9 research outputs found
Fractional diffusion emulates a human mobility network during a simulated disease outbreak
From footpaths to flight routes, human mobility networks facilitate the
spread of communicable diseases. Control and elimination efforts depend on
characterizing these networks in terms of connections and flux rates of
individuals between contact nodes. In some cases, transport can be
parameterized with gravity-type models or approximated by a diffusive random
walk. As a alternative, we have isolated intranational commercial air traffic
as a case study for the utility of non-diffusive, heavy-tailed transport
models. We implemented new stochastic simulations of a prototypical
influenza-like infection, focusing on the dense, highly-connected United States
air travel network. We show that mobility on this network can be described
mainly by a power law, in agreement with previous studies. Remarkably, we find
that the global evolution of an outbreak on this network is accurately
reproduced by a two-parameter space-fractional diffusion equation, such that
those parameters are determined by the air travel network.Comment: 26 pages, 4 figure
The end time of SIS epidemics driven by random walks on edge-transitive graphs
Network epidemics is a ubiquitous model that can represent different
phenomena and finds applications in various domains. Among its various
characteristics, a fundamental question concerns the time when an epidemic
stops propagating. We investigate this characteristic on a SIS epidemic induced
by agents that move according to independent continuous time random walks on a
finite graph: Agents can either be infected (I) or susceptible (S), and
infection occurs when two agents with different epidemic states meet in a node.
After a random recovery time, an infected agent returns to state S and can be
infected again. The End of Epidemic (EoE) denotes the first time where all
agents are in state S, since after this moment no further infections can occur
and the epidemic stops.
For the case of two agents on edge-transitive graphs, we characterize EoE as
a function of the network structure by relating the Laplace transform of EoE to
the Laplace transform of the meeting time of two random walks. Interestingly,
this analysis shows a separation between the effect of network structure and
epidemic dynamics. We then study the asymptotic behavior of EoE (asymptotically
in the size of the graph) under different parameter scalings, identifying
regimes where EoE converges in distribution to a proper random variable or to
infinity. We also highlight the impact of different graph structures on EoE,
characterizing it under complete graphs, complete bipartite graphs, and rings
The Effect of Weekend Curfews on Epidemics: A Monte Carlo Simulation
The ongoing COVID-19 pandemic is being responded with various methods,
applying vaccines, experimental treatment options, total lockdowns or partial
curfews. Weekend curfews is one of the methods to reduce the amount of infected
persons and this method is practically applied in some countries such as
Turkey. In this study, the effect of weekend curfews on reducing the spread of
a contagious disease, such as COVID-19, is modeled using a Monte Carlo
algorithm with a hybrid lattice model. In the simulation setup, a fictional
country with three towns and 26,610 citizens were used as a model. Results
indicate that applying a weekend curfew reduces the active cases significantly
and is one of the efficient ways to fight the epidemic. The results also show
that applying personal precautions such as social distancing is important for
reducing the number of cases and deaths.Comment: Published version, 14 pages, 6 figure
Epidemic Thresholds with External Agents
We study the effect of external infection sources on phase transitions in
epidemic processes. In particular, we consider an epidemic spreading on a
network via the SIS/SIR dynamics, which in addition is aided by external agents
- sources unconstrained by the graph, but possessing a limited infection rate
or virulence. Such a model captures many existing models of externally aided
epidemics, and finds use in many settings - epidemiology, marketing and
advertising, network robustness, etc. We provide a detailed characterization of
the impact of external agents on epidemic thresholds. In particular, for the
SIS model, we show that any external infection strategy with constant virulence
either fails to significantly affect the lifetime of an epidemic, or at best,
sustains the epidemic for a lifetime which is polynomial in the number of
nodes. On the other hand, a random external-infection strategy, with rate
increasing linearly in the number of infected nodes, succeeds under some
conditions to sustain an exponential epidemic lifetime. We obtain similar sharp
thresholds for the SIR model, and discuss the relevance of our results in a
variety of settings.Comment: 12 pages, 2 figures (to appear in INFOCOM 2014
Viral processes by random walks on random regular graphs
We study the SIR epidemic model with infections carried by particles
making independent random walks on a random regular graph. Here we assume
, where is the number of vertices in the random graph,
and is some sufficiently small constant. We give an edge-weighted
graph reduction of the dynamics of the process that allows us to apply standard
results of Erd\H{o}s-R\'{e}nyi random graphs on the particle set. In
particular, we show how the parameters of the model give two thresholds: In the
subcritical regime, particles are infected. In the supercritical
regime, for a constant determined by the parameters of the
model, get infected with probability , and get
infected with probability . Finally, there is a regime in which all
particles are infected. Furthermore, the edge weights give information
about when a particle becomes infected. We exploit this to give a completion
time of the process for the SI case.Comment: Published in at http://dx.doi.org/10.1214/13-AAP1000 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Simulação escalável de epidemias em redes baseadas em passeios aleatórios com caracterização de transições de fase
Understanding how networks and dynamic processes relate is a important topic of research, and particularly in the context of epidemics spreading through networks. In this work, we consider the scenario where individuals move through a network. Contagion occur when two (or more) individuals are in the same location (vertex). The aim of this work is to build a scalable simulator to this type of epidemic and characterize the behavior of epidemic in function of the network structure. In particular, our results indicate that the simulator is scalable in network size, simulation time and number of individuals. In addiction, results on the epidemic indicate a phase transition in several parameters of the model, so that epidemics terminate quickly or last for a long time.Entender como redes e processos dinâmicos se relacionam é um tema central de pesquisa nos dias de hoje, e em particular no contexto de epidemias que se desdobram sobre redes. Neste trabalho, consideramos o cenário onde indivíduos se movimentam por uma rede, que representa a estrutura do espaço de movimentação. O contágio pode ocorrer quando dois (ou mais) indivíduos se encontram em um mesmo local (vértice). O objetivo deste trabalho é projetar e implementar um simulador de eventos discretos eficiente para este tipo de epidemia e caracterizar o comportamento da epidemia em função da estrutura da rede e parâmetros do modelo. Em particular, a avaliação teórica e empírica indicam que o simulador é escalável no tamanho da rede, tempo de simulação e número de indivíduos. Além disso, resultados obtidos sobre o comportamento de epidemias indicam uma transição de fase em diversos parâmetros do modelo, de forma que epidemias ou terminam rapidamente ou perduram por muito temp
Epidemic spreading and information dissemination in technological and social systems
In dieser Arbeit betrachten wir Probleme aus dem Bereich der Nachrichten- und Krankheitsverbreitung in dynamischen als auch statischen Strukturen aus dem Gebiet der technologischen und der sozialen Netzwerke. Als erste Fragestellung untersuchen wir, ob ein verteiltes Protokoll zur Nachrichtenverbreitung in Netzwerken mit Power Law Knotengradverteilung existiert, so dass sich die Knotengradverteilung nicht negativ bemerkbar macht. Wir präsentieren ein Protokoll, welches mit hoher Wahrscheinlichkeit nur O(log n) viele Runden mit O(n loglog n) vielen Nachrichten benötigt um alle n Knoten zu informieren. Als nächstes untersuchen wir wie Strategien zur Eindämmung einer solchen Ausbreitung aussehen könnten. Sei V der für die Ausbreitung der schädlichen Nachricht verantwortliche Prozess. Wir lassen V sich von jedem infizierten Knoten über eine konstante Anzahl von Verbindungen verbreiten. Unsere Strategie zur Bekämpfung von V wird an jedem infizierten Knoten nach einer konstanten Anzahl von Schritten aktiviert. Ist der minimale Knotengrad loglog n, so zeigen wir, dass die Immunisierung der direkten Nachbarschaft ausreicht um die Infektion mit hoher Wahrscheinlichkeit zu eliminieren. Ist der minimale Knotengrad eine Konstante und immunisiert jeder infizierte Knoten v alle Knoten in seiner O(log(d(v)))-Nachbarschaft, wobei d(v) den Knotengrad von Knoten v bezeichnet, lassen sich ähnliche Abschätzungen zeigen. Zudem betrachten wir eine Epidemie in einer städtischen Umgebung mit mobilen Einwohnern. Werden keinerlei Gegenmaßnahmen getroffen, so bleibt dennoch mit hoher Wahrscheinlichkeit ein polynomieller Anteil der Population von der Epidemie unberührt. Werden jedoch Gegenmaßnahmen genutzt, so werden mit Wahrscheinlichkeit 1-o(1) nur polylogarithmisch viele Individuen infiziert.In this thesis we consider the problems of information dissemination and epidemic spreading in dynamic as well as static technological and social networks. We start by wondering if there might be a fast decentralized dissemination protocol, such that a power law degree distribution does not slow down the dissemination process in the network. We present a protocol that informs all n nodes within O(log n) many rounds using O(n loglog n) many transmissions with high probability. But how do we design a counteracting dissemination process to combat the malicious one denoted by V? Suppose V uses a constant number of randomly chosen connections of each infected node to infect others for one time only and suppose that the counteracting dissemination process is activated on each infected node after a constant delay. We show that it suffices to immunize the neighborhood of each infected node, provided the minimum degree of the network is loglog n. Otherwise, if the minimum degree of the network is constant, we propose to immunize every node within O(log(d(v))) many hops of each infected node v, where d(v) denotes the degree of node v. Executing these strategies we prove that V does not infect more than o(n) many nodes until it is eliminated with high probability. Finally, we take mobility into account and examine an epidemic outbreak in an urban environment inhabited by mobile individuals on a small and on a large scale. Amongst others, we show that at least a polynomial fraction of the individuals remains uninfected even if they do not respond to the epidemic outbreak in any way. However, if the epidemic outbreak does influence the individual's behavioral pattern and certain countermeasures are applied, then only a polylogarithmic amount of individuals is infected until the epidemic is embanked with probability 1-o(1).Tag der Verteidigung: 24.10.2014Paderborn, Univ., Diss., 201