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Age heterogeneity in influenza transmission leads to significant differences in infection risk among different age groups. In this paper, an influenza model with vaccination and discrete age structure is constructed. First, we obtain the basic reproduction number R0$$ {R}_0 $$ and prove that the disease‐free equilibrium E0$$ {E}_0 $$ is globally stable at R0<1$$ {R}_0<1 $$. When R0>1$$ {R}_0>1 $$, the disease will persist uniformly, and there is a unique positive equilibrium, which is globally asymptotically stable under certain conditions. The model is used to analyze influenza data from 2016 to 2017 in China. By comparing various prevention and control measures, it can be found that by wearing masks to reduce contact between different age groups, while increasing vaccine coverage and reducing vaccine failure rates, the prevention and control goals can be achieved in the shortest time. However, if only the vaccine coverage rate is increased and the vaccine protection rate is strengthened, the time to reach the control target is 8 months later than the above case, and the cost is the lowest. [ABSTRACT FROM AUTHOR]

In this paper, to investigate the synthetic effect of PrEP (pre‐exposure prophylaxis) and ART (antiretrovial therapy) on HIV transmission among MSM (men who have sex with men) in heterogenous environment, a realistic HIV epidemic model with spatial diffusion is established. Here, HIV infectious people are divided into three immunity based compartments, that is, CD4+ T cell count less than 350, between 350 and 500, and more than 500, respectively. The basic reproduction number R0 is established and proved as a threshold parameter: The global asymptotic stability of the disease‐free steady state holds for R0<1, and the disease will be present if R0>1. Considering the substantial advantages of PrEP and ART in controlling HIV transmissions among MSM, the optimal control problem is presented for the case of positive constant diffusion coefficients, which minimize the total population of susceptible individual and HIV infected individual, the cost of PrEP and ART therapy. As an illustration of our theoretical results, we conduct numerical simulations. We also conduct an optimal control case study where model parameters are estimated from the demographic and epidemiological data from China. This work suggests the following: (1) Spatial factors cannot be ignored during the HIV intervention; (2)taking the PrEP intervention measure for HIV transmissions among MSM as early as possible will help to improve the control efficiency and reduces its cost; (3) reducing the PrEP drug costs will promote the efficiency of PrEP treatment in preventing the spread of HIV among MSM. [ABSTRACT FROM AUTHOR]

Many countries worldwide have been affected by the outbreak of the novel coronavirus (COVID‐19) that was first reported in China. To understand and forecast the transmission dynamics of this disease, fractional‐order derivative‐based modeling can be beneficial. We propose in this paper a fractional‐order mathematical model to examine the COVID‐19 disease outbreak. This model outlines the multiple mechanisms of transmission within the dynamics of infection. The basic reproduction number and the equilibrium points are calculated from the model to assess the transmissibility of the COVID‐19. Sensitivity analysis is discussed to explain the significance of the epidemic parameters. The existence and uniqueness of the solution to the proposed model have been proven using the fixed‐point theorem and by helping the Arzela–Ascoli theorem. Using the predictor–corrector algorithm, we approximated the solution of the proposed model. The results obtained are represented by using figures that illustrate the behavior of the predicted model classes. Finally, the study of the stability of the numerical method is carried out using some results and primary lemmas. [ABSTRACT FROM AUTHOR]

The self-adaptive intelligence gray predictive model (SAIGM) has an alterable-flexible model structure, and it can build a dynamic structure to fit different external environments by adjusting the parameter values of SAIGM. However, the order number of the raw SAIGM model is not optimal, which is an integer. For this, a new SAIGM model with the fractional order accumulating operator (SAIGM_FO) was proposed in this paper. Specifically, the final restored expression of SAIGM_FO was deduced in detail, and the parameter estimation method of SAIGM_FO was studied. After that, the Particle Swarm Optimization algorithm was used to optimize the order number of SAIGM_FO, and some steps were provided. Finally, the SAIGM_FO model was applied to simulate China's electricity consumption from 2001 to 2008 and forecast it during 2009 to 2015, and the mean relative simulation and prediction percentage errors of the new model were only 0.860% and 2.661%, in comparison with the ones obtained from the raw SAIGM model, the GM(1, 1) model with the optimal fractional order accumulating operator and the GM(1, 1) model, which were (1.201%, 5.321%), (1.356%, 3.324%), and (2.013%, 23.944%), respectively. The findings showed both the simulation and the prediction performance of the proposed SAIGM_FO model were the best among the 4 models. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Rayleigh–Taylor instability for the nonhomogeneous incompressible Navier–Stokes equations with Navier‐slip boundary conditions around a steady state in an infinite slab, where the Navier‐slip coefficients do not have defined sign and the slab is horizontally periodic. Motivated by Jiang et al. (Sci. China Math., 2013), we extend the result from Dirichlet boundary condition to Navier‐slip boundary conditions. Our results indicate the factor that "heavier density with increasing height" still plays a key role in the instability under Navier‐slip boundary conditions. [ABSTRACT FROM AUTHOR]

This paper deals with the global dynamics for a tuberculosis transmission model with age‐structure and relapse. The time delay in the progression from the latent individuals to becoming the infectious individuals is also considered in our model. We perform some rigorous analyses for the model, including presenting an explicit formula for the basic reproduction number of the model, addressing the persistence of the solution semiflow and the existence of a global attractor. Based on these analyses, we establish some results about stability and instability of the solutions for our model. At end, the model is applied to describe tuberculosis transmission in China. The number of the total population and the number of the annual newly reported TB cases both match the statistical data well. The number of the total population, the latent individuals, the infectious individuals, the Purified Protein Derivative (PPD) positive rate, and the prevalence rate from 2020 to 2035 all are presented. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with the development and design of a reduced order model in numerical simulation of the unsteady temperature field of the stadium building foundation in frozen areas, based the finite element (FE) method and proper orthogonal decomposition (POD) with the snapshot technique. We first derive the standard FE formulation of the unsteady temperature field and compute its FE full solutions, from which we choose a few spatio‐temporal solutions as snapshots. Based on POD technique, we then build a set of optimal POD bases maximizing the energy content in the original ensemble data, and in the new space spanned by the POD basis, we establish a low‐order numerical model of reduced‐order finite element (ROFE) formulation of the unsteady temperature field. And we prove the error estimates of the ROFE solutions of the unsteady temperature field. Finally, numerical tests are provided to simulate the temperature field of crushed stone clay under the natural pavement near the foundation of a stadium building in a frozen soil area of the northwest of Sichuan province in China. [ABSTRACT FROM AUTHOR]

Screening those individuals who are latent but at higher risk of rapidly developing active tuberculosis (TB) is one of the intervention measures to control the spread of TB. This work proposes a TB SVELIT (S‐Susceptible, V‐Vaccinated, E‐Early latent, L‐Late latent, I‐Infected, T‐Treated) transmission model with relapse. In particular, a complete threshold dynamical analysis for the model is performed and the existence of optimal control is obtained. Meanwhile, the validity of the model is shown by comparing the real data with the fitted curve and the future trend in the incidence of TB in China is predicted. More importantly, the effects of four strategies, including vaccination, media propaganda, screening latent individuals, and receiving treatment, are evaluated numerically. The results suggest that the above four strategies can effectively control TB and shorten the duration of the epidemic. Interestingly, treatment is more effective than vaccination in controlling TB, but media propaganda and latent screening are cheaper and easier to implement. [ABSTRACT FROM AUTHOR]

In 2013, in mainland China, a novel avian influenza A(H7N9) virus began to infect humans, followed by the annual outbreaks, and had aroused severe fatality in the infected humans. After introducing the statistical characteristics including the geographical distributions of the outbreaks, a SEV‐SIRS eco‐epidemiological model is established and analyzed. In this model, the factor of virus in environment is incorporated into the model as a class; the vaccine measure in poultry is taken into account in purpose of assessing its control effect in 2017 in China; the nonmonotonic contact function is adopted to characterize the psychosocial effect. The stability of disease‐free equilibrium point (DFE) is obtained by the threshold theory; the stability of the endemic equilibrium point is gotten by the Bendixson criterion based on the geometric approach. Sensitivity analyses of system parameters indicate that the measure of vaccination in poultry can play its role but only when the vaccine rate is more than 98% can the disease control effect be effectively exerted, and the virus in environment is an extremely sensitive factor in the disease transmission and the epidemic control. [ABSTRACT FROM AUTHOR]

By comparing the class ratio deviation and restoring error of first‐order accumulation with that of fractional‐order accumulation, a gray model for monotonically increasing sequences can obtain optimal simulation accuracy via selecting a proper cumulative order. In this study, a gray model for increasing sequences with nonhomogeneous index trends based on fractional‐order accumulation is proposed. To reduce the modeling error caused by the background value and to improve the prediction accuracy of the model, an optimized model using the 3/8 Simpson formula is constructed. Finally, the 2 proposed models are used to predict the total energy consumption in China and the monthly sales of new products in an enterprise. Compared with the GM(1,1) model based on fractional‐order accumulation, the proposed model exhibits better simulation and prediction accuracy. [ABSTRACT FROM AUTHOR]