395 research outputs found
Analysis of an epidemic model with awareness decay on regular random networks
The existence of a die-out threshold (different from the classic disease-invasion one) defining a region of slow extinction of an epidemic has been proved elsewhere for susceptible-aware-infectious-susceptible models without awareness decay, through bifurcation analysis. By means of an equivalent mean-field model defined on regular random networks, we interpret the dynamics of the system in this region and prove that the existence of bifurcation for of this second epidemic threshold crucially depends on the absence of awareness decay. We show that the continuum of equilibria that characterizes the slow die-out dynamics collapses into a unique equilibrium when a constant rate of awareness decay is assumed, no matter how small, and that the resulting bifurcation from the disease-free equilibrium is equivalent to that of standard epidemic models. We illustrate these findings with continuous-time stochastic simulations on regular random networks with different degrees. Finally, the behaviour of solutions with and without decay in awareness is compared around the second epidemic threshold for a small rate of awareness decay
Comment on ''Properties of highly clustered networks"
We consider a procedure for generating clustered networks previously reported by Newman [Phys. Rev. E 68, 026121 (2003)]. In the same study, clustered networks generated according to the proposed model have been reported to have a lower epidemic threshold under susceptible-infective-recovered-type network epidemic dynamics. By rewiring networks generated by this model, such that the degree distribution is conserved, we show that the lower epidemic threshold can be closely reproduced by rewired networks with close to zero clustering. The reported lower epidemic threshold can be explained by different degree distributions observed in the networks corresponding to different levels of clustering. Clustering results in networks with high levels of heterogeneity in node degree, a higher proportion of nodes with zero connectivity, and links concentrated within highly interconnected components of small size. Hence, networks generated by this model differ in both clustering and degree distribution, and the lower epidemic threshold is not explained by clustering alone
Epidemic threshold and control in a dynamic network
In this paper we present a model describing susceptible-infected-susceptible-type epidemics spreading on a dynamic contact network with random link activation and deletion where link activation can be locally constrained. We use and adapt an improved effective degree compartmental modeling framework recently proposed by Lindquist et al. [ J. Math Biol. 62 143 (2010)] and Marceau et al. [ Phys. Rev. E 82 036116 (2010)]. The resulting set of ordinary differential equations (ODEs) is solved numerically, and results are compared to those obtained using individual-based stochastic network simulation. We show that the ODEs display excellent agreement with simulation for the evolution of both the disease and the network and are able to accurately capture the epidemic threshold for a wide range of parameters. We also present an analytical R0 calculation for the dynamic network model and show that, depending on the relative time scales of the network evolution and disease transmission, two limiting cases are recovered: (i) the static network case when network evolution is slow and (ii) homogeneous random mixing when the network evolution is rapid. We also use our threshold calculation to highlight the dangers of relying on local stability analysis when predicting epidemic outbreaks on evolving networks
Comparative evaluation of bandwidth-bound applications on the Intel Xeon CPU MAX Series
In this paper we explore the performance of Intel Xeon MAX CPU Series,
representing the most significant new variation upon the classical CPU
architecture since the Intel Xeon Phi Processor. Given the availability of a
large on-package high-bandwidth memory, the bandwidth-to-compute ratio has
significantly shifted compared to other CPUs on the market. Since a large
fraction of HPC workloads are sensitive to the available bandwidth, we explore
how this architecture performs on a selection of HPC proxies and applications
that are mostly sensitive to bandwidth, and how it compares to the previous 3rd
generation Intel Xeon Scalable processors (codenamed Ice Lake) and an AMD EPYC
7003 Series Processor with 3D V-Cache Technology (codenamed Milan-X). We
explore performance with different parallel implementations (MPI, MPI+OpenMP,
MPI+SYCL), compiled with different compilers and flags, and executed with or
without hyperthreading. We show how performance bottlenecks are shifted from
bandwidth to communication latencies for some applications, and demonstrate
speedups compared to the previous generation between 2.0x-4.3x
Differential equation approximations of stochastic network processes: an operator semigroup approach
The rigorous linking of exact stochastic models to mean-field approximations
is studied. Starting from the differential equation point of view the
stochastic model is identified by its Kolmogorov equations, which is a system
of linear ODEs that depends on the state space size () and can be written as
. Our results rely on the convergence of the transition
matrices to an operator . This convergence also implies that the
solutions converge to the solution of . The limiting ODE
can be easily used to derive simpler mean-field-type models such that the
moments of the stochastic process will converge uniformly to the solution of
appropriately chosen mean-field equations. A bi-product of this method is the
proof that the rate of convergence is . In addition, it turns
out that the proof holds for cases that are slightly more general than the
usual density dependent one. Moreover, for Markov chains where the transition
rates satisfy some sign conditions, a new approach for proving convergence to
the mean-field limit is proposed. The starting point in this case is the
derivation of a countable system of ordinary differential equations for all the
moments. This is followed by the proof of a perturbation theorem for this
infinite system, which in turn leads to an estimate for the difference between
the moments and the corresponding quantities derived from the solution of the
mean-field ODE
A class of pairwise models for epidemic dynamics on weighted networks
In this paper, we study the (susceptible-infected-susceptible) and
(susceptible-infected-removed) epidemic models on undirected, weighted
networks by deriving pairwise-type approximate models coupled with
individual-based network simulation. Two different types of
theoretical/synthetic weighted network models are considered. Both models start
from non-weighted networks with fixed topology followed by the allocation of
link weights in either (i) random or (ii) fixed/deterministic way. The pairwise
models are formulated for a general discrete distribution of weights, and these
models are then used in conjunction with network simulation to evaluate the
impact of different weight distributions on epidemic threshold and dynamics in
general. For the dynamics, the basic reproductive ratio is
computed, and we show that (i) for both network models is maximised if
all weights are equal, and (ii) when the two models are equally matched, the
networks with a random weight distribution give rise to a higher value.
The models are also used to explore the agreement between the pairwise and
simulation models for different parameter combinations
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