Explicit non-Markovian susceptible-infected-susceptible mean-field epidemic threshold for Weibull and Gamma infections but Poisson curings

Mieghem, Piet Van; Liu, Qiang

doi:10.1103/physreve.100.022317

Cited by 21 publications

(26 citation statements)

References 25 publications

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“…Similar cohort studies found heavier-tailed distributions based on power laws to be more compatible with the time intervals between successive interactions, citing the bursty nature of social dynamics as the determining factor [ 57 , 58 ], yet the corresponding data fit was often imperfect while extensive comparisons against exponentials were not performed. In the epidemiological setting, several authors have argued for a shift towards more realistic and flexible Gamma (more commonly Erlang [ 59 , 60 ]) or Weibull distributions [ 61 – 63 ] for the infection waiting times, emphasizing the non-Markovian behavior that epidemics occasionally exhibit. That being said, exponentials have been shown to provide a particularly good fit to epidemiological data when the mean generation time is correctly fixed [ 59 ] or the mean infection duration is smaller [ 64 ].…”

Section: Methodsmentioning

confidence: 99%

Modelling digital and manual contact tracing for COVID-19. Are low uptakes and missed contacts deal-breakers?

2021

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Comprehensive testing schemes, followed by adequate contact tracing and isolation, represent the best public health interventions we can employ to reduce the impact of an ongoing epidemic when no or limited vaccine supplies are available and the implications of a full lockdown are to be avoided. However, the process of tracing can prove feckless for highly-contagious viruses such as SARS-CoV-2. The interview-based approaches often miss contacts and involve significant delays, while digital solutions can suffer from insufficient adoption rates or inadequate usage patterns. Here we present a novel way of modelling different contact tracing strategies, using a generalized multi-site mean-field model, which can naturally assess the impact of manual and digital approaches alike. Our methodology can readily be applied to any compartmental formulation, thus enabling the study of more complex pathogen dynamics. We use this technique to simulate a newly-defined epidemiological model, SEIR-T, and show that, given the right conditions, tracing in a COVID-19 epidemic can be effective even when digital uptakes are sub-optimal or interviewers miss a fair proportion of the contacts.

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Section: Methodsmentioning

confidence: 99%

Modelling digital and manual contact tracing for COVID-19. Are low uptakes and missed contacts deal-breakers?

2021

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“…and (1) = d 2 (z) dz 2 | z=1 = 1.97811 (see [28,Appendix]). Substituted in steady-state prevalence, (A7) gives us…”

Section: Estimate Of the Onset τ εmentioning

confidence: 99%

Explosive phase transition in susceptible-infected-susceptible epidemics with arbitrary small but nonzero self-infection rate

Mieghem

2020

Phys. Rev. E

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The ε-susceptible-infected-susceptible (SIS) epidemic model on a graph adds an independent, Poisson selfinfection process with rate ε to the "classical" Markovian SIS process. The steady state in the classical SIS process (with ε = 0) on any finite graph is the absorbing or overall-healthy state, in which the virus is eradicated from the network. We report that there always exists a phase transition around τ ε c = O(ε − 1 N−1) in the ε-SIS process on the complete graph K N with N nodes, above which the effective infection rate τ > τ ε c causes the average steady-state fraction of infected nodes to approach that of the mean-field approximation, no matter how small, but not zero, the self-infection rate ε is. For τ < τ ε c and small ε, the network is almost overall healthy. The observation was found by mathematical analysis on the complete graph K N , but we claim that the phase transition of explosive type may also occur in any other finite graph. We thus conclude that the overall-healthy state of the classical Markovian SIS model is unstable in the ε-SIS process and, hence, unlikely to exist in reality, where "background" infection ε > 0 is imminent.

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“…Using this theorem we calculate the generation time distribution for our model of infection propagation, and obtain a two parameter (effectively) distribution which can be used in epidemiological studies, as a logical replacement of hitherto used heuristic distributions, such as gamma, lognormal, Weibull, Gaussian etc. [26,27,31,32,41].…”

Section: The Distribution Of Generation Timementioning

confidence: 99%

“…The distribution of generation time or serial interval time for an infectious disease [24][25][26][27] is a very important quantity to understand the transmission potential, and to calculate the basic and effective reproduction number which is a key parameter to estimate the epi-demiological state of an infection in a population [28,29]. Until now, the distribution of generation time is estimated by fitting gamma, lognormal, Weibull, or Gaussian distributions to the transmission pairs data [26,[30][31][32]. However, there is no formal derivation available in favour of the particular choice of these distributions, and hence, they are chosen heuristically.…”

Section: Introductionmentioning

confidence: 99%

Hardness of Herd Immunity and Success Probability of Quarantine Measures: A Branching Process Approach

Nath

2020

Preprint

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We model the propagation of an infection, in a population, as a simplified age-dependent branching process. We analytically estimate the fraction of population, needed to be infected or immuned, to achieve herd immunity for an infection. We calculate this estimation as a function of the incubation period of the contagion, contact probability among the infected and susceptible population, and the probability of disease transmission from an infected to a susceptible individual. We show how herd immunity is strongly dependent on the incubation period, and it may be extremely difficult to achieve herd immunity in case of large incubation period. We derive the distribution of generation time from basic principles, which, by far, has been assumed in an ad hoc manner in epidemiological studies. We quantify the success probability of quarantine measures before achieving herd immunity, and discuss a novel method for designing effective quarantine measures in the absence of any pharmaceutical interventions. We also compare the effectiveness of an early imposition against a delayed imposition of lockdown, of the same duration, in mitigating infection from a population.

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Explicit non-Markovian susceptible-infected-susceptible mean-field epidemic threshold for Weibull and Gamma infections but Poisson curings

Cited by 21 publications

References 25 publications

Modelling digital and manual contact tracing for COVID-19. Are low uptakes and missed contacts deal-breakers?

Modelling digital and manual contact tracing for COVID-19. Are low uptakes and missed contacts deal-breakers?

Explosive phase transition in susceptible-infected-susceptible epidemics with arbitrary small but nonzero self-infection rate

Hardness of Herd Immunity and Success Probability of Quarantine Measures: A Branching Process Approach

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