A rumor transmission model with various contact interactions

We consider a rumor transmission model with various contact interactions and explore what effect such interactions have on the spread of a rumor, in particular whether they can explain the rumor recursion. Through mathematical analysis and computer simulations, we conjecture that rumor recursion remains a major challenge to mathematical models of rumors beyond our model proposed here.     

Rumor Diffusion and Convergence during the 3.11 Earthquake: A Twitter Case Study

We focus on Internet rumors and present an empirical analysis and simulation results of their diffusion and convergence during emergencies. In particular, we study one rumor that appeared in the immediate aftermath of the Great East Japan Earthquake on March 11, 2011, which later turned out to be misinformation. By investigating whole Japanese tweets that were sent one week after the quake, we show that one correction tweet, which originated from a city hall account, diffused enormously. We also demonstrate a stochastic agent-based model, which is inspired by contagion model of epidemics SIR, can reproduce observed rumor dynamics. Our model can estimate the rumor infection rate as well as the number of people who still believe in the rumor that cannot be observed directly. For applications, rumor diffusion sizes can be estimated in various scenarios by combining our model with the real data.     

Extinction Times of Epidemic Outbreaks in Networks

In the Susceptible–Infectious–Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the population. Infections that are not contagious enough die out before they spread to a large fraction of people. We characterize how the maximal extinction time in SIR simulations on networks depend on the network structure. For example we find that the average distances in isolated components, weighted by the component size, is a good predictor of the maximal time to extinction. Furthermore, the transmission probability giving the longest outbreaks is larger than, but otherwise seemingly independent of, the epidemic threshold.     

Emergence of scale-free leadership structure in social recommender systems

The study of the organization of social networks is important for the understanding of opinion formation, rumor spreading, and the emergence of trends and fashion. This paper reports empirical analysis of networks extracted from four leading sites with social functionality (Delicious, Flickr, Twitter and YouTube) and shows that they all display a scale-free leadership structure. To reproduce this feature, we propose an adaptive network model driven by social recommending. Artificial agent-based simulations of this model highlight a "good get richer" mechanism where users with broad interests and good judgments are likely to become popular leaders for the others. Simulations also indicate that the studied social recommendation mechanism can gradually improve the user experience by adapting to tastes of its users. Finally we outline implications for real online resource-sharing systems.     

Finding Influential Spreaders from Human Activity beyond Network Location

Most centralities proposed for identifying influential spreaders on social networks to either spread a message or to stop an epidemic require the full topological information of the network on which spreading occurs. In practice, however, collecting all connections between agents in social networks can be hardly achieved. As a result, such metrics could be difficult to apply to real social networks. Consequently, a new approach for identifying influential people without the explicit network information is demanded in order to provide an efficient immunization or spreading strategy, in a practical sense. In this study, we seek a possible way for finding influential spreaders by using the social mechanisms of how social connections are formed in real networks. We find that a reliable immunization scheme can be achieved by asking people how they interact with each other. From these surveys we find that the probabilistic tendency to connect to a hub has the strongest predictive power for influential spreaders among tested social mechanisms. Our observation also suggests that people who connect different communities is more likely to be an influential spreader when a network has a strong modular structure. Our finding implies that not only the effect of network location but also the behavior of individuals is important to design optimal immunization or spreading schemes.     

Exploiting temporal network structures of human interaction to effectively immunize populations

Decreasing the number of people who must be vaccinated to immunize a community against an infectious disease could both save resources and decrease outbreak sizes. A key to reaching such a lower threshold of immunization is to find and vaccinate people who, through their behavior, are more likely than average to become infected and to spread the disease further. Fortunately, the very behavior that makes these people important to vaccinate can help us to localize them. Earlier studies have shown that one can use previous contacts to find people that are central in static contact networks. However, real contact patterns are not static. In this paper, we investigate if there is additional information in the temporal contact structure for vaccination protocols to exploit. We answer this affirmative by proposing two immunization methods that exploit temporal correlations and showing that these methods outperform a benchmark static-network protocol in four empirical contact datasets under various epidemic scenarios. Both methods rely only on obtainable, local information, and can be implemented in practice. For the datasets directly related to contact patterns of potential disease spreading (of sexually-transmitted and nosocomial infections respectively), the most efficient protocol is to sample people at random and vaccinate their latest contacts. The network datasets are temporal, which enables us to make more realistic evaluations than earlier studies--we use only information about the past for the purpose of vaccination, and about the future to simulate disease outbreaks. Using analytically tractable models, we identify two temporal structures that explain how the protocols earn their efficiency in the empirical data. This paper is a first step towards real vaccination protocols that exploit temporal-network structure--future work is needed both to characterize the structure of real contact sequences and to devise immunization methods that exploit these.     

Global asymptotic stability for a vector disease model with spatial spread

Summary We analyze the global behaviour of a vector disease model which involves spatial spread and hereditary effects. This model can be applied to investigate growth and spread of malaria. No immunization is considered. We prove that, if the recovery rate is less than or equal to a threshold value, the disease dies out, otherwise the infectious people density tends to a homogeneous distribution. Our results follow using contracting convexes techniques and agree with the results given by K. L. Cooke for the model without diffusion.Work supported by C.N.R., Grant No. 79.00696.01.     

The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators

The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate numerically and analytically the transition in the behavior of threshold-limited cascades in the presence of multiple initiators as the distribution of thresholds is varied between the two extreme cases of identical thresholds and a uniform distribution. We accomplish this by employing a truncated normal distribution of the nodes’ thresholds and observe a non-monotonic change in the cascade size as we vary the standard deviation. Further, for a sufficiently large spread in the threshold distribution, the tipping-point behavior of the social influencing process disappears and is replaced by a smooth crossover governed by the size of initiator set. We demonstrate that for a given size of the initiator set, there is a specific variance of the threshold distribution for which an opinion spreads optimally. Furthermore, in the case of synthetic graphs we show that the spread asymptotically becomes independent of the system size, and that global cascades can arise just by the addition of a single node to the initiator set.     

Sterilizing vaccines or the politics of the womb: retrospective study of a rumor in Cameroon

In 1990 a rumor that public health workers were administering a vaccine to sterilize girls and women spread throughout Cameroon. Schoolgirls leapt from windows to escape the vaccination teams, and the vaccination campaign (part of the Year of Universal Child Immunization) was aborted. This article traces the origin and development of this rumor. Theories of rumor and ambiguous cultural response to new technologies shed some light on its genesis and spread, but explain neither its timing nor its content. For this task we need to examine the historical context of Cameroonian experience with colonial vaccination campaigns and the contemporary contexts of the turmoil of democratization movements and economic crisis, concurrent changes in contraceptive policy, and regional mistrust of the state and its "hegemonic project." Drawing on Bayart's politique du ventre and White's thoughts on gossip, we explore this rumor as diagnostic of local response to global and national projects. This response, expressed in this case through the idiom of threats to local reproductive capacity, reveals a feminine side to local-global relations, a politics of the womb.     

Spreading speeds and traveling waves in competitive recursion systems

This paper is concerned with the spreading speeds and traveling wave solutions of discrete time recursion systems, which describe the spatial propagation mode of two competitive invaders. We first establish the existence of traveling wave solutions when the wave speed is larger than a given threshold. Furthermore, we prove that the threshold is the spreading speed of one species while the spreading speed of the other species is distinctly slower compared to the case when the interspecific competition disappears. Our results also show that the interspecific competition does affect the spread of both species so that the eventual population densities at the coexistence domain are lower than the case when the competition vanishes.     

'A mate or a meal' – Pre-gravid behaviour of female Anopheles gambiae from the islands of São Tomé and Príncipe, West Africa

Background

The spread of drug resistance is making malaria control increasingly difficult. Mathematical models for the transmission dynamics of drug sensitive and resistant strains can be a useful tool to help to understand the factors that influence the spread of drug resistance, and they can therefore help in the design of rational strategies for the control of drug resistance.

Methods

We present an epidemiological framework to investigate the spread of anti-malarial resistance. Several mathematical models, based on the familiar Macdonald-Ross model of malaria transmission, enable us to examine the processes and parameters that are critical in determining the spread of resistance.

Results

In our simplest model, resistance does not spread if the fraction of infected individuals treated is less than a threshold value; if drug treatment exceeds this threshold, resistance will eventually become fixed in the population. The threshold value is determined only by the rates of infection and the infectious periods of resistant and sensitive parasites in untreated and treated hosts, whereas the intensity of transmission has no influence on the threshold value. In more complex models, where hosts can be infected by multiple parasite strains or where treatment varies spatially, resistance is generally not fixed, but rather some level of sensitivity is often maintained in the population.

Conclusions

The models developed in this paper are a first step in understanding the epidemiology of anti-malarial resistance and evaluating strategies to reduce the spread of resistance. However, specific recommendations for the management of resistance need to wait until we have more data on the critical parameters underlying the spread of resistance: drug use, spatial variability of treatment and parasite migration among areas, and perhaps most importantly, cost of resistance.     

Differential function of Listeria monocytogenes listeriolysin O and phospholipases C in vacuolar dissolution following cell-to-cell spread

We investigated the role of listeriolysin O (LLO) and the bacterial phospholipases PI-PLC and PC-PLC in cell-to-cell spread of Listeria monocytogenes. We showed that LLO is essential for cell-to-cell spread in primary murine macrophages. Electron micrographs revealed that in the absence of continued LLO expression, bacteria remain trapped in secondary spreading vacuoles having either a double or single membrane. In bacteria lacking PI-PLC and PC-PLC, cessation of LLO expression after initiation of infection resulted in a significant increase in the proportion of bacteria trapped in double-membrane compartments. We propose that the bacterial phospholipases are involved in the dissolution of the inner membrane of the spreading vacuole, yet are not sufficient for disruption of the outer membrane. As a consequence, we identified LLO as a key factor in the disruption of the outer membrane. This model is consistent with the observation that LLO is dispensable for cell-to-cell spread from human macrophages into a cell type in which LLO is not required for vacuolar escape. These data suggest that during human infection, spreading of L. monocytogenes to distant organs is likely to occur even in the absence of LLO expression, and that the bacterial phospholipases may be sufficient to mediate continued cell-to-cell spread.     

Thrombospondin modulates alpha v beta 3 function through integrin- associated protein

Integrin-associated protein (IAP) is a receptor for the carboxyl- terminal "cell-binding domain" (CBD) of thrombospondin 1 (TS1). IAP associates with alpha v beta 3 integrin and mAbs against IAP inhibit certain integrin functions. Here we examine the effects of the TS1 CBD and 4N1K (KRFYVVMWKK), a cell-binding peptide derived from it, on the adhesion and spreading on vitronectin (VN) of C32 human melanoma cells which express IAP, alpha v beta 3, and alpha v beta 5. Cells adhere to VN at low surface densities via alpha v beta 5 and spread very slowly while adhesion to higher density VN involves both alpha v beta 5 and alpha v beta 3 and results in rapid spreading. Spreading of the cells, but not adhesion, on sparse VN coatings is markedly enhanced by the presence of soluble TS1, the recombinant CBD and 4N1K, but not the "mutant" peptide 4NGG, KRFYGGMWKK, which fails to bind IAP. This enhanced spreading is completely blocked by mAb LM609 against alpha v beta 3 and the anti-IAP mAb B6H12. Correlated with this enhanced spreading is increased tyrosine phosphorylation of focal adhesion kinase (FAK), paxillin, and a protein of ca. 90 kD. The enhanced spreading induced by TS1 and 4N1K and the constitutive spreading on higher density VN are both blocked by calphostin C (100 nM), wortmannin (10 nM), and tyrosine kinase inhibitors. In contrast, pertussis toxin specifically blocks only the TS1 stimulated spreading on low density VN, indicating that IAP exerts its effects on signal transduction via a heterotrimeric Gi protein acting upstream of a common cell spreading pathway which includes PI-3 kinase, PKC, and tyrosine kinases.     

Temporal Percolation of the Susceptible Network in an Epidemic Spreading

In this work, we study the evolution of the susceptible individuals during the spread of an epidemic modeled by the susceptible-infected-recovered (SIR) process spreading on the top of complex networks. Using an edge-based compartmental approach and percolation tools, we find that a time-dependent quantity , namely, the probability that a given neighbor of a node is susceptible at time , is the control parameter of a node void percolation process involving those nodes on the network not-reached by the disease. We show that there exists a critical time above which the giant susceptible component is destroyed. As a consequence, in order to preserve a macroscopic connected fraction of the network composed by healthy individuals which guarantee its functionality, any mitigation strategy should be implemented before this critical time . Our theoretical results are confirmed by extensive simulations of the SIR process.     

Directedness of information flow in mobile phone communication networks

Without having direct access to the information that is being exchanged, traces of information flow can be obtained by looking at temporal sequences of user interactions. These sequences can be represented as causality trees whose statistics result from a complex interplay between the topology of the underlying (social) network and the time correlations among the communications. Here, we study causality trees in mobile-phone data, which can be represented as a dynamical directed network. This representation of the data reveals the existence of super-spreaders and super-receivers. We show that the tree statistics, respectively the information spreading process, are extremely sensitive to the in-out degree correlation exhibited by the users. We also learn that a given information, e.g., a rumor, would require users to retransmit it for more than 30 hours in order to cover a macroscopic fraction of the system. Our analysis indicates that topological node-node correlations of the underlying social network, while allowing the existence of information loops, they also promote information spreading. Temporal correlations, and therefore causality effects, are only visible as local phenomena and during short time scales. Consequently, the very idea that there is (intentional) information spreading beyond a small vecinity is called into question. These results are obtained through a combination of theory and data analysis techniques.     

A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold

Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this threshold is the mean field version of a transition in corresponding spatial models of immunization. The reinfection threshold corresponds to the transition between annular growth of an epidemics spreading into a susceptible area leaving recovered behind and compact growth of a susceptible-infected-susceptible region growing into a susceptible area. This transition between annular growth and compact growth was described in the physics literature long before the reinfection threshold debate broke out in the theoretical biology literature.     

A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold

Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this threshold is the mean field version of a transition in corresponding spatial models of immunization. The reinfection threshold corresponds to the transition between annular growth of an epidemics spreading into a susceptible area leaving recovered behind and compact growth of a susceptible-infected-susceptible region growing into a susceptible area. This transition between annular growth and compact growth was described in the physics literature long before the reinfection threshold debate broke out in the theoretical biology literature.     

Plant-soil feedbacks and invasive spread

Plant invaders have been suggested to change soil microbial communities and biogeochemical cycling in ways that can feedback to benefit themselves. In this paper, we ask when do these feedbacks influence the spread of exotic plants. Because answering this question is empirically challenging, we show how ecological theory on 'pushed' and 'pulled' invasions can be used to examine the problem. We incorporate soil feedbacks into annual plant invasion models, derive the conditions under which such feedbacks affect spread, and support our approach with simulations. We show that in homogeneous landscapes, strong positive feedbacks can influence spreading velocity for annual invaders, but that empirically documented feedbacks are not strong enough to do so. Moreover, to influence spread, invaders must modify the soil environment over a spatial scale larger than is biologically realistic. Though unimportant for annual invader spread in our models, feedbacks do affect invader density and potential impact. We discuss how future research might consider the way landscape structure, dispersal patterns, and the time scales over which plant–soil feedbacks develop regulate the effects of such feedbacks on invader spread.     

How to account for habitat suitability in weed management programmes?

Designing efficient management strategies for already established invasive alien species is challenging. Here, we ask whether environmental suitability, as predicted by species distribution models, is a useful basis of cost-effective spatial prioritization in large-scale surveillance and eradication programmes. We do so by means of spatially and temporarily explicit simulations of the spread of a case study species (Ambrosia artemisiifolia L.) in Austria and southern Germany under different management regimes. We ran these simulations on a contiguous grid of the study area with each grid cell (~35 km²) characterized by a habitat suitability value derived from the predictions of a species distribution model. The management regimes differed in terms of (a) a minimum habitat suitability rank p (suitability threshold) used to separate cells for surveillance from those which are not controlled; and (b) the strategy for selecting cells for annual campaigns from the pool defined by p. According to the results (i.e., number of cells infested in 2050 as well as infested on average per year) the most efficient way to base surveillance on suitability is to define the temporal sequence of management according to the grid cells’ suitability ranks. Management success declines sharply when the suitability threshold is set too high, but only moderately when it is set too low. We conclude that accounting for environmental suitability is important for large-scale management programmes of invasive alien species and that species distribution models are hence useful tools for designing such programmes.