Impact of media coverage on a fractional-order SIR epidemic model

In this work, we formulated and analyzed a fractional-order epidemic model of infectious disease (such as SARS, 2019-nCoV and COVID-19) concerning media effect. The model is based on classical susceptible-infected-recovered (SIR) model. Basic properties regarding positivity, boundedness and non-negative solutions are discussed. Basic reproduction number [Formula: see text] of the system has been calculated using next-generation matrix method and it is seen that the disease-free equilibrium is locally as well as globally asymptotically stable if [Formula: see text], otherwise unstable. The existence of endemic equilibrium point is established using the Lambert W function. The condition for global stability has been derived. Numerical simulation suggests that fractional order and media have a large effect on our system dynamics. When media impact is stronger enough, our fractional-order system stabilizes the oscillation.

Analytical Optimal Load Calculation of RF Energy Rectifiers Based on a Simplified Rectifying Model

Wireless power transfer (WPT) is an essential enabler for novel sensor networks such as the wireless powered communication network (WPCN). The efficiency of an energy rectifier is dependent on both input power and loading condition. In this work, to maximize the rectifier efficiency, we present a low-complexity numerical method based on an analytical rectifier model to calculate the optimal load for different rectifier topologies, including half-wave and voltage-multipliers, without needing time-consuming simulations. The method is based on a simplified analytical rectifier model based on the diode equivalent circuit including parasitic parameters. Furthermore, by using Lambert-W function and the perturbation method, closed-form solutions are given for low-input power cases. The method is validated by means of both simulations and measurements. Extensive transient simulation results using different diodes (Skyworks SMS7630 and Avago HSMS285x) and frequency bands (400 MHz, 900 MHz, and 2.4 GHz) are provided for validation of the method. A 400 MHz 1- and 2-stage voltage multiplier are designed and fabricated, and measurements are conducted. Different input signals are used when validating the proposed methods, including the single sinewave signal and the multisine signal. The proposed numerical method shows excellent accuracy with both signal types, as long as the output voltage ripple is sufficiently low.

Computing Approximate Equilibria in Weighted Congestion Games via Best-Responses

We present a deterministic polynomial-time algorithm for computing [Formula: see text]-approximate (pure) Nash equilibria in (proportional sharing) weighted congestion games with polynomial cost functions of degree at most [Formula: see text]. This is an exponential improvement of the approximation factor with respect to the previously best deterministic algorithm. An appealing additional feature of the algorithm is that it only uses best-improvement steps in the actual game, as opposed to the previously best algorithms, that first had to transform the game itself. Our algorithm is an adaptation of the seminal algorithm by Caragiannis at al. [Caragiannis I, Fanelli A, Gravin N, Skopalik A (2011) Efficient computation of approximate pure Nash equilibria in congestion games. Ostrovsky R, ed. Proc. 52nd Annual Symp. Foundations Comput. Sci. (FOCS) (IEEE Computer Society, Los Alamitos, CA), 532–541; Caragiannis I, Fanelli A, Gravin N, Skopalik A (2015) Approximate pure Nash equilibria in weighted congestion games: Existence, efficient computation, and structure. ACM Trans. Econom. Comput. 3(1):2:1–2:32.], but we utilize an approximate potential function directly on the original game instead of an exact one on a modified game. A critical component of our analysis, which is of independent interest, is the derivation of a novel bound of [Formula: see text] for the price of anarchy (PoA) of [Formula: see text]-approximate equilibria in weighted congestion games, where [Formula: see text] is the Lambert-W function. More specifically, we show that this PoA is exactly equal to [Formula: see text], where [Formula: see text] is the unique positive solution of the equation [Formula: see text]. Our upper bound is derived via a smoothness-like argument, and thus holds even for mixed Nash and correlated equilibria, whereas our lower bound is simple enough to apply even to singleton congestion games.