containment of epidemic spreading is a major challenge in science. Vaccination, whenever available, is the best way to prevent the spreading, because it eventually immunizes individuals. However, vaccines are not perfect, and total immunization is not guaranteed. Imperfect immunization has driven the emergence of anti-vaccine movements that totally alter the predictions about the epidemic incidence. Here, we propose a mathematically solvable mean-field vaccination model to mimic the spontaneous adoption of vaccines against influenza-like diseases, and the expected epidemic incidence. The r…
Containing an epidemic at its origin is the most desirable mitigation. Epidemics have often originated in rural areas, with rural communities among the first affected. Disease dynamics in rural regions have received limited attention, and results of general studies cannot be directly applied since population densities and human mobility factors are very different in rural regions from those in cities. We create a network model of a rural community in Kansas, USA, by collecting data on the contact patterns and computing rates of contact among a sampled population. We model the impact of differe…
In this work we consider a model of epidemic spreading coupled with an opinion dynamics in a fully-connected population. Regarding the opinion dynamics, the individuals may be in two distinct states, namely in favor or against a vaccination campaign. Individuals against the vaccination follow a standard SIS model, whereas the pro-vaccine individuals can also be in a third compartment, namely Vaccinated. In addition, the opinions change according to the majority-rule dynamics in groups with three individuals. We also consider that the vaccine can give permanent or temporary immunization to the …
The spreading of Covid-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of wealth distribution modelling, on the economic improvements induced by the vaccination campaign in terms of its effectiveness rate. The economic trend during the pandemic is evaluated resorting to a mathematical model joining a classical compartmental model including vaccinated individuals with a kinetic model of wealth dist…
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 study the Susceptible-Infected-Susceptible model of epidemic spreading on two layers of networks interconnected by adaptive links, which are rewired at random to avoid contacts between infected and susceptible nodes at the interlayer. We find that the rewiring reduces the effective connectivity for the transmission of the disease between layers, and may even totally decouple the networks. Weak endemic states, in which the epidemics spreads only if the two layers are interconnected, show a transition from the endemic to the healthy phase when the rewiring overcomes a threshold value that dep…
Adaptive Epidemic Dynamics on Hypergraphs with Group-Level Immunization and Rewiring
College of Artificial Intelligence, Southwest University（西南大学人工智能学院）；School of Systems Science/Institute of Nonequilibrium Systems, Beijing Normal University（北京师范大学系统科学学院/非平衡系统研究所）；Business College, Southwest University（西南大学商学院）；Faculty of Natural Sciences and Mathematics, University of Maribor（马里博尔大学自然科学与数学学院）；Community Healthcare Center Dr. Adolf Drolc Maribor（马里博尔阿道夫·德罗尔博士社区健康中心）；Department of Physics, Kyung Hee University（庆熙大学物理系）；University College, Korea University（高丽大学大学院）
The decision of whether or not to vaccinate is a complex one. It involves the contribution both to a social good -- herd immunity -- and to one's own well being. It is informed by social influence, personal experience, education, and mass media. In our work, we investigate a situation in which individuals make their choice based on how social neighbourhood responded to previous epidemics. We do this by proposing a minimalistic model using components from game theory, network theory and the modelling of epidemic spreading, and opinion dynamics. Individuals can use the information about the neig…
Epidemics on complex networks is a widely investigated topic in the last few years, mainly due to the last pandemic events. Usually, real contact networks are dynamic, hence much effort has been invested in studying epidemics on evolving networks. Here we propose and study a model for evolving networks based on varying degrees, where at each time step a node might get, with probability $r$, a new degree and new neighbors according to a given degree distribution, instead of its former neighbors. We find analytically, using the generating functions framework, the epidemic threshold and the proba…
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…
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…
We consider recurrent contagious processes on a time-varying network. As a control procedure to mitigate the epidemic, we propose an adaptive rewiring mechanism for temporary isolation of infected nodes upon their detection. As a case study, we investigate the network of pig trade in Germany. Based on extensive numerical simulations for a wide range of parameters, we demonstrate that the adaptation mechanism leads to a significant extension of the parameter range, for which most of the index nodes (origins of the epidemic) lead to vanishing epidemics. Furthermore the performance of adaptation …
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 …
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 work consists of an epidemic model with vaccination coupled with an opinion dynamics. Our objective was to study how disease risk perception can influence opinions about vaccination and therefore the spreading of the disease. Differently from previous works we have considered continuous opinions. The epidemic spreading is governed by a SIS-like model with an extra vaccinated state. In our model individuals vaccinate with a probability proportional to their opinions. The opinions change due to peer influence in pairwise interactions. The epidemic feedback to the opinion dynamics acts as an…
How to prevent the spread of human diseases is a great challenge for the scientific community and so far there are many studies in which immunization strategies have been developed. However, these kind of strategies usually do not consider that medical institutes may have limited vaccine resources available. In this manuscript, we explore the Susceptible-Infected-Recovered (SIR) model with local dynamic vaccination, and considering limited vaccines. In this model, susceptibles in contact with an infected individual, are vaccinated -with probability $ω$- and then get infected -with probability …
We interpret attitudes towards science and pseudosciences as cultural traits that diffuse in society through communication efforts exerted by agents. We present a tractable model that allows us to study the interaction among the diffusion of an epidemic, vaccination choices, and the dynamics of cultural traits. We apply it to study the impact of homophily between pro-vaxxers and anti-vaxxers on the total number of cases (the cumulative infection). We show that, during the outbreak of a disease, homophily has the direct effect of decreasing the speed of recovery. Hence, it may increase the numb…
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…
A model for epidemics on an adaptive network is considered. Nodes follow an SIRS (susceptible-infective-recovered-susceptible) pattern. Connections are rewired to break links from non-infected nodes to infected nodes and are reformed to connect to other non-infected nodes, as the nodes that are not infected try to avoid the infection. Monte Carlo simulation and numerical solution of a mean field model are employed. The introduction of rewiring affects both the network structure and the epidemic dynamics. Degree distributions are altered, and the average distance from a node to the nearest infe…
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…
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…
We study the interaction between epidemic spreading and a vaccination process. We assume that, similar to the disease spreading, also the vaccination process occurs through direct contact, i.e., it follows the standard susceptible-infected-susceptible (SIS) dynamics. The two competing processes are asymmetrically coupled as vaccinated nodes can directly become infected at a reduced rate with respect to susceptible ones. We study analytically the model in the framework of mean-field theory finding a rich phase-diagram. When vaccination provides little protection toward infection, two continuous…
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…
This paper presents a discrete time probabilistic dynamic for simulating a contact-based epidemic spreading based on discrete time Markov chain process, in particular the attention is addressed to the susceptible-infectious-removed (SIR) model and the phase diagram of such model will be presented. Then, this report presents the set of equations that represent the optimal control strategies, by the means of Pontryagin's maximum principle, in two different cases a vaccination policy and a combined vaccination-hospitalization policy and show a numerical simulation, with the standard forward-backw…
COVID-19 will be a continuous threat to human population despite having a few vaccines at hand until we reach the endemic state through natural herd immunity and total immunization through universal vaccination. However, the vaccine acts as a practical tool for reducing the massive public health problem and the emerging economic consequences that the continuing COVID -19 epidemic is causing worldwide, while the vaccine efficacy wanes. In this work, we propose and analyze an epidemic model of Susceptible-Exposed-Infected-Recovered-Vaccinated (SEIRV) population taking into account the rate of va…
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…
We analyse an extended SIRS epidemic model in which immunity at the individual level wanes gradually at exponential rate, but where the waning rate may differ between individuals, for instance as an effect of differences in immune systems. The model also includes vaccination schemes aimed to reach and maintain herd immunity. We consider both the informed situation where the individual waning parameters are known, thus allowing selection of vaccinees being based on both time since last vaccination as well as on the individual waning rate, and the more likely uninformed situation where individua…
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…
