On the Stability of the Endemic Equilibrium of A Discrete-Time Networked Epidemic Model

Liu, Fangzhou; Cui, Shaoxuan; Li, Xianwei; Buss, Martin

doi:10.48550/arxiv.2001.07451

Cited by 2 publications

(4 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Lastly, the curing rates are decreased to δ i ← cδ i , where the scalar c is chosen such that the basic reproduction number (4) equals R 0 = 3. To obtain the viral state v(t), we discretise NIMFA (1) with a sufficiently small sampling time, see [26,31,20] for a detailed analysis of the resulting discrete-time NIMFA model.…”

Section: Approximate Clusteringmentioning

confidence: 99%

“…Furthermore, since the matrix B is diagonalisable as (20), the matrices M 1 and M 2 are diagonalisable [11, Exercise 24, Section 5.4]. Thus, there is some orthogonal m × m matrix C 1 and some orthogonal (…”

Section: A Proof Of Lemmamentioning

confidence: 99%

“…where the m × m diagonal matrix Λ 1 and the (N − m) × (N − m) diagonal matrix Λ 2 contain the eigenvalues of B. In contrast to the N × N matrix Λ in (20), the diagonal entries of the matrices Λ 1 and Λ 2 may not be ordered with respect to their magnitude. Hence, there is some permutation φ : {1, ..., N } → {1, ..., N } of the eigenvalues λ 1 , ..., λ N such that Λ 1 = diag λ φ(1) , ..., λ φ(m) and Λ 2 = diag λ φ(m+1) , ..., λ φ(N ) .…”

Section: A Proof Of Lemmamentioning

confidence: 99%

See 2 more Smart Citations

Clustering for epidemics on networks: a geometric approach

Prasse,

Devriendt,

Van Mieghem

2021

Preprint

View full text Add to dashboard Cite

Infectious diseases typically spread over a contact network with millions of individuals, whose sheer size is a tremendous challenge to analysing and controlling an epidemic outbreak. For some contact networks, it is possible to group individuals into clusters. A high-level description of the epidemic between a few clusters is considerably simpler than on an individual level. However, to cluster individuals, most studies rely on equitable partitions, a rather restrictive structural property of the contact network. In this work, we focus on Susceptible-Infected-Susceptible (SIS) epidemics, and our contribution is threefold. First, we propose a geometric approach to specify all networks for which an epidemic outbreak simplifies to the interaction of only a few clusters. Second, for the complete graph and any initial viral state vectors, we derive the closed-form solution of the nonlinear differential equations of the N -Intertwined Mean-Field Approximation (NIMFA) of the SIS process. Third, by relaxing the notion of equitable partitions, we derive low-complexity approximations and bounds for epidemics on arbitrary contact networks. Our results are an important step towards understanding and controlling epidemics on large networks.

show abstract

Section: Approximate Clusteringmentioning

confidence: 99%

Section: A Proof Of Lemmamentioning

confidence: 99%

Section: A Proof Of Lemmamentioning

confidence: 99%

See 1 more Smart Citation

Clustering for epidemics on networks: a geometric approach

Prasse,

Devriendt,

Van Mieghem

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Currently, researchers have developed different types of modeling approaches to estimate the relationship between COVID-19 and various risk factors in different socio-demographic and geospatial settings" (6]. "There has been much recent theoretical work revisiting, expanding, and studying dynamical and control properties of classical epidemic models to understand the spread of COVID-19 during quarantine and social distancing" [11,12,13,14,15] including studies of (integral) input to state stability, network stability of epidemic spread [16,17], and optimal control strategies for meta-population models. "These models have been used to predict the potential number of infected individuals and virus-related deaths, as well as to aid government agencies in decision-making" [18].…”

Section: Introductionmentioning

confidence: 99%

SEIR Model on the Review Impact of Social Distancing for COVID-19 Transmission Dynamics

Madaki,

Sambo

2024

Asian Res. J. Math.

View full text Add to dashboard Cite

The COVID-19 pandemic has had a huge influence on world health, with many countries enacting lockdowns and social distancing measures to help reduce transmission. However, the efficiency of these efforts is questionable, particularly in locations like as North East Nigeria, where specific socioeconomic and demographic characteristics can alter virus transmission dynamics. In this paper, we assess the pandemic in North East Nigeria by modifying the SIR to SEIR compartmental model, which incorporates data from the National Centre for Disease Control. We exposed that social distancing techniques like face masks, hand washing, and avoiding big gatherings are more successful than lockdowns in slowing the spread of COVID-19 in the region. Our findings suggest that future pandemic response plans should concentrate on social distancing measures that are both effective and feasible while avoiding the economic and social disruptions caused by lockdowns. Our work emphasizes the significance of specialized approaches to pandemic control in varied situations, including North East Nigeria.

show abstract

On the Stability of the Endemic Equilibrium of A Discrete-Time Networked Epidemic Model

Cited by 2 publications

References 6 publications

Clustering for epidemics on networks: a geometric approach

Clustering for epidemics on networks: a geometric approach

SEIR Model on the Review Impact of Social Distancing for COVID-19 Transmission Dynamics

Contact Info

Product

Resources

About