Based on the fact that the incubation periods of epidemic disease in asymptomatically infected and infected individuals are inevitable and different, we propose a diffusive susceptible, asymptomatically infected, symptomatically infected and vaccinated (SAIV) epidemic model with delays in this paper. To see whether epidemic disease can propagate spatially with a constant speed, we focus on the travelling wave solution for this model. When the basic reproduction number of the corresponding spatial-homogenous delayed differential system is greater than one and the wave speed is greater than or equal to the critical speed, we prove that this model admits nontrivial positive travelling wave solutions. Our theoretical results are of benefit to the prevention and control of epidemic.

Recently we have proposed a monostable reaction-diffusion system to explain the Neolithic transition from hunter-gatherer life to farmer life in Europe. The system is described by a three-component system for the populations of hunter-gatherer (H), sedentary farmer (F1) and migratory one (F2). The conversion between F1 and F2 is specified by such a way that if the total farmers F1 + F2 are overcrowded, F1 actively changes to F2, while if it is less crowded, the situation is vice versa. In order to include this property in the system, the system incorporates a critical parameter (say F0) depending on the development of farming technology in a monotonically increasing way. It determines whether the total farmers are either over crowded (F1 + F2 >F0) or less crowded (F1 + F2 <F0) ( [9, 20]). Previous numerical studies indicate that the structure of travelling wave solutions of the system is qualitatively similar to the one of the Fisher-KPP equation, that the asymptotically expanding velocity of farmers is equal to the minimal velocity (say cm(F0)) of travelling wave solutions, and that cm(F0) is monotonically decreasing as F0 increases. The latter result suggests that the development of farming technology suppresses the expanding velocity of farmers. As a partial analytical result to this property, the purpose of this paper is to consider the two limiting cases where F0 = 0 and F0 → ∞, and to prove cm(0)>cm(∞).

This paper reports on an ultra-wideband low-noise distributed amplifier (LNDA) in a transferred-substrate InP double heterojunction bipolar transistor (DHBT) technology which exhibits a uniform low-noise characteristic over a large frequency range. To obtain very high bandwidth, a distributed architecture has been chosen with cascode unit gain cells. Each unit cell consists of two cascode-connected transistors with 500 nm emitter length and ft/fmax of ~360/492 GHz, respectively. Due to optimum line-impedance matching, low common-base transistor capacitance, and low collector-current operation, the circuit exhibits a low-noise figure (NF) over a broad frequency range. A 3-dB bandwidth from 40 to 185 GHz is measured, with an NF of 8 dB within the frequency range between 75 and 105 GHz. Moreover, this circuit demonstrates the widest 3-dB bandwidth operation among all reported single-stage amplifiers with a cascode configuration. Additionally, this work has proposed that the noise sources of the InP DHBTs are largely uncorrelated. As a result, a reliable prediction can be done for the NF of ultra-wideband circuits beyond the frequency range of the measurement equipment.

In a prior work, the authors proved a global bifurcation theorem for spatially periodic interfacial hydroelastic travelling waves on infinite depth, and computed such travelling waves. The formulation of the travelling wave problem used both analytically and numerically allows for waves with multi-valued height. The global bifurcation theorem required a one-dimensional kernel in the linearization of the relevant mapping, but for some parameter values, the kernel is instead two-dimensional. In the present work, we study these cases with two-dimensional kernels, which occur in resonant and non-resonant variants. We apply an implicit function theorem argument to prove existence of travelling waves in both of these situations. We compute the waves numerically as well, in both the resonant and non-resonant cases.

This note considers an established reaction–diffusion model for a combustion system, in which there are competing endothermic and exothermic reaction pathways. A combustion front is assumed to move at constant speed through the medium. An asymptotic theory is presented for solid fuels in which material diffusion is ignored, and it allows a simple and complete analysis of the approximate system in the phase plane. Both the adiabatic and nonadiabatic cases are discussed.

The paper is devoted to a reaction-diffusion equation in an infinite two-dimensionalstrip with nonlinear boundary conditions. The existence of travelling waves is proved inthe bistable case by the Leray-Schauder method. It is based on a topological degree forelliptic problems in unbounded domains and on a priori estimates of solutions.

Under the assumptions that the spatial variable is one dimensional and the distributed delay kernel is the general Gamma distributed delay kernel, when the average delay is small, the existence of travelling wave solutions for the population genetics model with distributed delay is obtained by using the linear chain trick and geometric singular perturbation theory. On the other hand, for the population genetics model with small discrete delay, the existence of travelling wave solutions is obtained by employing a technique which is based on a result concerning the existence of the inertial manifold for small discrete delay equations.

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independent of random motion, and intensities of reverses are defined by a particle's current direction. A solution of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) has a so-called McKean representation via such processes. Commonly this system possesses travelling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed. The paper realizes the McKean's program for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.

Consider a branching random walk in which each particle has a random number (one or more) of offspring particles that are displaced independently of each other according to a logconcave density. Under mild additional assumptions, we obtain the following results: the minimal position in the nth generation, adjusted by its α-quantile, converges weakly to a non-degenerate limiting distribution. There also exists a ‘conditional limit’ of the adjusted minimal position, which has a (Gumbel) extreme value distribution delayed by a random time-lag. Consequently, the unconditional limiting distribution is a mixture of extreme value distributions.

Using microelectrode structures, various forms of electric fields, such as non-uniform, rotating and travelling wave, can be imposed on particles of sizes ranging from proteins and viruses to micro-organisms and cells. Each type of particle responds to the forces exerted on them in a unique way, allowing for their controlled and selective manipulation as well as their characterization. Moreover, particles of the same type but of different viability can be distinguished in a simple, reliable manner. This review outlines the principles that govern the way in which bioparticles respond to these various field types, and how they can be exploited. Examples of current and potential biotechnological and biomedical applications are given, along with a critical comparison of current techniques.