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Article ; Online: Predicting network dynamics without requiring the knowledge of the interaction graph.

Prasse, Bastian / Van Mieghem, Piet

Proceedings of the National Academy of Sciences of the United States of America

2022 Volume 119, Issue 44, Page(s) e2205517119

Abstract: A network consists of two interdependent parts: the network topology or graph, consisting of the links between nodes and the network dynamics, specified by some governing equations. A crucial challenge is the prediction of dynamics on networks, such as ... ...

Abstract	A network consists of two interdependent parts: the network topology or graph, consisting of the links between nodes and the network dynamics, specified by some governing equations. A crucial challenge is the prediction of dynamics on networks, such as forecasting the spread of an infectious disease on a human contact network. Unfortunately, an accurate prediction of the dynamics seems hardly feasible, because the network is often complicated and unknown. In this work, given past observations of the dynamics on a fixed graph, we show the contrary: Even without knowing the network topology, we can predict the dynamics. Specifically, for a general class of deterministic governing equations, we propose a two-step prediction algorithm. First, we obtain a surrogate network by fitting past observations of every nodal state to the dynamical model. Second, we iterate the governing equations on the surrogate network to predict the dynamics. Surprisingly, even though there is no similarity between the surrogate topology and the true topology, the predictions are accurate, for a considerable prediction time horizon, for a broad range of observation times, and in the presence of a reasonable noise level. The true topology is not needed for predicting dynamics on networks, since the dynamics evolve in a subspace of astonishingly low dimension compared to the size and heterogeneity of the graph. Our results constitute a fresh perspective on the broad field of nonlinear dynamics on complex networks.
MeSH term(s)	Humans ; Algorithms ; Nonlinear Dynamics
Language	English
Publishing date	2022-10-24
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	209104-5
ISSN	1091-6490 ; 0027-8424
ISSN (online)	1091-6490
ISSN	0027-8424
DOI	10.1073/pnas.2205517119
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Article ; Online: Transition from time-variant to static networks: Timescale separation in N-intertwined mean-field approximation of susceptible-infectious-susceptible epidemics.

Persoons, Robin / Sensi, Mattia / Prasse, Bastian / Van Mieghem, Piet

Physical review. E

2024 Volume 109, Issue 3-1, Page(s) 34308

Abstract: We extend the N-intertwined mean-field approximation (NIMFA) for the susceptible-infectious-susceptible (SIS) epidemiological process to time-varying networks. Processes on time-varying networks are often analyzed under the assumption that the process ... ...

Abstract	We extend the N-intertwined mean-field approximation (NIMFA) for the susceptible-infectious-susceptible (SIS) epidemiological process to time-varying networks. Processes on time-varying networks are often analyzed under the assumption that the process and network evolution happen on different timescales. This approximation is called timescale separation. We investigate timescale separation between disease spreading and topology updates of the network. We introduce the transition times [under T]̲(r) and T[over ¯](r) as the boundaries between the intermediate regime and the annealed (fast changing network) and quenched (static network) regimes, respectively, for a fixed accuracy tolerance r. By analyzing the convergence of static NIMFA processes, we analytically derive upper and lower bounds for T[over ¯](r). Our results provide insights and bounds on the time of convergence to the steady state of the static NIMFA SIS process. We show that, under our assumptions, the upper-transition time T[over ¯](r) is almost entirely determined by the basic reproduction number R_{0} of the network. The value of the upper-transition time T[over ¯](r) around the epidemic threshold is large, which agrees with the current understanding that some real-world epidemics cannot be approximated with the aforementioned timescale separation.
Language	English
Publishing date	2024-04-18
Publishing country	United States
Document type	Journal Article
ZDB-ID	2844562-4
ISSN	2470-0053 ; 2470-0045
ISSN (online)	2470-0053
ISSN	2470-0045
DOI	10.1103/PhysRevE.109.034308
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Article ; Online: Accuracy of predicting epidemic outbreaks.

Prasse, Bastian / Achterberg, Massimo A / Van Mieghem, Piet

Physical review. E

2022 Volume 105, Issue 1-1, Page(s) 14302

Abstract: During the outbreak of a virus, perhaps the greatest concern is the future evolution of the epidemic: How many people will be infected and which regions will be affected the most? The accurate prediction of an epidemic enables targeted disease ... ...

Abstract	During the outbreak of a virus, perhaps the greatest concern is the future evolution of the epidemic: How many people will be infected and which regions will be affected the most? The accurate prediction of an epidemic enables targeted disease countermeasures (e.g., allocating medical staff and quarantining). But when can we trust the prediction of an epidemic to be accurate? In this work we consider susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemics on networks with time-invariant spreading parameters. (For time-varying spreading parameters, our results correspond to an optimistic scenario for the predictability of epidemics.) Our contribution is twofold. First, accurate long-term predictions of epidemics are possible only after the peak rate of new infections. Hence, before the peak, only short-term predictions are reliable. Second, we define an exponential growth metric, which quantifies the predictability of an epidemic. In particular, even without knowing the future evolution of the epidemic, the growth metric allows us to compare the predictability of an epidemic at different points in time. Our results are an important step towards understanding when and why epidemics can be predicted reliably.
Language	English
Publishing date	2022-02-23
Publishing country	United States
Document type	Journal Article
ZDB-ID	2844562-4
ISSN	2470-0053 ; 2470-0045
ISSN (online)	2470-0053
ISSN	2470-0045
DOI	10.1103/PhysRevE.105.014302
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Article ; Online: Time-dependent solution of the NIMFA equations around the epidemic threshold.

Prasse, Bastian / Van Mieghem, Piet

Journal of mathematical biology

2020 Volume 81, Issue 6-7, Page(s) 1299–1355

Abstract: The majority of epidemic models are described by non-linear differential equations which do not have a closed-form solution. Due to the absence of a closed-form solution, the understanding of the precise dynamics of a virus is rather limited. We solve ... ...

Abstract	The majority of epidemic models are described by non-linear differential equations which do not have a closed-form solution. Due to the absence of a closed-form solution, the understanding of the precise dynamics of a virus is rather limited. We solve the differential equations of the N-intertwined mean-field approximation of the susceptible-infected-susceptible epidemic process with heterogeneous spreading parameters around the epidemic threshold for an arbitrary contact network, provided that the initial viral state vector is small or parallel to the steady-state vector. Numerical simulations demonstrate that the solution around the epidemic threshold is accurate, also above the epidemic threshold and for general initial viral states that are below the steady-state.
MeSH term(s)	Communicable Diseases/epidemiology ; Disease Susceptibility/epidemiology ; Epidemics ; Humans ; Models, Theoretical ; Time ; Virus Diseases/epidemiology
Language	English
Publishing date	2020-09-22
Publishing country	Germany
Document type	Journal Article
ZDB-ID	187101-8
ISSN	1432-1416 ; 0303-6812
ISSN (online)	1432-1416
ISSN	0303-6812
DOI	10.1007/s00285-020-01542-6
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Article ; Online: Predicting subnational incidence of COVID-19 cases and deaths in EU countries.

Robert, Alexis / Chapman, Lloyd A C / Grah, Rok / Niehus, Rene / Sandmann, Frank / Prasse, Bastian / Funk, Sebastian / Kucharski, Adam J

BMC infectious diseases

2024 Volume 24, Issue 1, Page(s) 204

Abstract: Background: Recurring COVID-19 waves highlight the need for tools able to quantify transmission risk, and identify geographical areas at risk of outbreaks. Local outbreak risk depends on complex immunity patterns resulting from previous infections, ... ...

Abstract	Background: Recurring COVID-19 waves highlight the need for tools able to quantify transmission risk, and identify geographical areas at risk of outbreaks. Local outbreak risk depends on complex immunity patterns resulting from previous infections, vaccination, waning and immune escape, alongside other factors (population density, social contact patterns). Immunity patterns are spatially and demographically heterogeneous, and are challenging to capture in country-level forecast models. Methods: We used a spatiotemporal regression model to forecast subnational case and death counts and applied it to three EU countries as test cases: France, Czechia, and Italy. Cases in local regions arise from importations or local transmission. Our model produces age-stratified forecasts given age-stratified data, and links reported case counts to routinely collected covariates (e.g. test number, vaccine coverage). We assessed the predictive performance of our model up to four weeks ahead using proper scoring rules and compared it to the European COVID-19 Forecast Hub ensemble model. Using simulations, we evaluated the impact of variations in transmission on the forecasts. We developed an open-source RShiny App to visualise the forecasts and scenarios. Results: At a national level, the median relative difference between our median weekly case forecasts and the data up to four weeks ahead was 25% (IQR: 12-50%) over the prediction period. The accuracy decreased as the forecast horizon increased (on average 24% increase in the median ranked probability score per added week), while the accuracy of death forecasts was more stable. Beyond two weeks, the model generated a narrow range of likely transmission dynamics. The median national case forecasts showed similar accuracy to forecasts from the European COVID-19 Forecast Hub ensemble model, but the prediction interval was narrower in our model. Generating forecasts under alternative transmission scenarios was therefore key to capturing the range of possible short-term transmission dynamics. Discussion: Our model captures changes in local COVID-19 outbreak dynamics, and enables quantification of short-term transmission risk at a subnational level. The outputs of the model improve our ability to identify areas where outbreaks are most likely, and are available to a wide range of public health professionals through the Shiny App we developed.
MeSH term(s)	Humans ; COVID-19/epidemiology ; Incidence ; Disease Outbreaks ; Public Health ; Forecasting
Language	English
Publishing date	2024-02-14
Publishing country	England
Document type	Journal Article
ZDB-ID	2041550-3
ISSN	1471-2334 ; 1471-2334
ISSN (online)	1471-2334
ISSN	1471-2334
DOI	10.1186/s12879-024-08986-x
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Article ; Online: Clustering for epidemics on networks: A geometric approach.

Prasse, Bastian / Devriendt, Karel / Van Mieghem, Piet

Chaos (Woodbury, N.Y.)

2021 Volume 31, Issue 6, Page(s) 63115

Abstract: Infectious diseases typically spread over a contact network with millions of individuals, whose sheer size is a tremendous challenge to analyzing and controlling an epidemic outbreak. For some contact networks, it is possible to group individuals into ... ...

Abstract	Infectious diseases typically spread over a contact network with millions of individuals, whose sheer size is a tremendous challenge to analyzing 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 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 toward understanding and controlling epidemics on large networks.
MeSH term(s)	Cluster Analysis ; Communicable Diseases/epidemiology ; Disease Susceptibility/epidemiology ; Epidemics ; Humans ; Models, Biological ; Models, Theoretical
Language	English
Publishing date	2021-07-09
Publishing country	United States
Document type	Journal Article
ZDB-ID	1472677-4
ISSN	1089-7682 ; 1054-1500
ISSN (online)	1089-7682
ISSN	1054-1500
DOI	10.1063/5.0048779
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Book ; Online: Transition from time-variant to static networks

Persoons, Robin / Sensi, Mattia / Prasse, Bastian / Van Mieghem, Piet

timescale separation in NIMFA SIS

2023

Abstract: We extend the N-intertwined mean-field approximation (NIMFA) for the Susceptible-Infectious-Susceptible (SIS) epidemiological process to time-varying networks. We investigate the timescale separation between disease spreading and topology updates of the ... ...

Abstract	We extend the N-intertwined mean-field approximation (NIMFA) for the Susceptible-Infectious-Susceptible (SIS) epidemiological process to time-varying networks. We investigate the timescale separation between disease spreading and topology updates of the network. We introduce the transition times $\mathrm{\underline{T}}(r)$ and $\mathrm{\overline{T}}(r)$ as the boundaries between the intermediate regime and the annealed (fast changing network) and quenched (static network) regimes, respectively. By analysing the convergence of static NIMFA processes, we analytically derive upper and lower bounds for $\mathrm{\overline{T}}(r)$. We then illustrate these bounds numerically and we compare our simulations with a heuristic alternative for $\mathrm{\overline{T}}(r)$. We show that, under our assumptions, the upper transition time $\mathrm{\overline{T}}(r)$ is almost entirely determined by the basic reproduction number $R_0$. The value of the upper transition time $\mathrm{\overline{T}}(r)$ around the epidemic threshold is large, which agrees with the current understanding that some real-world epidemics cannot be approximated with the aforementioned timescale separation. Comment: 27 pages, 9 figures
Keywords	Mathematics - Dynamical Systems ; 92D30 ; 92D25 ; 34A34
Subject code	612
Publishing date	2023-05-21
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article: Predicting Dynamics on Networks Hardly Depends on the Topology

Prasse, Bastian / Mieghem, Piet Van

Abstract: Processes on networks consist of two interdependent parts: the network topology, consisting of the links between nodes, and the dynamics, specified by some governing equations. This work considers the prediction of the future dynamics on an unknown ... ...

Abstract	Processes on networks consist of two interdependent parts: the network topology, consisting of the links between nodes, and the dynamics, specified by some governing equations. This work considers the prediction of the future dynamics on an unknown network, based on past observations of the dynamics. For a general class of governing equations, we propose a prediction algorithm which infers the network as an intermediate step. Inferring the network is impossible in practice, due to a dramatically ill-conditioned linear system. Surprisingly, a highly accurate prediction of the dynamics is possible nonetheless: Even though the inferred network has no topological similarity with the true network, both networks result in practically the same future dynamics.
Keywords	covid19
Publisher	ArXiv
Document type	Article
Database	COVID19

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Article: Mobile smartphone tracing can detect almost all SARS-CoV-2 infections

Prasse, Bastian / Mieghem, Piet Van

Abstract: Currently, many countries are considering the introduction of tracing software on mobile smartphones with the main purpose to inform and alarm the mobile app user. Here, we demonstrate that, in addition to alarming and informing, mobile tracing can ... ...

Abstract	Currently, many countries are considering the introduction of tracing software on mobile smartphones with the main purpose to inform and alarm the mobile app user. Here, we demonstrate that, in addition to alarming and informing, mobile tracing can detect nearly all users that are infected by SARS-CoV-2. Our algorithm BETIS (Bayesian Estimation for Tracing Infection States) makes use of self-reports of the user's health status. Then, BETIS guarantees that almost all SARS-CoV-2 infections of the group of users can be detected. Furthermore, BETIS estimates the virus prevalence in the whole population, consisting of users and non-users. BETIS is based on a hidden Markov epidemic model and recursive Bayesian filtering. The potential that mobile tracing apps, in addition to medical testing and quarantining, can eradicate COVID-19 may persuade citizens to trade-off privacy against public health.
Keywords	covid19
Publisher	ArXiv
Document type	Article
Database	COVID19

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Book ; Online: Mobile smartphone tracing can detect almost all SARS-CoV-2 infections

Prasse, Bastian / Van Mieghem, Piet

2020

Abstract	Currently, many countries are considering the introduction of tracing software on mobile smartphones with the main purpose to inform and alarm the mobile app user. Here, we demonstrate that, in addition to alarming and informing, mobile tracing can detect nearly all users that are infected by SARS-CoV-2. Our algorithm BETIS (Bayesian Estimation for Tracing Infection States) makes use of self-reports of the user's health status. Then, BETIS guarantees that almost all SARS-CoV-2 infections of the group of users can be detected. Furthermore, BETIS estimates the virus prevalence in the whole population, consisting of users and non-users. BETIS is based on a hidden Markov epidemic model and recursive Bayesian filtering. The potential that mobile tracing apps, in addition to medical testing and quarantining, can eradicate COVID-19 may persuade citizens to trade-off privacy against public health.
Keywords	Computer Science - Social and Information Networks ; Physics - Physics and Society ; Quantitative Biology - Populations and Evolution ; covid19
Subject code	005
Publishing date	2020-06-25
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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