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

Statistical Physics of Opinion and Social Conflict

The rise and development of opinion groups, just as their clash in social conflict, are notoriously difficult to study due to a complex interplay between structure and dynamics. The intricate feedback between psychological and sociological processes, tied with an ample variability of individual traits, makes these systems challenging both intellectually and methodologically. Yet regular patterns do emerge from the collective behavior of dissimilar people, seen in population and crime rates, in protest movements and the adoption of innovations. Statistical physics comes then as an apt and successful framework for their study, characterizing society as the common product of single wills, interactions among people and external effects. The work in this Thesis provides mathematical descriptions for the evolution of opinions in society, based on simple mechanisms of individual conduct and group influence. Such models abstract the inherent complexity of human behavior by reducing people to opinion variables spread over a network of social interactions, with variables and interactions changing in time at the pace of a handful of equations. Their macroscopic properties are interpreted as the emergence of social groups and of conflict between them due to opinion disagreement, and compared with small controlled experiments or with large online records of social activity. The extensive analysis of these models, both numerical and analytical, leads to a couple of generic observations on the link between opinion and social conflict. First, the emergence of consensual groups in society may be regulated by well-separated time scales of opinion dynamics and network evolution, and by a distribution of personality traits in the population. Our social environment can then be fragmented as more people turn against the collective mood, ultimately forming minorities as a response to external influence. Second, the exchange of views in collaborative tasks may lead not only to the rise and resolution of opinion issues, but to an intermediate state where conflicts appear periodically. In this way strife and cooperation, so much a part of human nature, can be emulated by surprisingly simple interactions among individuals

Halting SARS-CoV-2 by Targeting High-Contact Individuals

Network scientists have proposed that infectious diseases involving person-to-person transmission may be effectively halted by targeting interventions at a minority of highly connected individuals. Can this strategy be effective in combating a virus partly transmitted in close-range contact, as many believe SARS-CoV-2 to be? Effectiveness critically depends on high between-person variability in the number of close-range contacts. We analyze population survey data showing that indeed the distribution of close-range contacts across individuals is characterized by a small fraction of individuals reporting very high frequencies. Strikingly, we find that the average duration of contact is mostly invariant in the number of contacts, reinforcing the criticality of hubs. We simulate a population embedded in a network with empirically observed contact frequencies. Simulations show that targeting hubs robustly improves containment

A generalized simplicial model and its application

Higher-order structures, consisting of more than two individuals, provide a new perspective to reveal the missed non-trivial characteristics under pairwise networks. Prior works have researched various higher-order networks, but research for evaluating the effects of higher-order structures on network functions is still scarce. In this paper, we propose a framework to quantify the effects of higher-order structures (e.g., 2-simplex) and vital functions of complex networks by comparing the original network with its simplicial model. We provide a simplicial model that can regulate the quantity of 2-simplices and simultaneously fix the degree sequence. Although the algorithm is proposed to control the quantity of 2-simplices, results indicate it can also indirectly control simplexes more than 2-order. Experiments on spreading dynamics, pinning control, network robustness, and community detection have shown that regulating the quantity of 2-simplices changes network performance significantly. In conclusion, the proposed framework is a general and effective tool for linking higher-order structures with network functions. It can be regarded as a reference object in other applications and can deepen our understanding of the correlation between micro-level network structures and global network functions

Deleting edges to restrict the size of an epidemic in temporal networks.

Spreading processes on graphs are a natural model for a wide variety of real-world phenomena, including information or behaviour spread over social networks, biological diseases spreading over contact or trade networks, and the potential flow of goods over logistical infrastructure. Often, the networks over which these processes spread are dynamic in nature, and can be modeled with graphs whose structure is subject to discrete changes over time, i.e. with temporal graphs. Here, we consider temporal graphs in which edges are available at specified timesteps, and study the problem of deleting edges from a given temporal graph in order to reduce the number of vertices (temporally) reachable from a given starting point. This could be used to control the spread of a disease, rumour, etc. in a temporal graph. In particular, our aim is to find a temporal subgraph in which a process starting at any single vertex can be transferred to only a limited number of other vertices using a temporally-feasible path (i.e. a path, along which the times of the edge availabilities increase). We introduce a natural deletion problem for temporal graphs and we provide positive and negative results on its computational complexity, both in the traditional and the parameterised sense (subject to various natural parameters), as well as addressing the approximability of this problem

Modelling the social dynamics of contagion and discovery using dynamical processes on complex networks.

PhD Thesis.Complex networks have been successfully used to describe the social structure on top of which many real-world social processes take place. In this thesis, I focus on the development of network models that aim at capturing the fundamental mechanisms behind the dynamics of adoption of ideas, behaviours, or items. I start considering the transmission of a single idea from one individual to another, in an epidemic-like fashion. Recent evidence has shown that mechanisms of complex contagion can effectively capture the fundamental rules of social reinforcement and peer pressure proper of social systems. Along this line, I propose a model of complex recovery in which the social influence mechanism acts on the recovery rule rather than on the infection one, leading to explosive behaviours. Yet, in human communication, interactions can occur in groups. I thus expand the pairwise representation given by graphs using simplicial complexes instead. I develop a model of simplicial contagion, showing how the inclusion of these higher-order interactions can dramatically alter the spreading dynamics. I then consider an individual and model the dynamics of discovery as paths of sequential adoptions, with the first visit of an idea representing a novelty. Starting from the empirically observed dynamics of correlated novelties, according to which one discovery leads to another, I develop a model of biased random walks in which the exploration of the interlinked space of possible discoveries has the byproduct of influencing also the strengths of their connections. Balancing exploration and exploitation, the model reproduces the basic footprints of real-world innovation processes. Nevertheless, people do not live and work in isolation, and social ties can shape their behaviours. Thus, I consider interacting discovery processes to investigate how social interactions contribute to the collective emergence of new ideas and teamwork, and explorers can exploit opportunities coming from their social contacts

Epidemics on dynamic networks

In many populations, the patterns of potentially infectious contacts are transients that can be described as a network with dynamic links. The relative timescales of link and contagion dynamics and the characteristics that drive their tempos can lead to important differences to the static case. Here, we propose some essential nomenclature for their analysis, and then review the relevant literature. We describe recent advances in they apply to infection processes, considering all of the methods used to record, measure and analyse them, and their implications for disease transmission. Finally, we outline some key challenges and opportunities in the field. Keywords: Social network analysis, Disease models, Network metrics, Network dat