162 research outputs found
Computation of epidemic final size distributions
We develop a new methodology for the efficient computation of epidemic final
size distributions for a broad class of Markovian models. We exploit a
particular representation of the stochastic epidemic process to derive a method
which is both computationally efficient and numerically stable. The algorithms
we present are also physically transparent and so allow us to extend this
method from the basic SIR model to a model with a phase-type infectious period
and another with waning immunity. The underlying theory is applicable to many
Markovian models where we wish to efficiently calculate hitting probabilities.Comment: final published versio
Statistical physics and epidemic inference: methods and applications
L'abstract è presente nell'allegato / the abstract is in the attachmen
Epidemic mitigation by statistical inference from contact tracing data
Contact-tracing is an essential tool in order to mitigate the impact of
pandemic such as the COVID-19. In order to achieve efficient and scalable
contact-tracing in real time, digital devices can play an important role. While
a lot of attention has been paid to analyzing the privacy and ethical risks of
the associated mobile applications, so far much less research has been devoted
to optimizing their performance and assessing their impact on the mitigation of
the epidemic. We develop Bayesian inference methods to estimate the risk that
an individual is infected. This inference is based on the list of his recent
contacts and their own risk levels, as well as personal information such as
results of tests or presence of syndromes. We propose to use probabilistic risk
estimation in order to optimize testing and quarantining strategies for the
control of an epidemic. Our results show that in some range of epidemic
spreading (typically when the manual tracing of all contacts of infected people
becomes practically impossible, but before the fraction of infected people
reaches the scale where a lock-down becomes unavoidable), this inference of
individuals at risk could be an efficient way to mitigate the epidemic. Our
approaches translate into fully distributed algorithms that only require
communication between individuals who have recently been in contact. Such
communication may be encrypted and anonymized and thus compatible with privacy
preserving standards. We conclude that probabilistic risk estimation is capable
to enhance performance of digital contact tracing and should be considered in
the currently developed mobile applications.Comment: 21 pages, 7 figure
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
Belief Propagation approach to epidemics prediction on networks
In my thesis I study the problem of predicting the evolution of the epidemic spreading on networks when incomplete information, in form of a partial observation, is available. I focus on the irreversible process described by the discrete time version of the Susceptible-Infected-Recovered (SIR) model on networks. Because of its intrinsic stochasticity, forecasting the SIR process is very difficult, even if the structure of individuals contact pattern is known. In today's interconnected and interdependent society, infectious diseases pose the threat of a worldwide epidemic spreading, hence governments and public health systems maintain surveillance programs to report and control the emergence of new disease event ranging from the seasonal influenza to the more severe HIV or Ebola. When new infection cases are discovered in the population it is necessary to provide real-time forecasting of the epidemic evolution. However the incompleteness of accessible data and the intrinsic stochasticity of the contagion pose a major challenge.
The idea behind the work of my thesis is that the correct inference of the contagion process before the detection of the disease permits to use all the available information and, consequently, to obtain reliable predictions. I use the Belief Propagation approach for the prediction of SIR epidemics when a partial observation is available. In this case the reconstruction of the past dynamics can be efficiently performed by this method and exploited to analyze the evolution of the disease. Although the Belief Propagation provides exact results on trees, it turns out that is still a good approximation on general graphs. In this cases Belief Propagation may present convergence related issues, especially on dense networks. Moreover, since this approach is based on a very general principle, it can be adapted to study a wide range of issues, some of which I analyze in the thesis
Validity of Markovian modeling for transient memory-dependent epidemic dynamics
The initial transient phase of an emerging epidemic is of critical importance
for data-driven model building, model-based prediction of the epidemic trend,
and articulation of control/prevention strategies. In principle, quantitative
models for real-world epidemics need to be memory-dependent or non-Markovian,
but this presents difficulties for data collection, parameter estimation,
computation and analyses. In contrast, the difficulties do not arise in the
traditional Markovian models. To uncover the conditions under which Markovian
and non-Markovian models are equivalent for transient epidemic dynamics is
outstanding and of significant current interest. We develop a comprehensive
computational and analytic framework to establish that the transient-state
equivalence holds when the average generation time matches and average removal
time, resulting in minimal Markovian estimation errors in the basic
reproduction number, epidemic forecasting, and evaluation of control strategy.
Strikingly, the errors depend on the generation-to-removal time ratio but not
on the specific values and distributions of these times, and this universality
will further facilitate prediction rectification. Overall, our study provides a
general criterion for modeling memory-dependent processes using the Markovian
frameworks
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