Contact tracing and epidemics control in social networks

A generalization of the standard susceptible-infectious-removed (SIR) stochastic model for epidemics in sparse random networks is introduced which incorporates contact tracing in addition to random screening. We propose a deterministic mean-field description which yields quantitative agreement with stochastic simulations on random graphs. We also analyze the role of contact tracing in epidemics control in small-world networks and show that its effectiveness grows as the rewiring probability is reduced.Comment: 4 pages, 4 figures, submitted to PR

The Behavior of Epidemics under Bounded Susceptibility

We investigate the sensitivity of epidemic behavior to a bounded susceptibility constraint -- susceptible nodes are infected by their neighbors via the regular SI/SIS dynamics, but subject to a cap on the infection rate. Such a constraint is motivated by modern social networks, wherein messages are broadcast to all neighbors, but attention spans are limited. Bounded susceptibility also arises in distributed computing applications with download bandwidth constraints, and in human epidemics under quarantine policies. Network epidemics have been extensively studied in literature; prior work characterizes the graph structures required to ensure fast spreading under the SI dynamics, and long lifetime under the SIS dynamics. In particular, these conditions turn out to be meaningful for two classes of networks of practical relevance -- dense, uniform (i.e., clique-like) graphs, and sparse, structured (i.e., star-like) graphs. We show that bounded susceptibility has a surprising impact on epidemic behavior in these graph families. For the SI dynamics, bounded susceptibility has no effect on star-like networks, but dramatically alters the spreading time in clique-like networks. In contrast, for the SIS dynamics, clique-like networks are unaffected, but star-like networks exhibit a sharp change in extinction times under bounded susceptibility. Our findings are useful for the design of disease-resistant networks and infrastructure networks. More generally, they show that results for existing epidemic models are sensitive to modeling assumptions in non-intuitive ways, and suggest caution in directly using these as guidelines for real systems

Optimal curing policy for epidemic spreading over a community network with heterogeneous population

The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of allocating recovery resources among the population, at the lowest cost possible to prevent the epidemic from persisting indefinitely in the network. Specifically, we analyze a susceptible-infected-susceptible epidemic process spreading over a weighted graph, by means of a first-order mean-field approximation. First, we describe the influence of the contact network on the dynamics of the epidemics among a heterogeneous population, that is possibly divided into communities. For the case of a community network, our investigation relies on the graph-theoretical notion of equitable partition; we show that the epidemic threshold, a key measure of the network robustness against epidemic spreading, can be determined using a lower-dimensional dynamical system. Exploiting the computation of the epidemic threshold, we determine a cost-optimal curing policy by solving a convex minimization problem, which possesses a reduced dimension in the case of a community network. Lastly, we consider a two-level optimal curing problem, for which an algorithm is designed with a polynomial time complexity in the network size.Comment: to be published on Journal of Complex Network

Epidemic Spreading in Random Rectangular Networks

The use of network theory to model disease propagation on populations introduces important elements of reality to the classical epidemiological models. The use of random geometric graphs (RGG) is one of such network models that allows for the consideration of spatial properties on disease propagation. In certain real-world scenarios -like in the analysis of a disease propagating through plants- the shape of the plots and fields where the host of the disease is located may play a fundamental role on the propagation dynamics. Here we consider a generalization of the RGG to account for the variation of the shape of the plots/fields where the hosts of a disease are allocated. We consider a disease propagation taking place on the nodes of a random rectangular graph (RRG) and we consider a lower bound for the epidemic threshold of a Susceptible-Infected-Susceptible (SIS) or Susceptible-Infected-Recovered (SIR) model on these networks. Using extensive numerical simulations and based on our analytical results we conclude that (ceteris paribus) the elongation of the plot/field in which the nodes are distributed makes the network more resilient to the propagation of a disease due to the fact that the epidemic threshold increases with the elongation of the rectangle. These results agree with accumulated empirical evidence and simulation results about the propagation of diseases on plants in plots/fields of the same area and different shapes.Comment: Version 4, 13 pages, 6 figures, 44 ref

A statistical network analysis of the HIV/AIDS epidemics in Cuba

The Cuban contact-tracing detection system set up in 1986 allowed the reconstruction and analysis of the sexual network underlying the epidemic (5,389 vertices and 4,073 edges, giant component of 2,386 nodes and 3,168 edges), shedding light onto the spread of HIV and the role of contact-tracing. Clustering based on modularity optimization provides a better visualization and understanding of the network, in combination with the study of covariates. The graph has a globally low but heterogeneous density, with clusters of high intraconnectivity but low interconnectivity. Though descriptive, our results pave the way for incorporating structure when studying stochastic SIR epidemics spreading on social networks

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

Characterizing the Initial Phase of Epidemic Growth on some Empirical Networks

A key parameter in models for the spread of infectious diseases is the basic reproduction number $R_0$, which is the expected number of secondary cases a typical infected primary case infects during its infectious period in a large mostly susceptible population. In order for this quantity to be meaningful, the initial expected growth of the number of infectious individuals in the large-population limit should be exponential. We investigate to what extent this assumption is valid by performing repeated simulations of epidemics on selected empirical networks, viewing each epidemic as a random process in discrete time. The initial phase of each epidemic is analyzed by fitting the number of infected people at each time step to a generalised growth model, allowing for estimating the shape of the growth. For reference, similar investigations are done on some elementary graphs such as integer lattices in different dimensions and configuration model graphs, for which the early epidemic behaviour is known. We find that for the empirical networks tested in this paper, exponential growth characterizes the early stages of the epidemic, except when the network is restricted by a strong low-dimensional spacial constraint, such as is the case for the two-dimensional square lattice. However, on finite integer lattices of sufficiently high dimension, the early development of epidemics shows exponential growth.Comment: To be included in the conference proceedings for SPAS 2017 (International Conference on Stochastic Processes and Algebraic Structures), October 4-6, 201

Worm Epidemics in Wireless Adhoc Networks

A dramatic increase in the number of computing devices with wireless communication capability has resulted in the emergence of a new class of computer worms which specifically target such devices. The most striking feature of these worms is that they do not require Internet connectivity for their propagation but can spread directly from device to device using a short-range radio communication technology, such as WiFi or Bluetooth. In this paper, we develop a new model for epidemic spreading of these worms and investigate their spreading in wireless ad hoc networks via extensive Monte Carlo simulations. Our studies show that the threshold behaviour and dynamics of worm epidemics in these networks are greatly affected by a combination of spatial and temporal correlations which characterize these networks, and are significantly different from the previously studied epidemics in the Internet