Periodic Reporting for period 2 - ViSioN (Virus Spread in Networks)
Okres sprawozdawczy: 2023-07-01 do 2024-12-31
Network science studies dynamic processes on graphs and considers the duality of process and graph as its fundamental cornerstone. For example, an epidemic can be described by a viral transmission process on a human contact network. If both components, process and graph, are known, then network science aims to compute the probability of infection for each node in the graph at a given time.
The current management of a pandemic (e.g. COVID-19) in most countries follows the recipes of the traditional field of epidemics and operates half blind: it focuses on the viral dynamics, but abstracts the contact graph to a complete graph in which each node is connected to each other; a so-called homogeneous population. The human contact network is not simply available somewhere, nor easy to measure, but it can be done in principle, via digital technology, e.g. mobile apps. Of course, solving the dual process-graph problem is more challenging than reducing the contact network to a complete graph, but the physics of virus spread in networks clearly points out that real epidemics follow the network science view.
In spite of the larger complexity and if society were convinced earlier that both process and graph are equally essential ingredients in any epidemic, then the Coronavirus crisis would have been under control much faster. Besides more measurements of both virus process and contact network, the recipe book of epidemic model ingredients, containing both process and graph, is also needed to manage an epidemic.
The high-level objective of Virus Spread in Networks (ViSioN) is to construct an entire set of models for virus spread with corresponding algorithms/software to optimally manage and control a next pandemic outbreak. Each research theme in ViSioN aims to push the current knowledge about epidemics in networks to the extreme boundary of theoretical tractability and computational feasibility to model and predict any outbreak as accurately as possible. The ViSioN modelling framework provides all ingredients, physical insight and understanding complemented with algorithms and computational methods, to manage and control any epidemic in the best possible way. Managing and controlling of an epidemic need accurate models, that are the pillars in an optimization problem with constraints, including also law, privacy and social limitations.
The rich underlying theory of the ViSioN framework can be exploited for other applications in network science, such as human brain networks
The current management of a pandemic (e.g. COVID-19) in most countries follows the recipes of the traditional field of epidemics and operates half blind: it focuses on the viral dynamics, but abstracts the contact graph to a complete graph in which each node is connected to each other; a so-called homogeneous population. The human contact network is not simply available somewhere, nor easy to measure, but it can be done in principle, via digital technology, e.g. mobile apps. Of course, solving the dual process-graph problem is more challenging than reducing the contact network to a complete graph, but the physics of virus spread in networks clearly points out that real epidemics follow the network science view.
In spite of the larger complexity and if society were convinced earlier that both process and graph are equally essential ingredients in any epidemic, then the Coronavirus crisis would have been under control much faster. Besides more measurements of both virus process and contact network, the recipe book of epidemic model ingredients, containing both process and graph, is also needed to manage an epidemic.
The high-level objective of Virus Spread in Networks (ViSioN) is to construct an entire set of models for virus spread with corresponding algorithms/software to optimally manage and control a next pandemic outbreak. Each research theme in ViSioN aims to push the current knowledge about epidemics in networks to the extreme boundary of theoretical tractability and computational feasibility to model and predict any outbreak as accurately as possible. The ViSioN modelling framework provides all ingredients, physical insight and understanding complemented with algorithms and computational methods, to manage and control any epidemic in the best possible way. Managing and controlling of an epidemic need accurate models, that are the pillars in an optimization problem with constraints, including also law, privacy and social limitations.
The rich underlying theory of the ViSioN framework can be exploited for other applications in network science, such as human brain networks
Markovian epidemics in any graph have been mathematically extended to a fractional setting by replacing the ordinary differential operator with a Caputo fractional operator. The strength is that the fractional non-Markovian generalization is analytically solvable. Roughly speaking, exponential time dependencies are generalized to Mittag-Leffler functions in a scaling parameter alpha. If alpha = 1, we retrieve the Markovian regime. Since the Mittag-Leffler distribution is, for small and realistic times, close to a Weibull distribution, measurements from real data may determine the important scaling parameter that quantifies the deviation from Markovian theory. Current mean-field models, used during e.g. the COVID-19 pandemic, are deduced from Markovian epidemics. Generally, the epidemic threshold, which is more precise than the basic reproduction number R0, is very sensitive to perturbations with non-Markovian dynamics. As most of us still recall from the last pandemic, the basic reproduction number R0 was the major control parameter used by governmental agencies. Despites the beautiful mathematical analysis, the physics of fractional process extensions are still insufficiently understood: we cannot precisely simulate the processes to achieve the fractional results. This challenge stand as a main problem for future ViSioN research.
The second pilar concerns the human contact network, that is changing over time and is not a fixed graph. A first result, based on system's theory and periodicity, is able to produce any given graph sequence exactly, but does not lead to good predictions (due to the fact that one finite-in-time realization of the human contact process contains insufficient information to reproduce the entire process). A second result concerns an estimate of the boundary between the time-scale of the epidemic process and the time-scale of the human contact process. In particular, if the human contact process changes much slower than the epidemics, we can regard the graph as fixed and the classical theory applies. If both dynamics are comparable in time, then no obvious simplifications can be made. The boundary estimate determines the highest time-scale of the contact process that still can be regarded as fixed.
A third achievement, dealing with incomplete information, is integrating the epidemics in a network model into a Metropolis algorithm. Many epidemiological data are time series: incidence or prevalence tabulated on a daily, weekly, or monthly basis. Epidemiological data are often incomplete because they cover only a small proportion of the population or because the time resolution is too coarse. The Metropolis algorithm takes these incomplete data as inputs and gives as an output the probable contact graphs and infectivity of the virus. With these outputs, we can construct probabilistic forecasts about the future state of an epidemic in similar language to weather forecasts: e.g. a 90% chance that incidence will decrease this week. With sufficient information, we can even recover the true contact graph.
At last, we have started to explore a generative model for contact graphs, based on the notion of random walkers on a Markov graph. Its properties will be further explored.
The second pilar concerns the human contact network, that is changing over time and is not a fixed graph. A first result, based on system's theory and periodicity, is able to produce any given graph sequence exactly, but does not lead to good predictions (due to the fact that one finite-in-time realization of the human contact process contains insufficient information to reproduce the entire process). A second result concerns an estimate of the boundary between the time-scale of the epidemic process and the time-scale of the human contact process. In particular, if the human contact process changes much slower than the epidemics, we can regard the graph as fixed and the classical theory applies. If both dynamics are comparable in time, then no obvious simplifications can be made. The boundary estimate determines the highest time-scale of the contact process that still can be regarded as fixed.
A third achievement, dealing with incomplete information, is integrating the epidemics in a network model into a Metropolis algorithm. Many epidemiological data are time series: incidence or prevalence tabulated on a daily, weekly, or monthly basis. Epidemiological data are often incomplete because they cover only a small proportion of the population or because the time resolution is too coarse. The Metropolis algorithm takes these incomplete data as inputs and gives as an output the probable contact graphs and infectivity of the virus. With these outputs, we can construct probabilistic forecasts about the future state of an epidemic in similar language to weather forecasts: e.g. a 90% chance that incidence will decrease this week. With sufficient information, we can even recover the true contact graph.
At last, we have started to explore a generative model for contact graphs, based on the notion of random walkers on a Markov graph. Its properties will be further explored.
The epidemic infection state of any node/person in a network can be deduced accurately from one realization (measurement of the infection probability per node over time) of an epidemic. However, almost nothing can be told about the underlying contact graph. This deep and important insight [Prasse, B. and P. Van Mieghem, 2022, "Predicting network dynamics without requiring the knowledge of the interaction graph", Proceedings of the National Academy of Sciences (PNAS), Vol. 119, No. 44, e2205517119. (DOI pnas.2205517119)] has arisen during the Covid pandemic, after several papers on prediction (see website PI). It means that, even with all the power of artificial intelligence (AI) and even knowing the precise epidemic process, reconstructing the human contact graph from a single outbreak of an epidemic, is impossible. On the other hand, prediction of the nodal infection probability during an epidemic is possible without the precise knowledge of a fixed contact graph.
The second contribution [Ma, L, Z. Qiu, P. Van Mieghem and M. Kitsak, 2024, "Reporting delays: a widely neglected impact factor in COVID-19 forecasts", PNAS Nexus, Vol. 3, No. 6 (June), pgae204. ( DOI: 10.1093/pnasnexus/pgae204)] was the first to demonstrate that different measurements (e.g. of the number of people in a hospital, number of deaths, number of infected in a town, etc.), which are daily reported, but do not reflect the measurement at that day due to delay in reporting/measurements can be corrected. We demonstrate how and show that the corrected data provides a much clearer reflection of the actual epidemic.
The second contribution [Ma, L, Z. Qiu, P. Van Mieghem and M. Kitsak, 2024, "Reporting delays: a widely neglected impact factor in COVID-19 forecasts", PNAS Nexus, Vol. 3, No. 6 (June), pgae204. ( DOI: 10.1093/pnasnexus/pgae204)] was the first to demonstrate that different measurements (e.g. of the number of people in a hospital, number of deaths, number of infected in a town, etc.), which are daily reported, but do not reflect the measurement at that day due to delay in reporting/measurements can be corrected. We demonstrate how and show that the corrected data provides a much clearer reflection of the actual epidemic.