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 enforcing mitigation and vaccination strategy. The spreading rate is measured by the ratio between the reproductive number Rt(t) and the doubling time Td(t) called RIC-index and the daily fatalities number. The dynamics of the Covid-19 epidemics has been studied by wavelet analysis and represented by a non-linear helicoid vortex in a 3D space where both RIC-index and fatalities change with time. The onset of periodic recurrent waves has been identified by the transition from convergent to divergent trajectories on the helicoid vortex. We report a main period of recurrent waves of 120 days and the elongation of this period after the vaccination campaign
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 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 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…
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…
We define and analyze an inductive reasoning game of voluntary yearly vaccination in order to establish whether or not a population of individuals acting in their own self-interest would be able to prevent influenza epidemics. We find that epidemics are rarely prevented. We also find that severe epidemics may occur without the introduction of pandemic strains. We further address the situation where market incentives are introduced to help ameliorating epidemics. Surprisingly, we find that vaccinating families exacerbates epidemics. However, a public health program requesting prepayment of vacc…
Inspired by Minority Games, we constructed a novel individual-level game of adaptive decision-making based on the dilemma of deciding whether to participate in voluntary influenza vaccination programs. The proportion of the population vaccinated (i.e., the vaccination coverage) determines epidemic severity. Above a critical vaccination coverage, epidemics are prevented; hence individuals find it unnecessary to vaccinate. The adaptive dynamics of the decisions directly affect influenza epidemiology and, conversely, influenza epidemiology strongly influences decision-making. This feedback mechan…
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…
In the context of the ongoing Ebola epidemic in DRC, active conflict and community distrust are undermining control efforts, including vaccination strategies. In this paper, we employed an individual-level stochastic structured transmission model to assess the impact of vaccination strategies on epidemic control in the context of variable levels of household inaccessibility. We found that a ring vaccination strategy of close contacts would not be effective for containing the epidemic in the context of significant delays to vaccinating contacts even for low levels of household inaccessibility a…
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 …
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 …
With the unprecedented global vaccination campaign against SARS-CoV-2 attention has now turned to the potential impact of this large-scale intervention on the evolution of the virus. In this perspective we summarize what is currently known about evolution in the context of vaccination from research on other pathogen species, with an eye towards the future evolution of SARS-CoV-2.
The unfolding of pandemic influenza A(H1N1) for Fall 2009 in the Northern Hemisphere is still uncertain. Plans for vaccination campaigns and vaccine trials are underway, with the first batches expected to be available early October. Several studies point to the possibility of an anticipated pandemic peak that could undermine the effectiveness of vaccination strategies. Here we use a structured global epidemic and mobility metapopulation model to assess the effectiveness of massive vaccination campaigns for the Fall/Winter 2009. Mitigation effects are explored depending on the interplay between…
We consider a SIR model with temporary immunity and time dependent transmission rate. We assume time dependent vaccination which confers the same immunity as natural infection. We study two types of vaccination strategies: i) optimal vaccination, in the sense that it minimizes the effort of vaccination in the set of vaccination strategies for which, for any sufficiently small perturbation of the disease free state, the number of infectious individuals is monotonically decreasing; ii) Nash-equilibria strategies where all individuals simultaneously minimize the joint risk of vaccination versus t…
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 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…
We investigate stochastic extinction in an epidemic model and the impact of random vaccinations in large populations formulated in terms of an optimal escape path. We find that different random vaccination strategies can have widely different results in decreasing expected time till extinction, for the same total amount of vaccines used. Vaccination strategies are considered in terms of two parameters: average frequency of vaccinations, given by $γ$, and the amplitude of the vaccinations, $ε$, where $ε\ll 1$ refers to the proportion of the population being vaccinated at some particular instant…
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 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 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…
We use analytical methods to investigate a continuous vaccination strategy effects on the infectious disease dynamics in a closed population and a demographically open population. The methodology and key assumptions are based on Breda et al (2012). We show that the cumulative force of infection for the closed population and the endemic force of infection in the demographically open population can be reduced significantly by combining two factors: the vaccine effectiveness and the vaccination rate. The impact of these factors on the force of infection can transform an endemic steady state into …
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…
We analyze the susceptible-infected-susceptible model for epidemic spreading in which a fraction of the individuals become immune by vaccination. This process is understood as a dilution by vaccination, which decreases the fraction of the susceptible individuals. For a nonzero fraction of vaccinated individuals, the model predicts a new state in which the disease spreads but eventually becomes extinct. The new state emerges when the fraction of vaccinated individuals is greater than a critical value. The model predicts that this critical value increases as one increases the infection rate reac…
We consider three regions with different public health conditions. In the absence of migration among these regions, the first two have good health conditions and the disease free state is stable; for the third region, on the other hand, the only stable state is the endemic one. When migration is included in the model, we assume that the second region has a disease risk that makes its inhabitants prone to accept to be vaccinated, while the population in the first region tends to reject the vaccination, considered riskier that the disease. Therefore, the second region is a "buffer zone" between …
We propose a simple rule of thumb for countries which have embarked on a vaccination campaign while still facing the need to keep non-pharmaceutical interventions (NPI) in place because of the ongoing spread of SARS-CoV-2. If the aim is to keep the death rate from increasing, NPIs can be loosened when it is possible to vaccinate more than twice the growth rate of new cases. If the aim is to keep the pressure on hospitals under control, the vaccination rate has to be about four times higher. These simple rules can be derived from the observation that the risk of death or a severe course requiri…
The Beyond-Linear-Use-of-Equation-Superposition (BLUES) function method is extended to coupled nonlinear ordinary differential equations and applied to the epidemiological SIRS model with vaccination. Accurate analytic approximations are obtained for the time evolution of the susceptible and infected population fractions. The results are compared with those obtained with alternative methods, notably Adomian decomposition, variational iteration and homotopy perturbation. In contrast with these methods, the BLUES iteration converges rapidly, globally, and captures the exact asymptotic behavior f…
Our paper presents three new classes of models: SIR-PH, SIR-PH-FA, and SIR-PH-IA, and states two problems we would like to solve about them. Recall that deterministic mathematical epidemiology has one basic general law, the R0 alternative" of [52, 51], which states that the local stability condition of the disease free equilibrium may be expressed as R0 < 1, where R0 is the famous basic reproduction number, which plays also a major role in the theory of branching processes. The literature suggests that it is impossible to find general laws concerning the endemic points. However, it is quite co…
The results of Kermack-McKendrick SIR model are planned to be reproduced by cellular automata (CA) lattice model. The CA algorithms are proposed to study the model of epidemic, systematically. The basic goal is to capture the effects of spreading of infection over a scale of length. This CA model can provide the rate of growth of the infection over the space which was lacking in the mean-field like SIR model. The motion of the circular front of an infected cluster shows a linear behaviour in time. The correlation of a particular site to be infected, with respect to the central site is also stu…
Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that enables us to calculate the complete probability distribution for the final epidemic size in a stochastic Susceptible-Infected-Recovered (SIR) model. Based on these results, we determine the optimal allocations of a limited quantity of vaccine between two non-interacting populations. We compare the stochastic solution to results obtained for the traditional…
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…
Motivated by the increasing number of COVID-19 cases that have been observed in many countries after the vaccination and relaxation of non-pharmaceutical interventions, we propose a mathematical model on time-varying networks for the spread of recurrent epidemic diseases in a partially vaccinated population. The model encapsulates several realistic features, such as the different effectiveness of the vaccine against transmission and development of severe symptoms, testing practices, the possible implementation of non-pharmaceutical interventions to reduce the transmission, isolation of detecte…
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 paper, we carry out a computational study using the spectral decomposition of the fluctuations of a two-pathogen epidemic model around its deterministic attractor, i.e., steady state or limit cycle, to examine the role of partial vaccination and between-host pathogen interaction on early pathogen replacement during seasonal epidemics of influenza and respiratory syncytial virus.
Dengue is one of the most important infectious diseases in the world, in terms of death and economic cost. Hence, the modeling of dengue is of great importance to help us understand the dynamics disease, and interfering with its spreading mathematical by the proposition of control methods. In this work, control strategies in an attempt to eliminate the Aedes aegypti mosquito, as well as proposals for the vaccination campaign are evaluated. In our mathematical model, the mechanical control is accomplished through the environmental support capacity affected by a discrete function that represents…
Several epidemiological models have been proposed to study the evolution of COVID-19 pandemic. In this paper, we propose an extension of the SUIHTER model, first introduced in [Parolini et al, Proc R. Soc. A., 2021] to analyse the COVID-19 spreading in Italy, which accounts for the vaccination campaign and the presence of new variants when they become dominant. In particular, the specific features of the variants (e.g. their increased transmission rate) and vaccines (e.g. their efficacy to prevent transmission, hospitalization and death) are modeled, based on clinical evidence. The new model i…
This paper is concerned with Crump-Mode-Jagers branching processes, describing spread of an epidemic depending on the proportion of the population that is vaccinated. Births in the branching process are aborted independently with a time-dependent probability given by the fraction of the population vaccinated. Stochastic monotonicity and continuity results for a wide class of functions (e.g., extinction time and total number of births over all time) defined on such a branching process are proved using coupling arguments, leading to optimal vaccination schemes to control corresponding functions …
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…
We estimate patterns of covariation between COVID-19 vaccination rates and a set of widely used indicators of human, social, and economic capital across 146 countries in July 2021 and February 2022. About 70% of the variability in COVID-19 vaccination rates worldwide can be explained by differences in the Human Development Index (HDI) and, specifically, in life expectancy at birth, one year after the campaign debut. Trust in doctors and nurses adds predictive value beyond the HDI, clarifying controversial discrepancies between vaccination rates in countries with similar levels of human develop…
The June software package is an open-source framework for the detailed simulation of epidemics based on social interactions in a virtual population reflecting age, gender, ethnicity, and socio-economic indicators in England. In this paper, we present a new version of the framework specifically adapted for Germany, which allows the simulation of the entire German population using publicly available information on households, schools, universities, workplaces, and mobility data for Germany. Moreover, JuneGermany incorporates testing and vaccination strategies within the population as well as the…
Population-wide vaccination is critical for containing the SARS-CoV-2 (Covid-19) pandemic when combined with restrictive and prevention measures. In this study, we introduce SAIVR, a mathematical model able to forecast the Covid-19 epidemic evolution during the vaccination campaign. SAIVR extends the widely used Susceptible-Infectious-Removed (SIR) model by considering the Asymptomatic (A) and Vaccinated (V) compartments. The model contains several parameters and initial conditions that are estimated by employing a semi-supervised machine learning procedure. After training an unsupervised neur…
In this paper we aim to study an optimal insurance premium level for health-care in a deterministic and stochastic SIR models with migration fluxes and vaccination of population. The studied model considers two standard SIR centres connected via links and continuous migration fluxes. The premium is calculated using the basic equivalence principle. Even in this simple setup there are non-intuitive results that illustrate how the premium depends on migration rates, severeness of a disease and initial distribution of healthy and infected individuals through the centres. We investigate how the vac…
