Epidemic spreading on interconnected networks

Many real networks are not isolated from each other but form networks of networks, often interrelated in non trivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop a heterogeneous mean field approach that allows us to calculate the conditions for the emergence of an endemic state. Interestingly, a global endemic state may arise in the coupled system even though the epidemics is not able to propagate on each network separately, and even when the number of coupling connections is small. Our analytic results are successfully confronted against large-scale numerical simulations

Modular networks emerge from multiconstraint optimization

Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing robustness against perturbations in node activity. We show that the optimal networks satisfying these three constraints are characterized by the existence of multiple subnetworks (modules) sparsely connected to each other. In addition, these modules have distinct hubs, resulting in an overall heterogeneous degree distribution.Comment: 5 pages, 4 figures; Published versio

Promiscuity and the Evolution of Sexual Transmitted Diseases

We study the relation between different social behaviors and the onset of epidemics in a model for the dynamics of sexual transmitted diseases. The model considers the society as a system of individual sexuated agents that can be organized in couples and interact with each other. The different social behaviors are incorporated assigning what we call a promiscuity value to each individual agent. The individual promiscuity is taken from a distributions and represents the daily probability of going out to look for a sexual partner, abandoning its eventual mate. In terms of this parameter we find a threshold for the epidemic which is much lower than the classical fully mixed model prediction, i.e. $R_0$ (basic reproductive number) $= 1$. Different forms for the distribution of the population promiscuity are considered showing that the threshold is weakly sensitive to them. We study the homosexual and the heterosexual case as well.Comment: 6 pages, 4 figure

Statistics of Certain Models of Evolution

In a recent paper, Newman surveys the literature on power law spectra in evolution, self-organised criticality and presents a model of his own to arrive at a conclusion that self-organised criticality is not necessary for evolution. Not only did he miss a key model (Ecolab) that has a clear self-organised critical mechanism, but also Newman's model exhibits the same mechanism that gives rise to power law behaviour as does Ecolab. Newman's model is, in fact, a ``mean field'' approximation of a self-organised critical system. In this paper, I have also implemented Newman's model using the Ecolab software, removing the restriction that the number of species remains constant. It turns out that the requirement of constant species number is non-trivial, leading to a global coupling between species that is similar in effect to the species interactions seen in Ecolab. In fact, the model must self-organise to a state where the long time average of speciations balances that of the extinctions, otherwise the system either collapses or explodes. In view of this, Newman's model does not provide the hoped-for counter example to the presence of self-organised criticality in evolution, but does provide a simple, almost analytic model that can used to understand more intricate models such as Ecolab.Comment: accepted in Phys Rev E.; RevTeX; See http://parallel.hpc.unsw.edu.au/rks/ecolab.html for more informatio

Shift of percolation thresholds for epidemic spread between static and dynamic small-world networks

The aim of the study was to compare the epidemic spread on static and dynamic small-world networks. The network was constructed as a 2-dimensional Watts-Strogatz model (500x500 square lattice with additional shortcuts), and the dynamics involved rewiring shortcuts in every time step of the epidemic spread. The model of the epidemic is SIR with latency time of 3 time steps. The behaviour of the epidemic was checked over the range of shortcut probability per underlying bond 0-0.5. The quantity of interest was percolation threshold for the epidemic spread, for which numerical results were checked against an approximate analytical model. We find a significant lowering of percolation thresholds for the dynamic network in the parameter range given. The result shows that the behaviour of the epidemic on dynamic network is that of a static small world with the number of shortcuts increased by 20.7 +/- 1.4%, while the overall qualitative behaviour stays the same. We derive corrections to the analytical model which account for the effect. For both dynamic and static small-world we observe suppression of the average epidemic size dependence on network size in comparison with finite-size scaling known for regular lattice. We also study the effect of dynamics for several rewiring rates relative to latency time of the disease.Comment: 13 pages, 6 figure

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

The Social Behavior and the Evolution of Sexually Transmitted Diseases

We introduce a model for the evolution of sexually transmitted diseases, in which the social behavior is incorporated as a determinant factor for the further propagation of the infection. The system may be regarded as a society of agents where in principle anyone can sexually interact with any other one in the population. Different social behaviors are reflected in a distribution of sexual attitudes ranging from the more conservative to the more promiscuous. This is measured by what we call the promiscuity parameter. In terms of this parameter, we find a critical behavior for the evolution of the disease. There is a threshold below what the epidemic does not occur. We relate this critical value of the promiscuity to what epidemiologist call the basic reproductive number, connecting it with the other parameters of the model, namely the infectivity and the infective period in a quantitative way. We consider the possibility of subjects be grouped in couples. In this contribution only the homosexual case is analyzed.Comment: 4 pages, 4 figure

Multi-state epidemic processes on complex networks

Infectious diseases are practically represented by models with multiple states and complex transition rules corresponding to, for example, birth, death, infection, recovery, disease progression, and quarantine. In addition, networks underlying infection events are often much more complex than described by meanfield equations or regular lattices. In models with simple transition rules such as the SIS and SIR models, heterogeneous contact rates are known to decrease epidemic thresholds. We analyze steady states of various multi-state disease propagation models with heterogeneous contact rates. In many models, heterogeneity simply decreases epidemic thresholds. However, in models with competing pathogens and mutation, coexistence of different pathogens for small infection rates requires network-independent conditions in addition to heterogeneity in contact rates. Furthermore, models without spontaneous neighbor-independent state transitions, such as cyclically competing species, do not show heterogeneity effects.Comment: 7 figures, 1 tabl

Transmission of severe acute respiratory syndrome in dynamical small-world networks

The outbreak of severe acute respiratory syndrome (SARS) is still threatening the world because of a possible resurgence. In the current situation that effective medical treatments such as antiviral drugs are not discovered yet, dynamical features of the epidemics should be clarified for establishing strategies for tracing, quarantine, isolation, and regulating social behavior of the public at appropriate costs. Here we propose a network model for SARS epidemics and discuss why superspreaders emerged and why SARS spread especially in hospitals, which were key factors of the recent outbreak. We suggest that superspreaders are biologically contagious patients, and they may amplify the spreads by going to potentially contagious places such as hospitals. To avoid mass transmission in hospitals, it may be a good measure to treat suspected cases without hospitalizing them. Finally, we indicate that SARS probably propagates in small-world networks associated with human contacts and that the biological nature of individuals and social group properties are factors more important than the heterogeneous rates of social contacts among individuals. This is in marked contrast with epidemics of sexually transmitted diseases or computer viruses to which scale-free network models often apply.Comment: 4 figure

Aortic Insufficiency in LVAD Patients

Aortic insufficiency (AI) is a common complication that increases morbidity and mortality in patients with left ventricular assist devices (LVAD). Significant AI during LVAD support creates a substantial regurgitant flow loop, negatively affecting cardiac recovery and exposing blood to longer residence time and higher shear stress. The mechanism of AI development and progression is linked to a lack of aortic valve opening, which alters the valvular tissue mechanics. Pre-existing AI also worsens following LVAD implantation, interfering with the pump benefits. This chapter will evaluate AI development with LVAD support compared with naturally occurring AI and present the features, mechanisms, and links to clinical treatment options