A Susceptible-infected Epidemic Model with Voluntary Vaccinations

Chen, Frederick

doi:10.1007/s00285-006-0006-1

Cited by 131 publications

(81 citation statements)

References 19 publications

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“…Mean field epidemiological models with vaccination choices derived from classical utility-based economic approaches were used in [494] to demonstrate the conflict between individual and social optimum, and the nature of externalities arising from vaccination. Deeper utility maximization frameworks were used to investigate a number of discrete-time coupled disease-behavior models considering both risky behavior and vaccination decisions in [495,496]. In particular [495,496] revisited Francis' work [481], showing that (a) the free market solution always yields inefficiently low levels of vaccine uptake, and that (b) higher coverage can only result from frictions such as vaccine imperfection, agents heterogeneity, and in general from strategic interactions.…”

Section: Other Contributions To Mean-field Coupled Disease-behavior Mmentioning

confidence: 99%

Statistical physics of vaccination

et al. 2016

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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 report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research.

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Section: Other Contributions To Mean-field Coupled Disease-behavior Mmentioning

confidence: 99%

Statistical physics of vaccination

et al. 2016

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“…Author details 1 School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, P. R. China. 2 School of Science, Changchun University, Changchun, Jilin 130022, P. R. China.…”

Section: Appendixmentioning

confidence: 99%

The asymptotic behavior of a stochastic SIS epidemic model with vaccination

2015

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In this paper, we discuss a stochastic SIS epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction number R 0 . When the perturbation is large, the number of infected decays exponentially to zero and the solution converges to the disease-free equilibrium regardless of the magnitude of R 0 . Moreover, we get the same exponential stability and the convergence if R 0 < 1. When the perturbation and the disease-related death rate are small, we derive that the disease will persist, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model on average in time if R 0 > 1. Furthermore, we prove that the system is persistent in the mean. Finally, the results are illustrated by computer simulations.MSC: 34F05; 37H10; 60H10; 92D25; 92D30

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“…Many subsequent developments were made in order to include the human behaviour in epidemiological models (cf. Chen (2006); d 'Onofrio et al (2007); Manfredi et al (2009);Coelho and Codeço (2009);Mbah et al (2012); Manfredi and D'Onofrio (2013); Morin et al (2013); Bhattacharyya et al (2015); Laguzet and Turinici (2015b)). See also (Funk et al, 2010;Wang et al, 2015) for a review, and (Funk et al, 2015) for further discussion on the subject.…”

Section: Introductionmentioning

confidence: 99%

Optimal vaccination strategies and rational behaviour in seasonal epidemics

et al. 2016

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We consider a SIRS model with 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 the risk of the disease. The former case corresponds to an optimal solution for mandatory vaccinations, while the second corresponds to the equilibrium to be expected if vaccination is fully voluntary. We are able to show the existence of both optimal and Nash strategies in a general setting. In general, these strategies will not be functions but Radon measures. For specific forms of the transmission rate, we provide explicit formulas for the optimal and the Nash vaccination strategies.

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A Susceptible-infected Epidemic Model with Voluntary Vaccinations

Cited by 131 publications

References 19 publications

Statistical physics of vaccination

Statistical physics of vaccination

The asymptotic behavior of a stochastic SIS epidemic model with vaccination

Optimal vaccination strategies and rational behaviour in seasonal epidemics

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