Adaptive Epidemic Dynamics in Networks: Thresholds and Control

Theoretical modeling of computer virus/worm epidemic dynamics is an important problem that has attracted many studies. However, most existing models are adapted from biological epidemic ones. Although biological epidemic models can certainly be adapted to capture some computer virus spreading scenarios (especially when the so-called homogeneity assumption holds), the problem of computer virus spreading is not well understood because it has many important perspectives that are not necessarily accommodated in the biological epidemic models. In this paper we initiate the study of such a perspective, namely that of adaptive defense against epidemic spreading in arbitrary networks. More specifically, we investigate a non-homogeneous Susceptible-Infectious-Susceptible (SIS) model where the model parameters may vary with respect to time. In particular, we focus on two scenarios we call semi-adaptive defense and fully-adaptive} defense, which accommodate implicit and explicit dependency relationships between the model parameters, respectively. In the semi-adaptive defense scenario, the model's input parameters are given; the defense is semi-adaptive because the adjustment is implicitly dependent upon the outcome of virus spreading. For this scenario, we present a set of sufficient conditions (some are more general or succinct than others) under which the virus spreading will die out; such sufficient conditions are also known as epidemic thresholds in the literature. In the fully-adaptive defense scenario, some input parameters are not known (i.e., the aforementioned sufficient conditions are not applicable) but the defender can observe the outcome of virus spreading. For this scenario, we present adaptive control strategies under which the virus spreading will die out or will be contained to a desired level.Comment: 20 pages, 8 figures. This paper was submitted in March 2009, revised in August 2009, and accepted in December 2009. However, the paper was not officially published until 2014 due to non-technical reason

Non-systemic transmission of tick-borne diseases: a network approach

Tick-Borne diseases can be transmitted via non-systemic (NS) transmission. This occurs when tick gets the infection by co-feeding with infected ticks on the same host resulting in a direct pathogen transmission between the vectors, without infecting the host. This transmission is peculiar, as it does not require any systemic infection of the host. The NS transmission is the main efficient transmission for the persistence of the Tick-Borne Encephalitis virus in nature. By describing the heterogeneous ticks aggregation on hosts through a \hyphenation{dynamical} bipartite graphs representation, we are able to mathematically define the NS transmission and to depict the epidemiological conditions for the pathogen persistence. Despite the fact that the underlying network is largely fragmented, analytical and computational results show that the larger is the variability of the aggregation, and the easier is for the pathogen to persist in the population.Comment: 15 pages, 4 figures, to be published in Communications in Nonlinear Science and Numerical Simulatio

Interacting epidemics and coinfection on contact networks

The spread of certain diseases can be promoted, in some cases substantially, by prior infection with another disease. One example is that of HIV, whose immunosuppressant effects significantly increase the chances of infection with other pathogens. Such coinfection processes, when combined with nontrivial structure in the contact networks over which diseases spread, can lead to complex patterns of epidemiological behavior. Here we consider a mathematical model of two diseases spreading through a single population, where infection with one disease is dependent on prior infection with the other. We solve exactly for the sizes of the outbreaks of both diseases in the limit of large population size, along with the complete phase diagram of the system. Among other things, we use our model to demonstrate how diseases can be controlled not only by reducing the rate of their spread, but also by reducing the spread of other infections upon which they depend.Comment: 9 pages, 3 figure

Spreading processes in Multilayer Networks

Several systems can be modeled as sets of interconnected networks or networks with multiple types of connections, here generally called multilayer networks. Spreading processes such as information propagation among users of an online social networks, or the diffusion of pathogens among individuals through their contact network, are fundamental phenomena occurring in these networks. However, while information diffusion in single networks has received considerable attention from various disciplines for over a decade, spreading processes in multilayer networks is still a young research area presenting many challenging research issues. In this paper we review the main models, results and applications of multilayer spreading processes and discuss some promising research directions.Comment: 21 pages, 3 figures, 4 table

Complexity and anisotropy in host morphology make populations safer against epidemic outbreaks

One of the challenges in epidemiology is to account for the complex morphological structure of hosts such as plant roots, crop fields, farms, cells, animal habitats and social networks, when the transmission of infection occurs between contiguous hosts. Morphological complexity brings an inherent heterogeneity in populations and affects the dynamics of pathogen spread in such systems. We have analysed the influence of realistically complex host morphology on the threshold for invasion and epidemic outbreak in an SIR (susceptible-infected-recovered) epidemiological model. We show that disorder expressed in the host morphology and anisotropy reduces the probability of epidemic outbreak and thus makes the system more resistant to epidemic outbreaks. We obtain general analytical estimates for minimally safe bounds for an invasion threshold and then illustrate their validity by considering an example of host data for branching hosts (salamander retinal ganglion cells). Several spatial arrangements of hosts with different degrees of heterogeneity have been considered in order to analyse separately the role of shape complexity and anisotropy in the host population. The estimates for invasion threshold are linked to morphological characteristics of the hosts that can be used for determining the threshold for invasion in practical applications.Comment: 21 pages, 8 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