Extinction times in the subcritical stochastic SIS logistic epidemic

Brightwell, Graham; House, Thomas; Luczak, Malwina J.

doi:10.1007/s00285-018-1210-5

Cited by 14 publications

(32 citation statements)

References 46 publications

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“…If new susceptible individuals are introduced into the population (for example, new susceptible individuals are born), it is possible that the disease will persist after its first wave and become endemic [66]. These theoretical results can be extended to populations with household and network structure [67,68] and scenarios in which R 0 is very close to one [69]. Epidemiological theory and data from different diseases indicate that extinction can be a slow process, often involving a long 'tail' of cases with significant random fluctuations (electronic supplementary material, figure S1).…”

Section: (D) Is Global Eradication Of Sars-cov-2 a Realistic Possibilmentioning

confidence: 89%

Section: Key Epidemiological Quantitiesmentioning

confidence: 99%

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Key questions for modelling COVID-19 exit strategies

et al. 2020

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Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute ‘Models for an exit strategy’ workshop (11–15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

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Section: (D) Is Global Eradication Of Sars-cov-2 a Realistic Possibilmentioning

confidence: 89%

Section: Key Epidemiological Quantitiesmentioning

confidence: 99%

Key questions for modelling COVID-19 exit strategies

et al. 2020

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“…It considers similar ideas as ours, and obtains concentration and spectral bounds depending on the contraction properties of the measures describing multiple steps in the Markov chain. The approach was further developed in Luczak (2012), Brightwell and Luczak (2013b) and Brightwell and Luczak (2013a). Our results in this paper are more precise, since they take into account the typical size of the jump of the Markov chain, as well as the dimension of the state space, which were not considered in the earlier work.…”

Section: Introductionmentioning

confidence: 95%

Mixing and concentration by Ricci curvature

Paulin

2016

Journal of Functional Analysis

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We generalise the coarse Ricci curvature method of Ollivier by considering the coarse Ricci curvature of multiple steps in the Markov chain. This implies new spectral bounds and concentration inequalities. We also extend this approach to the bounds for MCMC empirical averages obtained by Joulin and Ollivier. We prove a recursive lower bound on the coarse Ricci curvature of multiple steps in the Markov chain, making our method broadly applicable. Applications include the split-merge random walk on partitions, Glauber dynamics with random scan and systemic scan for statistical physical spin models, and random walk on a binary cube with a forbidden region.

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“…The steady state of the Markovian SIS process (with ε = 0) on any finite graph is the absorbing state, that complicates the analysis [5,12] and, perhaps more importantly, is only attained after an exponentially in N long time [13,14]. Brightwell et al [15] have shown that the (scaled) time to extinction or absorption below the mean-field epidemic threshold τ (1) c = 1 N tends to a Gumbel distribution [9, p. 57] if N → ∞. The mean-field SIS epidemic threshold in any graph is [16] τ (1)…”

Section: Introductionmentioning

confidence: 99%

Time dependence of susceptible-infected-susceptible epidemics on networks with nodal self-infections

Mieghem

Wang

2020

Phys. Rev. E

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The average fraction of infected nodes, in short the prevalence, of the Markovian ε-SIS (susceptible-infectedsusceptible) process with small self-infection rate ε > 0 exhibits, as a function of time, a typical "two-plateau" behavior, which was first discovered in the complete graph K N. Although the complete graph is often dismissed as an unacceptably simplistic approximation, its analytic tractability allows to unravel deeper details, that are surprisingly also observed in other graphs as demonstrated by simulations. The time-dependent mean-field approximation for K N performs only reasonably well for relatively large self-infection rates, but completely fails to mimic the typical Markovian ε-SIS process with small self-infection rates. While self-infections, particularly when their rate is small, are usually ignored, the interplay of nodal self-infection and spread over links may explain why absorbing processes are hardly observed in reality, even over long time intervals.

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Extinction times in the subcritical stochastic SIS logistic epidemic

Cited by 14 publications

References 46 publications

Key questions for modelling COVID-19 exit strategies

Key questions for modelling COVID-19 exit strategies

Mixing and concentration by Ricci curvature

Time dependence of susceptible-infected-susceptible epidemics on networks with nodal self-infections

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