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 rate and accelerating the vaccination process. Counterintuitively, if the individual's attitude towards vaccination is more reliant on his neighbors' vaccination behavior, more individuals will get vaccinated, and the vaccination process will speed up. Besides, individuals are more willing to get vaccinated if they have more neighbors.
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…
The mitigation of an infectious disease spreading has recently gained considerable attention from the research community. It may be obtained by adopting sanitary measurements social rules, together with an extensive vaccination campaign. Vaccination is currently the primary way for mitigating the Coronavirus Disease (COVID-19) outbreak without severe lockdown. Its effectiveness also depends on the number and timeliness of administrations and thus demands strict prioritization criteria. Almost all countries have prioritized similar classes of exposed workers obtaining to maximize the survival o…
There are often multiple diseases with cross immunity competing for vaccination resources. Here we investigate the optimal vaccination program in a two-layer Susceptible-Infected-Removed (SIR) model, where two diseases with cross immunity spread in the same population, and vaccines for both diseases are available. We identify three scenarios of the optimal vaccination program, which prevents the outbreaks of both diseases at the minimum cost. We analytically derive a criterion to specify the optimal program based on the costs for different vaccines.
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 …
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…
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…
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…
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…
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…
The disease spreading on complex networks is studied in SIR model. Simulations on empirical complex networks reveal two specific regimes of disease spreading: local containment and epidemic outbreak. The variables measuring the extent of disease spreading are in general characterized by a bimodal probability distribution. Phase diagrams of disease spreading for empirical complex networks are introduced. A theoretical model of disease spreading on m-ary tree is investigated both analytically and in simulations. It is shown that the model reproduces qualitative features of phase diagrams of dise…
Although there is always an interplay between the dynamics of information diffusion and disease spreading, the empirical research on the systemic coevolution mechanisms connecting these two spreading dynamics is still lacking. Here we investigate the coevolution mechanisms and dynamics between information and disease spreading by utilizing real data and a proposed spreading model on multiplex network. Our empirical analysis finds asymmetrical interactions between the information and disease spreading dynamics. Our results obtained from both the theoretical framework and extensive stochastic nu…
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…
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…
Several European countries have suspended the inoculation of the AstraZeneca vaccine out of suspicion of causing deep vein thrombosis. In this letter we report some Fermi estimates performed using a stochastic model aimed at making a risk-benefit analysis of the interruption of the delivery of the AstraZeneca vaccine in France and Italy. Our results clearly show that excess deaths due to the interruption of the vaccination campaign injections largely overrun those due to thrombosis even in worst case scenarios of frequency and gravity of the vaccine side effects.
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 …
COVID-19 has devastated the entire global community. Vaccines present an opportunity to mitigate the pandemic; however, the effect of vaccination coupled with the behavioral response of the population is not well understood. We propose a model that incorporates two important dynamically varying population behaviors: level of caution and sense of safety. Level of caution increases with the number of infectious cases, while an increasing sense of safety with increased vaccination lowers precautionary behaviors. To the best of our knowledge, this is the first model that can effectively reproduce …
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…
The study proposes a modeling framework for investigating the disease dynamics with adaptive human behavior during a disease outbreak, considering the impacts of both local observations and global information. One important application scenario is that commuters may adjust their behavior upon observing the symptoms and countermeasures from their physical contacts during travel, thus altering the trajectories of a disease outbreak. We introduce the heterogeneous mean-field (HMF) approach in a multiplex network setting to jointly model the spreading dynamics of the infectious disease in the cont…
A pandemic, the worldwide spread of a disease, can threaten human beings from the social as well as biological perspectives and paralyze existing living habits. To stave off the more devastating disaster and return to a normal life, people make tremendous efforts at multiscale levels from individual to worldwide: paying attention to hand hygiene, developing social policies such as wearing masks, social distancing, quarantine, and inventing vaccines and remedy. Regarding the current severe pandemic, namely the coronavirus disease 2019, we explore the spreading-suppression effect when adopting t…
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…
In this paper we introduce a compartmental epidemic model describing the transmission of the COVID-19 disease in presence of non-mandatory vaccination. The model takes into account the hesitancy and refusal of vaccination. To this aim, we employ the information index, which mimics the idea that individuals take their decision on vaccination based not only on the present but also on the past information about the spread of the disease. Theoretical analysis and simulations show clearly as a voluntary vaccination can certainly reduce the impact of the disease but it is unable to eliminate it. We …
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…
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…
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…
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…
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…
An insufficient supply of effective SARS-CoV-2 vaccine in most countries demands an effective vaccination strategy to minimize the damage caused by the disease. Currently, many countries vaccinate their population in descending order of age (i.e. descending order of fatality rate) to minimize the deaths caused by the disease; however, the effectiveness of this strategy needs to be quantitatively assessed. We employ the susceptible-infected-recovered-dead (SIRD) model to investigate various vaccination strategies. We constructed a metapopulation model with heterogeneous contact and fatality rat…
There is great interest in the dynamics of health behaviors in social networks and how they affect collective public health outcomes, but measuring population health behaviors over time and space requires substantial resources. Here, we use publicly available data from 101,853 users of online social media collected over a time period of almost six months to measure the spatio-temporal sentiment towards a new vaccine. We validated our approach by identifying a strong correlation between sentiments expressed online and CDC- estimated vaccination rates by region. Analysis of the network of opinio…
The crisis caused by the COVID-19 outbreak around the globe raised an increasing concern about the ongoing emergence of variants of SARS-CoV-2 that may evade the immune response provided by vaccines. New variants appear due to mutation, and as the cases accumulate, the probability of the emergence of a variant of concern increases. In this article, we propose a modified SIR model with waning immunity that captures the competition of two strain classes of an infectious disease under the effect of vaccination with a highly contagious and deadly strain class emerging from a prior strain due to mu…
By the end of 2020, a year since the first cases of infection by the Covid-19 virus have been reported, there is a light at the end of the tunnel. Several pharmaceutical companies made significant progress in developing effective vaccines against the Covid-19 virus that has claimed the lives of more than a million people over the world. On the other hand, there is growing evidence of re-infection by the virus, which can cause further outbreaks. In this paper, we apply statistical physics tools to examine the vaccination rate required to control the pandemic for three different vaccine efficien…
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…
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…
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 widely recognized as the most effective way of immunization against many infectious diseases. However, unfounded claims about supposed side effects of some vaccines have contributed to spread concern and fear among people, thus inducing vaccination refusal. For instance, MMR vaccine coverage has undergone an important decrease in a large part of Europe and US as a consequence of erroneously alleged side effects, leading to recent measles outbreaks. In this work, we propose a general agent-based model to study the spread of vaccination behavior in social networks, not as an isola…
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…
Social network analysis is now widely used to investigate the dynamics of infectious disease spread from person to person. Vaccination dramatically disrupts the disease transmission process on a contact network, and indeed, sufficiently high vaccination rates can disrupt the process to such an extent that disease transmission on the network is effectively halted. Here, we build on mounting evidence that health behaviors - such as vaccination, and refusal thereof - can spread through social networks through a process of complex contagion that requires social reinforcement. Using network simulat…
Information diffusion and disease spreading in communication-contact layered network are typically asymmetrically coupled with each other, in which how an individual being aware of disease responds to the disease can significantly affect the disease spreading. Many recent studies have demonstrated that human behavioral adoption is a complex and non-Markovian process, where the probability of adopting one behavior is dependent on the cumulative times of the received information and the social reinforcement effect of these cumulative information. We study the impact of such a non-Markovian vacci…
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 …
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…
We investigate disease spreading on eight empirical data sets of human contacts (mostly proximity networks recording who is close to whom, at what time). We compare three levels of representations of these data sets: temporal networks, static networks and a fully connected topology. We notice that the difference between the static and fully-connected networks -- with respect to time to extinction and average outbreak size -- is smaller than between the temporal and static topologies. This suggests that, for these data sets, temporal structures influence disease spreading more than static netwo…
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 study the effect of motion on disease spreading in a system of random walkers which additionally perform long-distance jumps. A small percentage of jumps in the agent motion is sufficient to destroy the local correlations and to produce a large drop in the epidemic threshold, well explained in terms of a mean-field approximation. This effect is similar to the crossover found in static small-world networks, and can be furthermore linked to the structural properties of the dynamical network of agent interactions.
Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination - one of the most important preventive measures of modern times - is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our repor…
One of the major issues in the theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to stop a disease from spreading or to reduce its burden, as individuals aware of the presence of a disease can take measures to reduce their exposure to contagion. In this paper, we propose a mathematical model for the spread of diseases with awareness in complex networks. Unlike previous models, the information is propagated following a generalized Maki-Thom…
Nowadays, one of the challenges we face when carrying out modeling of epidemic spreading is to develop methods to control disease transmission. In this article we study how the spreading of knowledge of a disease affects the propagation of that disease in a population of interacting individuals. For that, we analyze the interaction between two different processes on multiplex networks: the propagation of an epidemic using the susceptible-infected-susceptible dynamics and the dissemination of information about the disease --and its prevention methods-- using the unaware-aware-unaware dynamics, …
Motivated by massive outbreaks of COVID-19 that occurred even in populations with high vaccine uptake, we propose a novel multi-population temporal network model for the spread of recurrent epidemic diseases. We study the effect of human behavior, testing, and vaccination campaigns on the control of local outbreaks and infection prevalence. Our modeling framework decouples the vaccine effectiveness in protecting against transmission and the development of severe symptoms. Furthermore, the framework accounts for the polarizing effect of the decision to vaccinate and captures homophily, i.e., th…
