Pairwise models for non-Markovian epidemics on networks

Vizi, Zsolt

doi:10.14232/phd.3117

Cited by 2 publications

(3 citation statements)

References 85 publications

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“…We calculate the basic reproduction number, R 0 , of Model ( 9) according to the method in [44]. Here, R 0 is the expected lifetime of an S-I link multiplied by the number of newly generated S-I links per unit time [31].…”

Section: The Basic Reproduction Numbermentioning

confidence: 99%

“…The numerical simulations are performed with N = 1000, β = 0.1, α = 1/20, γ = 1/3, and m = 10. The initial conditions are [S](0) = 999, [44], we assume the initial distribution of awareness process is ϕ(s) [Q a ] 0 δ(s), where δ(s) is the Dirac delta function. Then, First, we focus on the effects of different contact tracing rates and awareness processes on the epidemic spreading.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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Effects of contact tracing and non-Markovian awareness process on the spread of air-borne diseases

Sun

Ren²,

Li³

et al. 2022

Front. Phys.

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Contact tracing is an important tool to contain the spread of many airborne diseases. We develop an approximated pairwise model to investigate the impact of non-Markovian awareness process among infectious individuals represented by pairwise endemic models. We derive the basic reproduction number and the final epidemic size, which are dependent on the tracing rate and the distribution of awareness process. The model analysis provides the threshold of contact tracing rate. When the contact tracing rate is greater than the threshold, the basic reproduction number will be less than one, then the epidemic will eventually die out. The analysis further shows that, higher variance in the awareness process generates smaller basic reproduction number, lower tracing threshold, and larger final epidemic size, when the mean awareness period is fixed. Extensive numerical analysis show the comprehensive effects of tracing rates and non-Markovian awareness processes on human behavior and the transmissibility ability of epidemic. It turns out that large tracing rates and high variances in awareness process lead to obvious reductions in contacts between susceptible and infectious individuals, so as to curb the transmission of infectious diseases. Moreover, contact tracing is more effective in reducing the number of infected individuals and the contacts between susceptible and infected individuals when the awareness process has a larger variance.

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Section: The Basic Reproduction Numbermentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

Effects of contact tracing and non-Markovian awareness process on the spread of air-borne diseases

Sun

Ren²,

Li³

et al. 2022

Front. Phys.

View full text Add to dashboard Cite

show abstract

“…The vast majority of existing literature on pandemic modeling focuses on Markovian processes, not least owing to a broader understanding of decision making strategies in such frameworks and optimization techniques thereof, as well as the existence of ready software. While non-Markovian processes have been investigated in epidemic propagation contexts, and mostly so in network based analysis (see [26], [29], [41], [37] and references therein), the literature in this arena is significantly sparser, and very few works in the recent slew of papers on the pandemic have considered this angle. However, we believe that exploration of non-Markovian models is quite important since the standard Markovian compartment models used in practice do not quite describe epidemic transmission accurately.…”

Section: Statewise Numerical Analysismentioning

confidence: 99%

Markovian And Non-Markovian Processes with Active Decision Making Strategies For Addressing The COVID-19 Pandemic

Eftekhari,

Mukherjee,

Banerjee

et al. 2020

Preprint

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We study and predict the evolution of Covid-19 in six US states from the period May 1 through August 31 using a discrete compartment-based model and prescribe active intervention policies, like lockdowns, on the basis of minimizing a loss function, within the broad framework of partially observed Markov decision processes. For each state, Covid-19 data for 40 days (starting from May 1 for two northern states and June 1 for four southern states) are analyzed to estimate the transition probabilities between compartments and other parameters associated with the evolution of the epidemic.These quantities are then used to predict the course of the epidemic in the given state for the next 50 days (test period) under various policy allocations, leading to different values of the loss function over the training horizon. The optimal policy allocation is the one corresponding to the smallest loss. Our analysis shows that none of the six states need lockdowns over the test period, though the 'no lockdown' prescription is to be interpreted with caution: responsible mask use and social distancing of course need to be continued. The caveats involved in modeling epidemic propagation of this sort are discussed at length. A sketch of a non-Markovian formulation of Covid-19 propagation (and more general epidemic propagation) is presented as an attractive avenue for future research in this area.

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Pairwise models for non-Markovian epidemics on networks

Cited by 2 publications

References 85 publications

Effects of contact tracing and non-Markovian awareness process on the spread of air-borne diseases

Effects of contact tracing and non-Markovian awareness process on the spread of air-borne diseases

Markovian And Non-Markovian Processes with Active Decision Making Strategies For Addressing The COVID-19 Pandemic

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