Time-dependent solution of the NIMFA equations around the epidemic threshold

Prasse, Bastian; Mieghem, Piet Van

doi:10.1007/s00285-020-01542-6

Cited by 27 publications

(25 citation statements)

References 35 publications

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“…On certain networks, the stationary states x of system (1) can coincide with eigenvectors of the network Laplacian Q. As developed in detail in Prasse and Van Mieghem (2020) for contagion dynamics, this allows for an exact solution of the state evolution. Applied to our system, we find the following result:…”

Section: Exact Solutionsmentioning

confidence: 99%

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Nonlinear Network Dynamics with Consensus–Dissensus Bifurcation

Devriendt

Lambiotte

2021

J Nonlinear Sci

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We study a nonlinear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and the dominating behaviour of a general class of nonlinear dynamical systems. The equilibrium behaviour of the system exhibits a global bifurcation with respect to the system parameter, with a transition from a single constant stationary state to a large range of possible stationary states. Our main result classifies the stability of (a subset of) these stationary states in terms of the effective resistances of the underlying graph; this classification clearly discerns the influence of the specific topology in which the local pitchfork systems are interconnected. We further describe exact solutions for graphs with external equitable partitions and characterize the basins of attraction on tree graphs. Our technical analysis is supplemented by a study of the system on a number of prototypical networks: tree graphs, complete graphs and barbell graphs. We describe a number of qualitative properties of the dynamics on these networks, with promising modelling consequences.

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Section: Exact Solutionsmentioning

confidence: 99%

“…The authors would like to thank Christian Bick, Alain Goriely and Michael Schaub for helpful discussions, suggestions and references, Bastian Prasse for suggesting to study the exact solutions as in Prasse and Van Mieghem (2020) and Marc Homs Dones for carefully reading the manuscript. K.D.…”

Section: Acknowledgementsmentioning

confidence: 99%

Nonlinear Network Dynamics with Consensus–Dissensus Bifurcation

Devriendt

Lambiotte

2021

J Nonlinear Sci

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“…Given the level of granularity provided by contact networks, along with the difficulty in capturing agent-specific conditions through more traditional epidemiological methods (i.e. compartmental modeling for the population at large), we model the state of each agent in the institution probabilistically using N -Intertwined Mean-Field Approximation (NIMFA) [17]. A widely-used and computationally-efficient approximation for the true stochastic process, the NIMFA approximates the joint probability of some agent i being susceptible and some other agent j being infectious as the product of the marginals.…”

Section: A Methodsmentioning

confidence: 99%

“…For these agents, we modeled viral states probabilistically via an adapted N -intertwined mean-field approximation (NIMFA). In its original form, the NIMFA states that at a given time, the rate of transmission from agent j to adjacent agent i is proportional to the product of the marginal probabilities that i is susceptible and that j is infectious [17,18]. This approach offers the flexibility to encompass a wide range of epidemiological compartments while capturing the granularity of graphical contact networks [13,21,25].…”

Section: Epidemiological Modelmentioning

confidence: 99%

The Case for Altruism in Institutional Diagnostic Testing

Specht

Sani

Botti-Lodovico

et al. 2021

Preprint

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Amid COVID-19, many institutions deployed vast resources to test their members regularly for safe reopening. This self-focused approach, however, not only overlooks surrounding communities but also remains blind to community transmission that could breach the institution. To test the relative merits of a more altruistic strategy, we built an epidemiological model that assesses the differential impact on case counts when institutions instead allocate a proportion of their tests to members' close contacts in the larger community. We found that testing outside the institution benefits the institution in all plausible circumstances, with the optimal proportion of tests to use externally landing at 45% under baseline model parameters. Our results were robust to local prevalence, secondary attack rate, testing capacity, and contact reporting level, yielding a range of optimal community testing proportions from 18% to 58%. The model performed best under the assumption that community contacts are known to the institution; however, it still demonstrated a significant benefit even without complete knowledge of the contact network.

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“…The use of this surrogate measure allows for a fast exploration of the space of possible resections, which is followed by a slower analysis using the SI dynamics to fine-tune the solution and measure the actual decrease in seizure propagation. In future studies exact results of the SI propagation on a network could also be implemented to avoid the need for random search methods [75,88], taking advantage of the mathematical tractability of the SI model.…”

Section: Modelling Resectionsmentioning

confidence: 99%

Epidemic models characterize seizure propagation and the effects of epilepsy surgery in individualized brain networks based on MEG and invasive EEG recordings

Millán

Straaten

Stam

et al. 2021

Preprint

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Background Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients. However, seizure-freedom is currently achieved in only 2/3 of the patients after surgery. In this study we have developed an individualized computational model based on functional brain networks to explore seizure propagation and the efficacy of different virtual resections. Eventually, the goal is to obtain individualized models to optimize resection strategy and outcome. Methods We have modelled seizure propagation as an epidemic process using the susceptible-infected (SI) model on individual functional networks derived from presurgical MEG. We included 10 patients who had received epilepsy surgery and for whom the surgery outcome at least one year after surgery was known. The model parameters were tuned in order to reproduce the patient-specific seizure propagation patterns as recorded with invasive EEG. We defined a personalized search algorithm that combined structural and dynamical information to find resections that maximally decreased seizure propagation for a given resection size. The optimal resection for each patient was defined as the smallest resection leading to at least a $90\%$ reduction in seizure propagation. Results The individualized model reproduced the basic aspects of seizure propagation for 9 out of 10 patients when using the resection area as the origin of epidemic spreading, and for 10 out of 10 patients with an alternative definition of the seed region. We found that, for 7 patients, the optimal resection was smaller than the resection area, and for 4 patients we also found that a resection smaller than the resection area could lead to a 100% decrease in propagation. Moreover, for two cases these alternative resections included nodes outside the resection area. Conclusion Epidemic spreading models fitted with patient specific data can capture the fundamental aspects of clinically observed seizure propagation, and can be used to test virtual resections in silico. Combined with optimization algorithms, smaller or alternative resection strategies, that are individually targeted for each patient, can be determined with the ultimate goal to improve surgery outcome.

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Time-dependent solution of the NIMFA equations around the epidemic threshold

Cited by 27 publications

References 35 publications

Nonlinear Network Dynamics with Consensus–Dissensus Bifurcation

Nonlinear Network Dynamics with Consensus–Dissensus Bifurcation

The Case for Altruism in Institutional Diagnostic Testing

Epidemic models characterize seizure propagation and the effects of epilepsy surgery in individualized brain networks based on MEG and invasive EEG recordings

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