Moment closure approximations of susceptible-infected-susceptible epidemics on adaptive networks

Achterberg, Massimo A.; Mieghem, Piet Van

doi:10.1103/physreve.106.014308

Cited by 3 publications

(9 citation statements)

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“…In particular, it was assumed that links are broken between susceptible and infected nodes and (re)created between susceptible nodes. The aNIMFA approximation of the ASIS model was already analysed in [ 12 ] and the functional responses were derived as and . The link-breaking response is similar to Example 2, but the term was added to account for the fact that for large epidemic outbreaks, the susceptible population may be depleted and the possibility to break links between susceptible and infected individuals decreases, simply because of the lack of susceptible individuals.…”

Section: Examplesmentioning

confidence: 99%

“…The link-breaking response is similar to Example 2, but the term was added to account for the fact that for large epidemic outbreaks, the susceptible population may be depleted and the possibility to break links between susceptible and infected individuals decreases, simply because of the lack of susceptible individuals. The factor 2 is a conversion factor from the original Markovian model; we keep this factor for consistency with [ 12 ]. The link-creation response is more intuitive; we expect many links to be created if the disease is almost nonexistent.…”

Section: Examplesmentioning

confidence: 99%

“…We model the creation and removal of edges as an overall increase or decrease of the link density of the contact network. We call the model adaptive NIMFA (aNIMFA), in line with earlier work [ 12 ]. The core aspect of aNIMFA are the functional responses of individuals to create or break links in the network, based on the current number of infected people.…”

Section: Introductionmentioning

confidence: 99%

“…In predator–prey systems like Volterra-Lotka dynamics, Holling introduced functional responses to describe the food intake by predators as a function of the number of available prey [ 13 ]. A preliminary analysis of the aNIMFA model was performed by Achterberg and Van Mieghem [ 12 ], but only for specific functional responses. We extend the results from [ 12 ] by considering general functional responses and by providing a more detailed analysis.…”

Section: Introductionmentioning

confidence: 99%

“…A preliminary analysis of the aNIMFA model was performed by Achterberg and Van Mieghem [ 12 ], but only for specific functional responses. We extend the results from [ 12 ] by considering general functional responses and by providing a more detailed analysis.…”

Section: Introductionmentioning

confidence: 99%

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A minimal model for adaptive SIS epidemics

Achterberg

Sensi

2023

Nonlinear Dyn

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The interplay between disease spreading and personal risk perception is of key importance for modelling the spread of infectious diseases. We propose a planar system of ordinary differential equations (ODEs) to describe the co-evolution of a spreading phenomenon and the average link density in the personal contact network. Contrary to standard epidemic models, we assume that the contact network changes based on the current prevalence of the disease in the population, i.e. the network adapts to the current state of the epidemic. We assume that personal risk perception is described using two functional responses: one for link-breaking and one for link-creation. The focus is on applying the model to epidemics, but we also highlight other possible fields of application. We derive an explicit form for the basic reproduction number and guarantee the existence of at least one endemic equilibrium, for all possible functional responses. Moreover, we show that for all functional responses, limit cycles do not exist. This means that our minimal model is not able to reproduce consequent waves of an epidemic, and more complex disease or behavioural dynamics are required to reproduce epidemic waves.

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Section: Examplesmentioning

confidence: 99%

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A minimal model for adaptive SIS epidemics

Achterberg

Sensi

2023

Nonlinear Dyn

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Analysis of continuous-time Markovian ɛ -SIS epidemics on networks

2022

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We analyze continuous-time Markovian ε-SIS epidemics with self-infections on the complete graph. The majority of the graphs are analytically intractable, but many physical features of the ε-SIS process observed in the complete graph can occur in any other graph. In this work, we illustrate that the timescales of the ε-SIS process are related to the eigenvalues of the tridiagonal matrix of the SIS Markov chain. We provide a detailed analysis of all eigenvalues and illustrate that the eigenvalues show staircases, which are caused by the nearly degenerate (but strictly distinct) pairs of eigenvalues. We also illustrate that the ratio between the second-largest and third-largest eigenvalue is a good indicator of metastability in the ε-SIS process. Additionally, we show that the epidemic threshold of the Markovian ε-SIS process can be accurately approximated by the effective infection rate for which the third-largest eigenvalue of the transition matrix is the smallest. Finally, we derive the exact mean-field solution for the ε-SIS process on the complete graph, and we show that the mean-field approximation does not correctly represent the metastable behavior of Markovian ε-SIS epidemics.

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