Mathematical and computational approaches are important tools for understanding epidemic spread patterns and evaluating policies of disease control. In recent years, epidemiology has become increasingly integrated with mathematics, sociology, management science, complexity science, and computer science. The cross of multiple disciplines has caused rapid development of mathematical and computational approaches to epidemic modeling. In this article, we carry out a comprehensive review of epidemic models to provide an insight into the literature of epidemic modeling and simulation.We introduce major epidemic models in three directions, including mathematical models, complex network models, and agent-based models. We discuss the principles, applications, advantages, and limitations of these models. Meanwhile, we also propose some future research directions in epidemic modeling. Table 1 Classification of epidemic models Types Names Methods Mathematical models Compartmental models, Reed-Frost models Differential equations, stochastic process, Monte Carlo, Markov chains Complex network models System dynamics models in complex networks, numerical simulations of epidemics in complex networks, metapopulation models, weighted networks, adaptive networks Differential equations, stochastic processes Agent-based models

Based on non-affine models of hypersonic space vehicles, the tracking control problem of hypersonic vehicles is studied and analyzed in this article using funnel robust model-free control mechanism considering parametric uncertainty and external disturbances. First, the control system is decomposed into altitude subsystem and velocity subsystem. For altitude subsystem, we propose a concise funnel robust model-free control mechanism based on error driving, and a novel model transformation approach is applied to the controller design. The new model-free controller only contains a Hurwitz stable term and a filtering term, and does not need precise motion model and too much calculation, so it can improve the calculation speed of the system. For velocity subsystem, only a concise proportional-integral controller is needed to meet the tracking requirements. Moreover, the devised controller is capable of guaranteeing funnel performance on the altitude and velocity tracking errors. Finally, numerical simulation results are presented to verify the efficiency of the design.

Potassium-ion batteries (KIBs) are considered to be an effective alternative to lithium-ion batteries (LIBs) due to their abundant resources, low cost, and similar electrochemical properties of K+ to Li+, and they have a good application prospect in the field of large-scale energy storage batteries. Polymer materials play a very important role in the battery field, such as polymer electrode materials, polymer binders, and polymer electrolytes. Here in this review, we focus on the research progress of polymers in KIBs and systematically summarize the research status and achievements of polymer electrode materials, electrolytes, and binders in potassium ion batteries in recent years. Finally, based on the latest representative research of polymers in KIBs, some suggestions and prospects are put forward, which provide possible directions for future research.

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Lifetime prediction method for memS gyroScope baSed on acceLerated degradation teSt and acceLeration factor modeL metoda prognozowania czaSu pracy żyroSkopu memS na podStawie teStu przySpieSzonej degradacji i modeLu wSpółczynnika przySpieSzenia The reliability analysis of MEMS gyroscope under long-term operating condition has become an urgent requirement with the enlargement of its application scope and the requirement of good durability. In this study we propose a lifetime prediction method for MEMS gyroscope based on accelerated degradation tests (ADTs) and acceleration factor model. Firstly, the degradation characteristic (bias instability) is extracted based on Allan variance. The effect of temperature stress on the degradation rate of bias instability is analyzed, and it shows that the degradation rate of bias instability would increase with the increase of the temperature. Secondly, the ADTs of MEMS gyroscope are designed and conducted, the degradation model of MEMS gyroscope is established based on the output voltage of MEMS gyroscope and Allan variance. Finally, the acceleration factor model of MEMS gyroscope under temperature stress is derived, and the lifetime of the MEMS gyroscope is predicted based on two group tests data under high stress level. The results show that the lifetime calculated by the acceleration factor model and mean lifetime under high stress levels is close to the mean lifetime calculated by the linear equation at normal temperature stress.

A modified CD*I model for the origin of structure in the universe, based on an inflation model with two iuteracting scalar fields, is analyzed to make predictions for the statistical properties of the density and velocity fields aud the microwave background anisotropy. The initial gauge-invariant potential (which is defined as (, = £p/(p + p) + 3_, where ? is the curvature perturbation amplitude and p is the pressure, is tl_e stt,n of a Gaussian feld oi and the square of a Gaussian field _2. We assume a Har,'ison-Zel'dovicla scale-invariant power spectrum for _bl, and a log-normal 'peak' power spectru,u for o,.. The location and the width of the peak are described by parameters/,'_ aud a. respectively. Comparing our theoretical calculations for two dimensional density angular correlation function to the results of the APM su,'vey, we set certain pa,-a,neter regime for k_, a and the amplitude ratio of Gaussian and non-Gaussian fields. The model is motivated to some extent by inflation models with two interacting scalar fields, but is mainly interesting as an example of a model whose statistical properties change with scale. On small scales, it is almost identical to a standard scale-invariant Gaussian CD,N{model. On scales near the location of the peak of the non-Gaussian field, the distributions have long tails in high positive values of the density and velocity fields. Thus, it is easier to get large-scale streaming velocities than the standard CDM model. \Ve calculate the quadrupole amplitude of fluctuations of the cosmic microwave background radiation and the ,'ms va,'iation of the temperature field smoothed with a 10°F\VHM Gaussian. and find a reasonable agreement with the new COBE results. Biasing should be important in our model. \Ve discuss one of the possible biasing schemes very b,'iefly, and further discussions on this will be in our future work. Subject. headin9._" large scale structure-statistics-cosmic background radiation

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