A note on fractional linear pure birth and pure death processes in epidemic models

In this note we highlight the role of fractional linear birth and linear death processes, recently studied in Orsingher et al. (2010) [5] and Orsingher and Polito (2010) [6], in relation to epidemic models with empirical power law distribution of the events. Taking inspiration from a formal analogy between the equation for self-consistency of the epidemic type aftershock sequences (ETAS) model and the fractional differential equation describing the mean value of fractional linear growth processes, we show some interesting applications of fractional modelling in studying ab initio epidemic processes without the assumption of any empirical distribution. We also show that, in the framework of fractional modelling, subcritical regimes can be linked to linear fractional death processes and supercritical regimes to linear fractional birth processes.Moreover we discuss a simple toy model in order to underline the possible application of these stochastic growth models to more general epidemic phenomena such as tumoral growth.     

Effects of disease characteristics and population distribution on dynamics of epidemic spreading among residential sites

We investigate the spreading processes of epidemic diseases among many residential sites for different disease characteristics and different population distributions by constructing and solving a set of integrodifferential equations for the evolutions of position-dependent infected and infective rates, taking into account the infection processes both within a single site and among different sites. In a spreading process the states of an individual include susceptible (S), incubative (I), active (A) and recovered (R) states. Although the transition from S to I mainly depends on the active rate, the susceptible rate and the connectivity among individuals, the transitions from I to A and from A to R are determined by intrinsic characteristics of disease development in individuals. We adopt incubation and infection periods to describe the intrinsic features of the disease. By numerically solving the equations we find that the asymptotic behavior of the spreading crucially depends on the infection period and the population under affection of an active individual. Other factors, such as the structure of network and the popular distribution, play less important roles. The study may provide useful information for analyzing the key parameters affecting the dynamics and the asymptotic behavior.     

Rate coefficients measurement for the energy-pooling collisions Cs(5D) + Cs(5D) → Cs(6S) + Cs(nl = 9D, 11S, 7F)

We report experimental rate coefficients for the energy-pooling collisions Cs(5D) + Cs(5D) → Cs(6S) + Cs(nl = 9D, 11S, 7F). In the experiment the Cs(5D) state was populated via photodissociation of Cs₂ molecules using an argon-ion laser at wavelength 488.0 nm. We also consider the competing process 6P_1/2 + 7S → 6S + (nl = 9D, 11S, 7F) that might also populate 9D, 11S and 7F. An intermodulation technique was used to select the fluorescence contributions due only to the process 6P_1/2 + 7S → 6S + (nl = 9D, 11S, 7F). The excited atom (nl_J) density and spatial distribution were mapped by monitoring the absorption of a counterpropagating probe laser beam tuned to various transitions. The measured excited atom densities are combined with measured fluorescence ratios to yield rate coefficients for the energy-pooling collisions Cs(5D) + Cs(5D) → Cs(6S) + Cs(nl = 9D, 11S, 7F). The rate coefficients for nl = 9D, 11S, 7F are (4.1 ± 2.0) × 10⁻¹⁰ cm³ s⁻¹, (1.6 ± 0.8) × 10⁻¹⁰ cm³ s⁻¹ and (3.6 ± 1.8) × 10⁻¹⁰ cm³ s⁻¹, respectively. The contributions to the rate coefficients from other energy transfer processes are also discussed.     

Sulfur-catalyzed phase transition in MoS2 under high pressure and temperature

We report phase transition and stability of MoS₂ with and without the presence of sulfur melt under high-pressure and high-temperature conditions. Rhombohedral (3R) phase is found to be a high-temperature phase of MoS₂ at high pressures. Excess sulfur melt catalyzes the hexagonal (2H) to rhombohedral (3R) phase transformation and lowers the conversion temperature by more than 280 K. Boundary between 2H and 3R phases has been delineated with a negative slope. Based on experimental observations, sulfur-catalyzed 2H→3R transformation mechanisms are proposed involving atomic exchange between MoS₂ and sulfur, which is different from the case of without excess sulfur that proceeds through rotation and translation of the S–Mo–S sandwich layers.     

Absorbing phase transition in contact process on fractal lattices

We investigate the critical behavior of nonequilibrium phase transition from an active phase to an absorbing state on two selected fractal lattices, i.e., on a checkerboard fractal and on a Sierpinski carpet. The checkerboard fractal is finitely ramified with many dead ends, while the Sierpinski carpet is infinitely ramified. We measure various critical exponents of the contact process with a diffusion-reaction scheme A→AA and A→0, characterized by a spreading with a rate λ and an annihilation with a rate μ, and the results are confirmed by a crossover scaling and a finite-size scaling. The exponents, compared with the ?-expansion results assuming , being the fractal dimension of the underlying fractal lattice, exhibit significant deviations from the analytical results for both the checkerboard fractal and the Sierpinski carpet. On the other hand, the exponents on a checkerboard fractal agree well with the interpolated results of the regular lattice for the fractional dimensionality, while those on a Sierpinski carpet show marked deviations.     

Periodic Wave of Epidemic Spreading in Community Networks

It was reported by Cummings ef al. [Nature 427 （2004） 344] that there are periodic waves in the spatiotemporal data of epidemics. For understanding the mechanism, we study the epidemic spreading on community networks by both the SIS model and the SIRS model. We find that with the increase of infection rate, the number of total infected nodes may be stabilized at a fixed point, oscillatory waves, and periodic cycles. Moreover, the epidemic spreading in the SIS model can be explained by an analytic map.     

Dissipative oscillations in spatially restricted ecosystems due to long range migration

An ecosystem containing three interacting species is studied using both Mean Field approach and Kinetic Monte Carlo simulations on a lattice substrate. The so called 3rd order LLV model involves birth, death and reaction processes with 3rd order nonlinearities and feedbacks. At the mean field level this system exhibits conservative oscillations; the analytic form of the constant of motion is presented. The stochastic simulations show that the density oscillations disappear for sufficiently large lattices, while they are present locally, on small lattice windows. Introduction of mixing via long range migration in the two reacting species changes this picture. For small migration rates p, the behavior remains as with p = 0 and the system is divided into local asynchronous oscillators. As p increases the system passes through a phase transition and exhibits a weak disorder limit cycle through a supercritical Hopf-like bifurcation. The amplitude of the limit cycle depends on the rate p, on the range of migration r and on the system kinetic rates k₁, k₂ and k₃.     

Discrete Stochastic Modeling for Epidemics in Networks

In this paper, we construct a microscopic mechanism for the epidemic processes in heterogeneous populations, which contains two basic assumptions: all edges of the network are broken and reconnected at every time step among the epidemic process; the probability of randomly chosen two half-edges to make a pair is identical. We define the stochastic epidemic process and get the epidemic distributions numerically according to the transmission probability λ. Two different phases are observed, which means the onset of phase transition, and the threshold value is very small. Under the thermodynamic limit, the process can be approximated by a deterministic dynamical system. About this deterministic system, we get the analytical threshold value, which is consistent with the numerical results of the epidemic distributions.     

A simple stochastic lattice gas model for H1N1 pandemic. Application to the Italian epidemiological data

We construct a very simple epidemic model for influenza spreading in an age-class-distributed population, by coupling a lattice gas model for the population dynamics with a SIR stochastic model for susceptible, infected and removed/immune individuals. We use as a test case the age-distributed Italian epidemiological data for the novel influenza A(H1N1). The most valuable features of this model are its country-independent and virus-independent structure (few demographic, social and virological data are used to fix some parameters), its large statistic due to a very short run-time machine, and its easy generalizability to include mitigation strategies. In spite of its simplicity, the model presented reproduces the epidemiological Italian data, with sensible predictions for the reproduction number and theoretically interesting results for the generation time distribution.     

Magnetic properties of smooth terminating dipole bands in Te

Three strongly coupled sequences have been established in ^110,112Te up to high spins. They are interpreted in terms of deformed structures built on proton 1-particle–1-hole excitations that reach termination at I∼40?$I\sim 40?$. This is the first observation of smooth terminating dipole structures in this mass region. Lifetime measurements have allowed the extraction of experimental B(M1;I→I−1)$B(\mathrm{M}1;I\to I-1)$ and B(E2;I→I−2)$B(\mathrm{E}2;I\to I-2)$ reduced transition rates for one of the dipole bands in ¹¹⁰Te. The results support the deformed interpretation.     

Quantum chemical and RRKM calculations of reactions in the H/S/O system

Quantum chemical calculations at the MRCI/aug-cc-pV5Z level are used to describe the conversions between HSO, HOS, H + SO, S + OH and O + SH on the doublet H/S/O potential energy surface. An RRKM analysis of this multiple-well system was carried out in the temperature range 300-2000 K between 0.1 and 10 atm. At these pressures, the stabilization reaction H + SO → HSO or HOS is at the low pressure limit, and stabilization from S + OH and O + SH was not detected. The reactions S + OH → H + SO and O + SH → H + SO were found to be barrierless and very fast at room temperature (4 × 10¹⁴ and 1.5 × 10¹⁴ cm³ mol⁻¹ s⁻¹, respectively). The reaction channel O + SH → S + OH is two orders of magnitude slower than the more exothermic O + SH → H + SO reaction, although a second pathway involving direct H-abstraction (O + SH → S + OH) on the quartet surface appears as a minor channel at high temperatures.     

Lévy-flight spreading of epidemic processes leading to percolating clusters

We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of short-range infections that lead, at the critical point, to directed and isotropic percolation respectively, we consider long-range infections with a probability distribution decaying in d dimensions with the distance as . By means of Wilson's momentum shell renormalization-group recursion relations, the critical exponents characterizing the growing fractal clusters are calculated to first order in an -expansion. It is shown that the long-range critical behavior changes continuously to its short-range counterpart for a decay exponent of the infection . Received: 17 July 1998 / Revised: 20 July 1998 / Accepted: 28 July 1998     

Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

We investigate the critical behavior of a stochastic lattice model describing a General Epidemic Process. By means of a Monte Carlo procedure, we simulate the model on a regular square lattice and follow the spreading of an epidemic process with immunization. A finite size scaling analysis is employed to determine the critical point as well as some critical exponents. We show that the usual scaling analysis of the order parameter moment ratio does not provide an accurate estimate of the critical point. Precise estimates of the critical quantities are obtained from data of the order parameter variation rate and its fluctuations. Our numerical results corroborate that this model belongs to the dynamic isotropic percolation universality class. We also check the validity of the hyperscaling relation and present data collapse curves which reinforce the accuracy of the estimated critical parameters.     

Ultrasound-assisted soil washing processes for the remediation of heavy metals contaminated soils: The mechanism of the ultrasonic desorption

Ultrasound-assisted soil washing processes were investigated for the removal of heavy metals (Cu, Pb, and Zn) in real contaminated soils using HCl and EDTA. The ultrasound-assisted soil washing (US/Mixing) process was compared with the conventional soil washing (Mixing) process based on the mechanical mixing. High removal efficiency (44.8% for HCl and 43.2% for EDTA) for the metals was obtained for the most extreme conditions (HCl 1.0 M or EDTA 0.1 M and L:S = 10:1) in the Mixing process. With the aide of ultrasound, higher removal efficiency (57.9% for HCl and 50.0% for EDTA) was obtained in the same extreme conditions and similar or higher removal efficiency (e.g., 54.7% for HCl 0.5 M and L:S = 10:1 and 50.5% for EDTA 0.05 M and L:S = 5:1) was achieved even in less extreme conditions (lower HCl or EDTA concentration and L:S ratio). Therefore, it was revealed that the US/Mixing was advantageous over the conventional Mixing processes in terms of metal removal efficiency, consumption of chemicals, amount of generated washing leachate, and volume/size of washing reactor. In addition, the heavy metals removal was enhanced for the smaller soil particles in the US/Mixing process. It was due to more violent movement of smaller particles in slurry phase and more violent sonophysical effects. In order to understand the mechanism of ultrasonic desorption, the desorption test was conducted using the paint-coated beads with three sizes (1, 2, and 4 mm) for the free and attached conditions. It was found that no significant desorption/removal of paint from the beads was observed without the movement of beads in the water including floatation, collision, and scrubbing. Thus, it was suggested that the simultaneous application of the ultrasound and mechanical mixing could enhance the physical movement of the particles significantly and the very high removal/desorption could be attained.     

Epidemic spreading in a scale-free network of regular lattices

The susceptible-infected-susceptible (SIS) epidemics in a scale-free network in which each node is a square lattice itself is investigated through large-scale computer simulations. The model combines a local contact process among individuals in a node (or city) with stochastic long-range infections due to people traveling between cities interconnected by the national transportation scale-free network. A nonzero epidemic threshold is found and it is approached with a power-law behavior by the density of infected individuals, as observed in the small-world network of Watts and Strogatz. Also, the epidemic propagation follows a 1/f$1/f$, hierarchical dynamics from the highly connected square lattices to the smaller degree nodes in outbreaks with sizes distributed accordingly a Gaussian function.     

New mechanism for non-trivial intra-molecular vibrational dynamics

We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state S, coupled to all other intra-molecular vibrational states R of the same molecule, and also to its environment Q. Molecular states forming the first reservoir R are characterized by a discrete dense spectrum, whereas the environment reservoir Q states form a continuous spectrum. Assuming the equidistant reservoir R states we find the exact analytical solution of the quantum dynamic equations. S-Q and R-Q couplings yield to spontaneous decay of the S and R states, whereas S-R exchange leads to recurrence cycles and Loschmidt echo at frequencies of S-R transitions and double resonances at the interlevel reservoir R transitions. Due to these couplings the system S time evolution is not reduced to a simple exponential relaxation. We predict various regimes of the system S dynamics, ranging from exponential decay to irregular damped oscillations. Namely, we show that there are possible four dynamic regimes of the evolution: (i) independent of the environment Q exponential decay suppressing backward R - S transitions, (ii) Loschmidt echo regime, (iii) incoherent dynamics with multicomponent Loschmidt echo, when the system state is exchanged its energy with many states of the reservoir, (iv) cycle mixing regime, when long time system dynamics looks as a random-like. We suggest applications of our results for interpretation of femtosecond vibration spectra of large molecules and nano-systems.     

Upconversion studies in Er doped TeO2-M2O (M=Li, Na and K) binary glasses

The luminescence properties of Er³⁺ doped alkali tellurite [ TeO₂-M₂O (M=Li, Na and K)] glasses are investigated. Infrared to visible upconversion emissions are observed at 410, 525, 550 and 658 nm using 797 nm excitation. These bands are assigned to the ²H_9/2  →⁴I_15/2, ²H_11/2  →⁴I_15/2, ⁴S_3/2  →⁴I_15/2, ⁴F_9/2  →⁴I_15/2 transitions of Er³⁺ respectively. Detailed study reveals that the ²H_9/2  →⁴I_15/2 transition at 410 nm involves a three-step process while the other transitions involve two-steps. Excitation with 532 nm radiation gives additional bands at 380, 404, 475 and 843 nm wavelengths due to the ⁴G_11/2  →⁴I_15/2, ²P_3/2  →⁴I_13/2, ²P_3/2  →⁴I_11/2, and ⁴S_3/2  →⁴I_13/2 transitions, respectively, along with the bands observed on NIR excitation. The fluorescence yield is found to be largest for the TeO₂-Na₂O glass. The lifetime of the ⁴S_3/2 level has been measured for all the three cases and used to explain the upconversion mechanisms. The fluorescence intensity ratio corresponding to the two thermally coupled levels (²H_11/2, ⁴S_3/2) has been used to estimate the temperature of the glass. It is observed that the temperature sensing capacity of TeO₂-Li₂O glass is better than the other two glasses.     

Epidemic spreading on random surfer networks with infected avoidance strategy

In this paper, we study epidemic spreading on random surfer networks with infected avoidance(IA) strategy. In particular, we consider that susceptible individuals' moving direction angles are affected by the current location information received from infected individuals through a directed information network. The model is mainly analyzed by discrete-time numerical simulations. The results indicate that the IA strategy can restrain epidemic spreading effectively. However,when long-distance jumps of individuals exist, the IA strategy's effectiveness on restraining epidemic spreading is heavily reduced. Finally, it is found that the influence of the noises from information transferring process on epidemic spreading is indistinctive.     

Impedance spectroscopy of carbon nanotube/solid polymer electrolyte composites

New composite polymer electrolytes (CPE) have been prepared by a solution-casting technique, using polyethylene oxide, lithium hexafluorate (LiPF₆) as the doping salt, ethylene carbonate (EC) as the plasticizer and amorphous carbon nanotubes (αCNTs) as the filler. The crystallinity and ionic conductivity of the CPE are examined. Differential scanning calorimetry shows a decrease in melting temperature and crystallinity upon the addition of LiPF₆, EC and αCNTs to the polymer electrolyte system. The addition of salt increases the conductivity up to 10⁻⁵ S cm⁻¹. The incorporation of EC and αCNTs into the salted polymer shows a significant conductivity increase of 10⁻⁴ and 10⁻³ S cm⁻¹. The complexation process is examined using Fourier transform infrared spectroscopy. The Vogel-Tamman-Fulcher (VTF) plots suggest that the temperature dependence of conductivity is a thermally activated process.     

Influenza epidemic spread simulation for Poland — a large scale, individual based model study

In this work a construction of an agent based model for studying the effects of influenza epidemic in large scale (38 million individuals) stochastic simulations, together with the resulting various scenarios of disease spread in Poland are reported. Simple transportation rules were employed to mimic individuals’ travels in dynamic route-changing schemes, allowing for the infection spread during a journey. Parameter space was checked for stable behaviour, especially towards the effective infection transmission rate variability. Although the model reported here is based on quite simple assumptions, it allowed to observe two different types of epidemic scenarios: characteristic for urban and rural areas. This differentiates it from the results obtained in the analogous studies for the UK or US, where settlement and daily commuting patterns are both substantially different and more diverse. The resulting epidemic scenarios from these ABM simulations were compared with simple, differential equations based, SIR models — both types of the results displaying strong similarities. The pDYN software platform developed here is currently used in the next stage of the project employed to study various epidemic mitigation strategies.