Pairwise approximation for SIR-type network epidemics with non-Markovian recovery

We present the generalized mean-field and pairwise models for non-Markovian epidemics on networks with arbitrary recovery time distributions. First we consider a hyperbolic partial differential equation (PDE) system, where the population of infective nodes and links are structured by age since infection. We show that the PDE system can be reduced to a system of integro-differential equations, which is analysed analytically and numerically. We investigate the asymptotic behaviour of the generalized model and provide an implicit analytical expression involving the final epidemic size and pairwise reproduction number. As an illustration of the applicability of the general model, we recover known results for the exponentially distributed and fixed recovery time cases. For gamma- and uniformly distributed infectious periods, new pairwise models are derived. Theoretical findings are confirmed by comparing results from the new pairwise model and explicit stochastic network simulation. A major benefit of the generalized pairwise model lies in approximating the time evolution of the epidemic

Can epidemic models describe the diffusion of research topics across disciplines?

This paper introduces a new approach to describe the spread of research topics across disciplines using epidemic models. The approach is based on applying individual-based models from mathematical epidemiology to the diffusion of a research topic over a contact network that represents knowledge flows over the map of science –as obtained from citations between ISI Subject Categories. Using research publications on the protein class kinesin as a case study, we report a better fit between model and empirical data when using the citation-based contact network. Incubation periods on the order of 4 to 15.5 years support the view that, whilst research topics may grow very quickly, they face difficulties to overcome disciplinary boundaries

Dispersion curves in the diffusional instability of reaction fronts

A (linear) stability analysis of planar reaction fronts to transverse perturbations is considered for systems based on cubic autocatalysis and a model for the chlorite-tetrathionate reaction. Dispersion curves (plots of the growth rate sigma against a transverse wave-number k) are obtained. In both cases it is seen that there is a nonzero value D-0 of D (the ratio of the diffusion coefficients of autocatalyst and substrate) at which sigma(max), the maximum value of sigma for a given value of D, achieves its largest value, with sigma(max) being less for other values of D and becoming small as D decreases to zero. The existence of the optimum value D-0 for initiating a diffusional instability is confirmed, in the cubic autocatalysis case, by an asymptotic analysis for small wave numbers

Homogenization induced by chaotic mixing and diffusion in an oscillatory chemical reaction

A model for an imperfectly mixed batch reactor with the chlorine dioxide-iodine-malonic acid (CDIMA) reaction, with the mixing being modelled by chaotic advection, is considered. The reactor is assumed to be operating in oscillatory mode and the way in which an initial spatial perturbation becomes homogenized is examined. When the kinetics are such that the only stable homogeneous state is oscillatory then the perturbation is always entrained into these oscillations. The rate at which this occurs is relatively insensitive to the chemical effects, measured by the Damkohler number, and is comparable to the rate of homogenization of a passive contaminant. When both steady and oscillatory states are stable, spatially homogeneous states, two possibilities can occur. For the smaller Damkohler numbers, a localized perturbation at the steady state is homogenized within the background oscillations. For larger Damkohler numbers, regions of both oscillatory and steady behavior can co-exist for relatively long times before the system collapses to having the steady state everywhere. An interpretation of this behavior is provided by the one-dimensional Lagrangian filament model, which is analyzed in detail

Impact of constrained rewiring on network structure and node dynamics

In this paper, we study an adaptive spatial network. We consider a susceptible-infected-susceptible (SIS) epidemic on the network, with a link or contact rewiring process constrained by spatial proximity. In particular, we assume that susceptible nodes break links with infected nodes independently of distance and reconnect at random to susceptible nodes available within a given radius. By systematically manipulating this radius we investigate the impact of rewiring on the structure of the network and characteristics of the epidemic.We adopt a step-by-step approach whereby we first study the impact of rewiring on the network structure in the absence of an epidemic, then with nodes assigned a disease status but without disease dynamics, and finally running network and epidemic dynamics simultaneously. In the case of no labeling and no epidemic dynamics, we provide both analytic and semianalytic formulas for the value of clustering achieved in the network. Our results also show that the rewiring radius and the network’s initial structure have a pronounced effect on the endemic equilibrium, with increasingly large rewiring radiuses yielding smaller disease prevalence

Solvable non-Markovian dynamic network

Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward equations utilizing the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law interevent times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excellent approximation to the case when the network dynamics is characterized by power-law-distributed interevent times. We further discuss possible generalizations of our result

Effects of constant electric fields on the buoyant stability of reaction fronts

The effects that applying constant electric fields have on the buoyant instability of reaction fronts propagating vertically in a Hele-Shaw cell are investigated for a range of electric field strengths and fluid parameters. The reaction produces a decrease in density across the front such that upwards propagating fronts are buoyantly unstable in the field-free situation. The reaction kinetics are modeled by cubic autocatalysis. A linear stability analysis reveals that a positive electric field increases the stability of a reaction front and can stabilize an otherwise unstable front. A negative field has the opposite effect, making the reaction front more unstable. Numerical simulations of the full nonlinear problem confirm these predictions and show the development of cellular fingers on unstable fronts. These simulations show that the electric field effects on the reaction within the front can alter the fluid density so as to give the possibility of destabilizing an otherwise stable downward propagating front

Cross section measurement of the astrophysically important 17O(p,gamma)18F reaction in a wide energy range

The 17O(p,g)18F reaction plays an important role in hydrogen burning processes in different stages of stellar evolution. The rate of this reaction must therefore be known with high accuracy in order to provide the necessary input for astrophysical models. The cross section of 17O(p,g)18F is characterized by a complicated resonance structure at low energies. Experimental data, however, is scarce in a wide energy range which increases the uncertainty of the low energy extrapolations. The purpose of the present work is therefore to provide consistent and precise cross section values in a wide energy range. The cross section is measured using the activation method which provides directly the total cross section. With this technique some typical systematic uncertainties encountered in in-beam gamma-spectroscopy experiments can be avoided. The cross section was measured between 500 keV and 1.8 MeV proton energies with a total uncertainty of typically 10%. The results are compared with earlier measurements and it is found that the gross features of the 17O(p,g)18F excitation function is relatively well reproduced by the present data. Deviation of roughly a factor of 1.5 is found in the case of the total cross section when compared with the only one high energy dataset. At the lowest measured energy our result is in agreement with two recent datasets within one standard deviation and deviates by roughly two standard deviations from a third one. An R-matrix analysis of the present and previous data strengthen the reliability of the extrapolated zero energy astrophysical S-factor. Using an independent experimental technique, the literature cross section data of 17O(p,g)18F is confirmed in the energy region of the resonances while lower direct capture cross section is recommended at higher energies. The present dataset provides a constraint for the theoretical cross sections.Comment: Accepted for publication in Phys. Rev. C. Abstract shortened in order to comply with arxiv rule